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aqua_rat__VMcY7yO5WfD5zTg2 | The numbers of students speaking English and Hindi are in the ratio of 4 : 5. If the number of students speaking English increased by 35% and that speaking Hindi increased by 20%, what would be the new respective ratio? Options:
A) 19 : 20
B) 7 : 8
C) 8 : 9
D) Cannot be determined
E) None of these | Reqd ratio = 4×13/55×120=9:10 Answer None of these
<result>E</result> | E | {
"A": "19 : 20",
"B": "7 : 8",
"C": "8 : 9",
"D": "Cannot be determined",
"E": "None of these"
} | The numbers of students speaking English and Hindi are in the ratio of 4 : 5. If the number of students speaking English increased by 35% and that speaking Hindi increased by 20%, what would be the new respective ratio? |
aqua_rat__sdzJfpMUm0ALLzqJ | A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work? Choose the correct choice from the following answers
A) 7 days
B) 2 days
C) 5 days
D) 3 days
E) 6 days | 2 days 2 days Work done by A in 2 days = 2/5 Remaining work = 3/5 Work done by both A and 2 days in one day = 1/5 + 1/10 = 3/10 Remaining work = 3/5 * 10/3=
<gadget id="calculator">3/5 * 10/3</gadget>
<output>2</output>
2 days.
<result>B</result> | B | {
"A": "7 days",
"B": "2 days",
"C": "5 days",
"D": "3 days",
"E": "6 days"
} | A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work? |
aqua_rat__vaEXZvW0eTXMxwgD | An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast? Choose the correct choice from the following answers.
A) 75% B) 58% C) 42% D) 34% E) 25% | Total Number of members = 1260 Number of members that cast votes = 525 Since , winning candidate received 60 percent of the votes cast Number of votes for winning candidate = (60/100)*525=
<gadget id="calculator">(60/100)*525</gadget>
<output>315</output>
315 Percent of total membership that voted for winning candidate= (315/1260)*100=
<gadget id="calculator">(315/1260)*100</gadget>
<output>25</output>
25% Answer 25%
<result>E</result> | E | {
"A": "75%",
"B": "58%",
"C": "42%",
"D": "34%",
"E": "25%"
} | An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast? |
aqua_rat__qSkCEvKBnCuq1yZ0 | A train passes a station platform in 32 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choose the correct choice from the following answers
A) 180 m B) 160 m C) 240 m D) 207 m E) 202 m | Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20)=
<gadget id="calculator">(15 * 20)</gadget>
<output>300</output>
300 m. Let the length of the platform be x meters. Then, x + 300 / 32= 15 x + 300 = 480 x =180m. 180 mnswer: 180 m
<result>A</result> | A | {
"A": "180 m",
"B": "160 m",
"C": "240 m",
"D": "207 m",
"E": "202 m"
} | A train passes a station platform in 32 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? |
aqua_rat__fq4ERvwqK3dojG4D | In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies
Pick:
A) 231
B) 150
C) 200
D) 450
E) 451 | (3 men out of 6) and (2 ladies out of 5) are to be chosen Required number of ways =(62003 * 52002) = 200 Ans: 200
<result>C</result> | C | {
"A": "231",
"B": "150",
"C": "200",
"D": "450",
"E": "451"
} | In how many a committee of 5 members can be selected from 6men 5 ladies consisting of 3 men and 2 ladies |
aqua_rat__Rzk3du98J8Wj2RVR | Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
Choose the correct answer
A) 29.25 B) 29.28 C) 79.28 D) 29.22 E) 29.21 | 29.25verage of 9 = x 9x = 8 * 3 + x * 2 x = 3.25 Total = 9 * 3.25=
<gadget id="calculator">9 * 3.25</gadget>
<output>29.25</output>
29.25 29.25nswer: 29.25
<result>A</result> | A | {
"A": "29.25",
"B": "29.28",
"C": "79.28",
"D": "29.22",
"E": "29.21"
} | Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them? |
aqua_rat__BGhyhUsF91lyGdMY | The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? Choose the correct choice:
A) 6 B) 7 C) 8 D) 5 E) 3 | S = 4 M = x DS = x + 4 US = x - 4 6/(x + 4) + 6/(x - 4) = 2 x = 8 Answer:8
<result>C</result> | C | {
"A": "6",
"B": "7",
"C": "8",
"D": "5",
"E": "3"
} | The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? |
aqua_rat__Fg5A4w9XHCJWER7g | A train covers a certain distance at a speed of 340kmph in 4 hours. To cover the same distance in 2 3/4 hours, it must travel at a speed of Choose the correct choice from the following answers:
A) 495km/hr B) 420km/hr C) 450km/hr D) 550km/hr E) 650km/hr | Explanation: Distance = 340×4 = 1360km Required speed = (1360× 4/11) = 495km/hr 495km/hrnswer: Option 495km/hr
<result>A</result> | A | {
"A": "495km/hr",
"B": "420km/hr",
"C": "450km/hr",
"D": "550km/hr",
"E": "650km/hr"
} | A train covers a certain distance at a speed of 340kmph in 4 hours. To cover the same distance in 2 3/4 hours, it must travel at a speed of |
aqua_rat__zqH9zkc1pZQjSuNf | 6 people meet for a business breakfast. Each person shakes hands once with each other person present. How many handshakes take place? Answers.
A) 30 B) 21 C) 18 D) 15 E) 10 | Let's look at the logic. Every person shakes hand with other '5'. So, 6 people shake hands with 6X5= 30 people But in this 30 we have counted two times the total handshakes (c shakes hand with d and d shakes hand with c) So just divide 30/2=
<gadget id="calculator">30/2</gadget>
<output>15</output>
15 total handshakes Answer is 15
<result>D</result> | D | {
"A": "30",
"B": "21",
"C": "18",
"D": "15",
"E": "10"
} | 6 people meet for a business breakfast. Each person shakes hands once with each other person present. How many handshakes take place? |
aqua_rat__Trrq6DVFNeVN3nBK | Find the odd man out?
396, 462, 572, 427, 671, 264. Choose the correct option
A) 2378 B) 427 C) 297 D) 2678 E) 187 | Explanation: In each number except 427, the middle digit is the sum of other two. Answer: 297) 427
<result>C</result> | C | {
"A": "2378",
"B": "427",
"C": "297",
"D": "2678",
"E": "187"
} | Find the odd man out?
396, 462, 572, 427, 671, 264. |
aqua_rat__KJaydfB2ELTwG7Fb | To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.
Select:
A) 347 B) 3667 C) 387 D) 675 E) 711 | Let xx be the number of days the company worked. Then 25x is the number of parts they planned to make. At the new production rate they made: 3⋅25+(x−3)⋅30=75+30(x−3)3⋅25+(x−3)⋅30=75+30(x−3) Therefore: 25x=75+30(x−3)−10025x=75+30(x−3)−100 25x=75+30x−90−10025x=75+30x−90−100 190−75=30x−25190−75=30x−25 115=5x115=5x x=23x=23 So the company worked 23 days and they made 23⋅25+100=67523⋅25+100=675 pieces. Answer:675
<result>D</result> | D | {
"A": "347",
"B": "3667",
"C": "387",
"D": "675",
"E": "711"
} | To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took. |
aqua_rat__PWzLA4Wr1iH5a3VN | The average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ? Select
A) 75 kg B) 65 kg C) 55 kg D) 97 kg E) 25 kg | Total weight increased = (8 x 4) kg = 32 kg. Weight of new person = (65 + 32)=
<gadget id="calculator">(65 + 32)</gadget>
<output>97</output>
97 kg. Answer: 97 kg
<result>D</result> | D | {
"A": "75 kg",
"B": "65 kg",
"C": "55 kg",
"D": "97 kg",
"E": "25 kg"
} | The average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ? |
aqua_rat__oB22ilmpbuKQ0g6m | Which of the following statements is not correct?
A. log10 (10) = 1
B. log (2 + 3) = log (2 x 3)
C. log10 (1) = 0
D. log (1 + 2 + 3) = log 1 + log 2 + log 3 Choose the correct option.
A) log10 (10) = 1 B) log (2 + 3) = log (2 x 3) C) log10 (1) = 0 D) log (1 + 2 + 3) = log 1 + log 2 + log 3 E) none of these | (a) Since loga (a) = 1, so log10 (10) = 1. (b) log (2 + 3)=
<gadget id="calculator"> (2 + 3)</gadget>
<output>5</output>
log 5 and log (2 x 3)= log 6 = log 2 + log 3 log (2 + 3) log (2 x 3) (c) Since loga (1) = 0, so log10 (1) = 0. (d) log (1 + 2 + 3)=
<gadget id="calculator"> (1 + 2 + 3)</gadget>
<output>6</output>
log 6= log (1 x 2 x 3) = log 1 + log 2 + log 3. So, (b) is incorrect. Answer is log (2 + 3) = log (2 x 3).
<result>B</result> | B | {
"A": "log10 (10) = 1",
"B": "log (2 + 3) = log (2 x 3)",
"C": "log10 (1) = 0",
"D": "log (1 + 2 + 3) = log 1 + log 2 + log 3",
"E": "none of these"
} | Which of the following statements is not correct?
A. log10 (10) = 1
B. log (2 + 3) = log (2 x 3)
C. log10 (1) = 0
D. log (1 + 2 + 3) = log 1 + log 2 + log 3 |
aqua_rat__H8NfXvqHzOCGP4Y0 | A pipe takes a hours to fill the tank. But because of a leakage it took 7 times of its original time. Find the time taken by the leakage to empty the tank Choose the correct choice from the following: A) 50 min B) 60 min C) 90 min D) 80 min E) 70 min | pipe a can do a work 60 min. lets leakage time is x; then 1/60 -1/x=1/420 x=70 min ANSW70 minR:70 min
<result>E</result> | E | {
"A": "50 min",
"B": "60 min",
"C": "90 min",
"D": "80 min",
"E": "70 min"
} | A pipe takes a hours to fill the tank. But because of a leakage it took 7 times of its original time. Find the time taken by the leakage to empty the tank |
aqua_rat__2N82kSO2C0eEklDw | Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? Choose the correct choice.
A) 23
B) 25
C) 27
D) 29
E) 31 | Solution: We know that the average value is 24 therefore (a+b+c)/3 = 24 so a+b+c = 72 and b = a + 11 therefore a + (a + 11) + c = 72 The least value of c is when c = b so take c = a + 11 hence, a + (a + 11) + (a + 11) = 72 i.e., a = 50/3 a non integer therefore c is not equal to b so take c = b+1 therefore c = a+12 a + (a + 11) + (a + 12) = 72 i.e., a= 49/3 again a non integer therefore c is not equal to b+1 next take c= b+2 therefore c = a+13 a + (a + 11) + (a + 13) = 72 i.e., a=48/3=
<gadget id="calculator">48/3</gadget>
<output>16</output>
16 hence, a= 16, b = 27, and c = 29 Answer: 29
<result>D</result> | D | {
"A": "23",
"B": "25",
"C": "27",
"D": "29",
"E": "31"
} | Three positive integers a, b, and c are such that their average is 24 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? |
aqua_rat__xO714MrniUGxXwmV | X and Y run a 100m race,where X beats Y by 20 m. To do a favor to Y, X starts 10m behind the starting line in a second 100m race. Both run at the same previous speed. Which of the following is true? Choose the correct choice from the following answers:
A) X Beats Y by 2m B) X Beats Y by 0.5 m C) X Beats Y by 4 m D) Y Beats X by 10m E) Beats X by 11m | Let's suppose that the speed of X is 10m/s and that the speed of Y is 8m/s. So, in the first race, the results are the following: X crosses the finish line in 10s. In other words, X has run 100m in 10 s. In 10s, Y has run 80 meters. Therefore, there is the difference of 20 meters mentioned in the question. Now, let's review the second race. In 12 seconds, X can complete the 120 meters race. We have to remember that X is 20 meters behind the starting line. But in 12 seconds, Y has covered (80+16)=
<gadget id="calculator">(80+16)</gadget>
<output>96</output>
96 meters. Also, it is important to notice that in 12 seconds Y cannot arrive to the finish line. So, 100 - 96= 4 meter Answer: X Beats Y by 4 m
<result>C</result> | C | {
"A": "X Beats Y by 2m",
"B": "X Beats Y by 0.5 m",
"C": "X Beats Y by 4 m",
"D": "Y Beats X by 10m",
"E": "Beats X by 11m"
} | X and Y run a 100m race,where X beats Y by 20 m. To do a favor to Y, X starts 10m behind the starting line in a second 100m race. Both run at the same previous speed. Which of the following is true? |
aqua_rat__j6t7QJlNWgZY1RYA | A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 25%. What was its profit on the items sold in February? Pick one:
A) 12.5%
B) 30%
C) 35%
D) 37.5%
E) 40% | 12.5%ssume the total price = 100x Price after 20% markup = 120x Price after 25%further markup = 1.25*120=
<gadget id="calculator">1.25*120</gadget>
<output>150</output>
150x Price after the discount= 0.75*150=
<gadget id="calculator">0.75*150</gadget>
<output>112.5</output>
112.5x Hence total profit= 12.5% Option 12.5%
<result>A</result> | A | {
"A": "12.5%",
"B": "30%",
"C": "35%",
"D": "37.5%",
"E": "40%"
} | A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 25%. What was its profit on the items sold in February? |
aqua_rat__lObi5D2ZnulrsVEb | Which of the following fractions terminates? Choose the correct choice:
A) 3/160 B) 5/900 C) 7/220 D) 9/120 E) 11/550 | For a fraction to have terminating decimal, it must either have only 2 and/or 5 in the denominator. All other values in the denominator leads to non terminating decimal values Hence, 1. 160 = 2 * 2 * 2 * 2 * 2 * 5, hence is terminating 2. There is a 3 in the denominator, hence it is a non terminating decimal 3. There is an 11 in the denominator, hence it is a non terminating decimal 4. There is a 3 in the denominator, hence it is a non terminating decimal 5. There is an 11 in the denominator, hence non terminating Option 3/160
<result>A</result> | A | {
"A": "3/160",
"B": "5/900",
"C": "7/220",
"D": "9/120",
"E": "11/550"
} | Which of the following fractions terminates? |
aqua_rat__HoffBOwPDvq3v3Pn | A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 9 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in Choose the correct choice from the following:
A) 6.75 sec
B) 12 sec
C) 15 sec
D) 20 sec
E) None of these | Length of train = 12 × 15 = 180 m. Then, speed of train = 180â„9 = 20 m/s Now, length of train = 9× 15 = 135m ∴ Required time = 135â„20 = 6.75 sec. 6.75 secnswer 6.75 sec
<result>A</result> | A | {
"A": "6.75 sec",
"B": "12 sec",
"C": "15 sec",
"D": "20 sec",
"E": "None of these"
} | A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 9 seconds. Due to some problem, three boggies were detached. The train now crosses a telegraph post in |
aqua_rat__SYFMQslDRxy93N2p | Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is Choose the correct option
A) 80 m B) 100 m C) 120 m D) 180 m E) None | Solution Relative Speed = (36 + 45) km/hr = (81 x 5/18) m/sec = (45/2) m/sec Length of the train = (45 / 2 x 8) m = 180 m. Answer 180 m
<result>D</result> | D | {
"A": "80 m",
"B": "100 m",
"C": "120 m",
"D": "180 m",
"E": "None"
} | Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is |
aqua_rat__0CVPPb6qfHQ2FW5W | A shopkeeper labeled the price of his articles so as to earn a profit of 40% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal? Choose the most appropriate option: A) 26% B) 20% C) 17% D) 18% E) None of these | Explanation: Let the CP of the article = Rs.100. Then labeled price = Rs.140. SP = Rs.140- 10% of 140 = Rs.140-14 = Rs.126. Gain = Rs.126 – Rs.100 = Rs.26 Therefore, gain/profit percent = 26%. 26%nswer: Option 26%
<result>A</result> | A | {
"A": "26%",
"B": "20%",
"C": "17%",
"D": "18%",
"E": "None of these"
} | A shopkeeper labeled the price of his articles so as to earn a profit of 40% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal? |
aqua_rat__qZbQuZHYDzgidLBA | the ratio of two no. addition and subtraction be 4:3.the what is the ratio of numbers?
Choose the correct choice from the following:
A) 3:2
B) 4:3
C) 5:1
D) 6:5
E) 7:1 | (x+y)/(x-y)=4/3 dividing numerator and denominator by y (x/y)+1/(x/y)-1=4/3 let x/y be z z+1/z-1=4/3 3z+3=4z-4 z=7 x/y=7 answer 7:1
<result>E</result> | E | {
"A": "3:2",
"B": "4:3",
"C": "5:1",
"D": "6:5",
"E": "7:1"
} | the ratio of two no. addition and subtraction be 4:3.the what is the ratio of numbers? |
aqua_rat__OMNHMn0G2BSQkpXw | If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? Select the correct option
A) 99.222 B) 223.22 C) 157.5 D) 222.88 E) 229.11 | (3500*1.5*3)/100=
<gadget id="calculator">(3500*1.5*3)/100</gadget>
<output>157.5</output>
> 157.50 Answer: 157.5
<result>C</result> | C | {
"A": "99.222",
"B": "223.22",
"C": "157.5",
"D": "222.88",
"E": "229.11"
} | If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? |
aqua_rat__mMIn13dNBmD7GGZQ | Three workers have a productivity ratio of 2 to 5 to 9. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest? Choices:
A) 12 to 1
B) 6 to 1
C) 15 to 2
D) 1 to 6
E) 1 to 5 | The fastest worker who does 9 units of job worked for all 10 hours, so he did 9*10=
<gadget id="calculator"> 9*10</gadget>
<output>90</output>
90 units of job; The slowest worker who does 2 unit of job worked for only 4+2=
<gadget id="calculator"> 4+2</gadget>
<output>6</output>
6 hours (first 4 hours and last 2 hours), so he did 2*6=
<gadget id="calculator"> 2*6</gadget>
<output>12</output>
12 units of job; The ratio thus is 90 to 12, or 15 to 2. Answer: 15 to 2.
<result>C</result> | C | {
"A": "12 to 1",
"B": "6 to 1",
"C": "15 to 2",
"D": "1 to 6",
"E": "1 to 5"
} | Three workers have a productivity ratio of 2 to 5 to 9. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest? |
aqua_rat__X427V0B3xW4D3hvB | A committee has 4 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee? Choose the correct choice from the following answers: A) 127 B) 120 C) 882 D) 272 E) 323 | The number of ways to select two men and three women = 4C₂ * ⁶C₃ = (4*3 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)=
<gadget id="calculator">(4*3 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)</gadget>
<output>120</output>
120 Answer: 120
<result>B</result> | B | {
"A": "127",
"B": "120",
"C": "882",
"D": "272",
"E": "323"
} | A committee has 4 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee? |
aqua_rat__kmEYLvYMcprv6QUG | Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
Choose the correct answer: A) 23 B) 28 C) 31 D) 36 E) 39 | Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation larger number – smaller number = 7 which is equivalent to Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31. 31
<result>C</result> | C | {
"A": "23",
"B": "28",
"C": "31",
"D": "36",
"E": "39"
} | Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part? |
aqua_rat__iio5dllmmtWwc0Y2 | As a bicycle salesperson, David earns a fixed salary of $40 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<2x II. y>x III. y>3
Choose the correct option
A) I,II only
B) I only
C) II only
D) II,III only
E) III only | II. y>x --> since this week, David earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week); III. y>3 --> if David sold 3 bicycles this week then this week he earned 40+3*6=
<gadget id="calculator">40+3*6</gadget>
<output>58</output>
$58, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $40. So y must be more than 3; I. y<2x --> is not always true. Answer: II,III only
<result>D</result> | D | {
"A": "I,II only",
"B": "I only",
"C": "II only",
"D": "II,III only",
"E": "III only"
} | As a bicycle salesperson, David earns a fixed salary of $40 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<2x II. y>x III. y>3 |
aqua_rat__X0kELWbeGa7jBIZ9 | A certain university will select 3 of 7 candidates eligible to fill a position in the mathematics department and 5 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? Choose the correct choice from the following answers:
A) 42232
B) 42170
C) 14008
D) 16510
E) 41160 | 7C3*8C5 = 35*56 = 41160 the answer is (41160)
<result>E</result> | E | {
"A": "42232",
"B": "42170",
"C": "14008",
"D": "16510",
"E": "41160"
} | A certain university will select 3 of 7 candidates eligible to fill a position in the mathematics department and 5 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? |
aqua_rat__0mq4DLAyM05no53p | a light flashes every 20 seconds, how many times will it flash in ? of an hour? Pick one:
A) 550 B) 600 C) 650 D) 180 E) 750 | 1flash=20sec for 1 min=3flashes so for 1 hour=3*60=
<gadget id="calculator">3*60</gadget>
<output>180</output>
180 flashes. ANSWER:180
<result>D</result> | D | {
"A": "550",
"B": "600",
"C": "650",
"D": "180",
"E": "750"
} | a light flashes every 20 seconds, how many times will it flash in ? of an hour? |
aqua_rat__ik0wbGtPkexIftwa | Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.2 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Choose the correct choice from the following answers: A) 3/8 B) 14/31 C) 7/15 D) 17/35 E) 1/2 | The easiest way for me is to plug in numbers. Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos. If it takes an hour to produce a basic stereo then it will take 1.2 hours to produce a deluxe stereo. 40 basic stereos = 40 hours. 20 delux stereos = 24 hours. Total hours = 64. Then the fraction would be 24/64 = 3/8. Therefore answer 3/8.
<result>A</result> | A | {
"A": "3/8",
"B": "14/31",
"C": "7/15",
"D": "17/35",
"E": "1/2"
} | Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.2 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos? |
aqua_rat__7u2YadSl64yk7lQM | What is the CP of Rs 100 stock at 2 discount, with 1/5% brokerage? Answers.
A) 99.6 B) 96.2 C) 97.5 D) 98.2 E) None of these | Explanation: Use the formula, CP= 100 – discount + brokerage% CP= 100-2+1/5 98.2 Thus the CP is Rs 98.2. ANSWER 98.2
<result>D</result> | D | {
"A": "99.6",
"B": "96.2",
"C": "97.5",
"D": "98.2",
"E": "None of these"
} | What is the CP of Rs 100 stock at 2 discount, with 1/5% brokerage? |
aqua_rat__3U7vCzE8lfFkp7K0 | The average of the marks of 10 students in a class is 40. If the marks of each student are doubled, find the new average? Options:
A) 78 B) 56 C) 80 D) 27 E) 40 | Sum of the marks for the 10 students = 10 * 40=
<gadget id="calculator">10 * 40</gadget>
<output>400</output>
400. The marks of each student are doubled, the sum also will be doubled. The new sum= 400 * 2=
<gadget id="calculator">400 * 2</gadget>
<output>800</output>
800. So, the new average= 800/10=
<gadget id="calculator">800/10</gadget>
<output>80</output>
80. Answer: 80
<result>C</result> | C | {
"A": "78",
"B": "56",
"C": "80",
"D": "27",
"E": "40"
} | The average of the marks of 10 students in a class is 40. If the marks of each student are doubled, find the new average? |
aqua_rat__iOaTQcDHY7bymDWr | A man can row upstream at 20 kmph and downstream at 60 kmph, and then find the speed of the man in still water? Select the correct option: A) 27 B) 29 C) 40 D) 20 E) 24 | US = 20 DS = 60 M = (20 + 60)/2=
<gadget id="calculator">(20 + 60)/2</gadget>
<output>40</output>
40 Answer: 40
<result>C</result> | C | {
"A": "27",
"B": "29",
"C": "40",
"D": "20",
"E": "24"
} | A man can row upstream at 20 kmph and downstream at 60 kmph, and then find the speed of the man in still water? |
aqua_rat__VYsyDPOrpxCVHiMh | The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam. Choose the correct choice from the following choices.
A) 15 B) 25 C) 30 D) 45 E) 55 | Let the number of students who wrote the exam be x. Total marks of students = 80 x. Total marks of (x - 5) students = 92(x - 5) 80x - (5 * 20) = 92(x - 5) 360 = 12x => x = 30 ANSWER:30
<result>C</result> | C | {
"A": "15",
"B": "25",
"C": "30",
"D": "45",
"E": "55"
} | The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam. |
aqua_rat__mWaAqRK5QaoKnSMf | The ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife? Choose the correct choice from the following choices:
A) 6.3 B) 4:3 C) 5:2 D) Cannot be determined E) 7:8 | Answer: Option D Let the present ages of anil and his son be 7x and 3x years respectively. Let the present age of the son's mother be m years. (m + 6)/(3x + 6) = 2/1 m = 6x + 6 Ratio of the present ages of anil and his son's mother = 7x/(6x + 6). This cannot be found uniquely.
<result>D</result> | D | {
"A": "6.3",
"B": "4:3",
"C": "5:2",
"D": "Cannot be determined",
"E": "7:8"
} | The ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife? |
aqua_rat__KE9fG74H9ZKTlS0c | On the coordinate plane , points P and B are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ? Choose the correct choice from the following answers:
A) (1.5,1)
B) (2,-5)
C) (0,0)
D) (1,1.5)
E) (2,2) | Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options. One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord). Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PB is the diameter of the circle. There can be a case when PB is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle. If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y COR(1,1.5)INATE and mark the ans=(1,1.5)
<result>D</result> | D | {
"A": "(1.5,1)",
"B": "(2,-5)",
"C": "(0,0)",
"D": "(1,1.5)",
"E": "(2,2)"
} | On the coordinate plane , points P and B are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ? |
aqua_rat__0n6q1pLZLBL8Z9fu | A does a work in 10 days and B does the same work in 5 days. In how many days they together will do the same work ? Choose the correct option:
A) 1/5
B) 2/7
C) 3/10
D) 3/11
E) 3/17 | Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them, So, A's 1 day work = 1/10 B's 1 day work = 1/15 (A+B)'s 1 day work = (1/10+1/5)=(1+2/10)= 3/10 3/10
<result>C</result> | C | {
"A": "1/5",
"B": "2/7",
"C": "3/10",
"D": "3/11",
"E": "3/17"
} | A does a work in 10 days and B does the same work in 5 days. In how many days they together will do the same work ? |
aqua_rat__V0DFEVwH127WDQFx | There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure e in inches of the width of the foil covered prism? Pick:
A) 4 B) 6 C) 8 D) 9 E) 10 | If the width is w, then length and height would be w/2. So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3) => w = 2*4=
<gadget id="calculator">2*4</gadget>
<output>8</output>
8 in. Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes= 8 +2=e =10 Ans 10.
<result>E</result> | E | {
"A": "4",
"B": "6",
"C": "8",
"D": "9",
"E": "10"
} | There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure e in inches of the width of the foil covered prism? |
aqua_rat__bmeGjAGIbSMAnLWE | The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 150 sq. cm, what is the length of the rectangle?
Choose the correct choice:
A) 12 cm B) 15 cm C) 18 cm D) 21 cm E) 24 cm | 2L+2W = 5W L = 3W/2 W*L = 150 3W^2/2 = 150 W^2 = 100 W = 10 L = 3(10)/2 = 15 The answer is 15 cm.
<result>B</result> | B | {
"A": "12 cm",
"B": "15 cm",
"C": "18 cm",
"D": "21 cm",
"E": "24 cm"
} | The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 150 sq. cm, what is the length of the rectangle? |
aqua_rat__s2uDVh1z2Gc5shn9 | A $500 investment and a $1,500 investment have a combined yearly return of 10 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have? Choose the correct choice from the following:
A) 9% B) 10% C) 105/8% D) 11% E) 12% | The equation we can form the question : Return on Total Investment = Sum of individual Investments (500+1500)(10)=(500∗7)+(1500x), where x is the return on investment of 1500. Solving the equation, we get x = 11% ( Option 11% ) ANSWER:11%
<result>D</result> | D | {
"A": "9%",
"B": "10%",
"C": "105/8%",
"D": "11%",
"E": "12%"
} | A $500 investment and a $1,500 investment have a combined yearly return of 10 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have? |
aqua_rat__l28VtDkND4fsjWUw | What is the diffference between the place value and face value of 4 in the numeral 2694? Choose the correct option:
A) 10 B) 0 C) 5 D) 3 E) 1 | place value of 4 = 4 * 1=
<gadget id="calculator">4 * 1</gadget>
<output>4</output>
4 face value of 4= 4 4 - 4=
<gadget id="calculator">4 - 4</gadget>
<output>0</output>
0 0
<result>B</result> | B | {
"A": "10",
"B": "0",
"C": "5",
"D": "3",
"E": "1"
} | What is the diffference between the place value and face value of 4 in the numeral 2694? |
aqua_rat__nB6ze9iiS2QxqoFr | A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? Choose the correct choice:
A) 5/5 B) 5/8 C) 5/3 D) 5/1 E) 5/6 | Two balls can be picked from nine balls in ⁹C₂ ways. We select one white ball and one red ball from five white balls and four red balls. This can be done 5C1 . 4C1 ways. The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9 Answer:5/8
<result>B</result> | B | {
"A": "5/5",
"B": "5/8",
"C": "5/3",
"D": "5/1",
"E": "5/6"
} | A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color? |
aqua_rat__XaAL2YQINeb5TUdy | Find the average of all prime numbers between 1 and 5. Pick:
A) 30
B) 3.6
C) 5.6
D) 6.6
E) None | Sol. There are five prime numbers between 1 and 5. They are 2, 3, 5, 7, 11 ∴ Required average = [2 + 3+ 5+ 7+ 11 / 5] = 28/ 5=
<gadget id="calculator">28/ 5</gadget>
<output>28/5 = around 5.6</output>
5.6 Answer 5.6
<result>C</result> | C | {
"A": "30",
"B": "3.6",
"C": "5.6",
"D": "6.6",
"E": "None"
} | Find the average of all prime numbers between 1 and 5. |
aqua_rat__qx7Mw3VAT9CgX3vg | Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? Select the correct option: A) 3:30 pm B) 3:45 pm C) 4:00 pm D) 4:15 pm E) 4:30 pm | Total distance, which should be covered by both cars is 190+35=
<gadget id="calculator"> 190+35</gadget>
<output>225</output>
225 miles. Let t be the time so the equation will be 46t+54t=225 thus, t=2.25 hours Answer: 4:15 pm
<result>D</result> | D | {
"A": "3:30 pm",
"B": "3:45 pm",
"C": "4:00 pm",
"D": "4:15 pm",
"E": "4:30 pm"
} | Cars P and Q are approaching each other on the same highway. Car P is moving at 46 mph northbound and Car Q is moving at 54 mph southbound. At 2:00 pm, they are approaching each other and 190 miles apart. Eventually they pass each other. At what clock time are they moving away from each other and 35 miles apart? |
aqua_rat__s9rSF0sOY9cSXxY1 | Peeta asks Katniss, 'It is 6 am as per my watch right now.Do you know what will be the time 23, 999, 998 hours later?'
Katniss knows the answer. Do you ? Choices: A) 5pm B) 6pm C) 4am D) 3am E) 8pm | D 3am The time after 24, 000, 000 hours will be the same as it is now. We want the time 3 hours before that and thus you can deduct three hours from 9 pm. So the time will be 6 pm.
<result>D</result> | D | {
"A": "5pm",
"B": "6pm",
"C": "4am",
"D": "3am",
"E": "8pm"
} | Peeta asks Katniss, 'It is 6 am as per my watch right now.Do you know what will be the time 23, 999, 998 hours later?'
Katniss knows the answer. Do you ? |
aqua_rat__E1tY0Xlt1NpZHmmN | In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes? Pick one:
A) 26 B) 34 C) 64 D) 60 E) 72 | Ans.(C) Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
<result>C</result> | C | {
"A": "26",
"B": "34",
"C": "64",
"D": "60",
"E": "72"
} | In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes? |
aqua_rat__RSS9ib83uqIsZ0Jy | Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ? Pick one.
A) 6 B) 8 C) 7 D) 25 E) data insufficient | given: x/2y = 3/2 => (x-2y)/2y = 1/2 => x = 3y Putting x = 3y in (7x+4y)/(x-3y) gives value 25. ANSWER:25
<result>D</result> | D | {
"A": "6",
"B": "8",
"C": "7",
"D": "25",
"E": "data insufficient"
} | Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ? |
aqua_rat__Vuu9szlSr0eQR5qK | What is the next number in this series?
4,12,84,3612.... Choose the correct choice from the following options
A) 6526884 B) 6526888 C) 6626884 D) 6527884 E) 6526984 | ((4^2)/2)+4=12 ((12^2)/2)+12=84 ((84^2)/2)+84=3612 ((3612^2)/2)+3612=6526884 6526884NSWER:6526884
<result>A</result> | A | {
"A": "6526884",
"B": "6526888",
"C": "6626884",
"D": "6527884",
"E": "6526984"
} | What is the next number in this series?
4,12,84,3612.... |
aqua_rat__R538tDEjacviF7Uz | In how many ways, a committee of 5 members can be selected from 4 men and 5 ladies, consisting of 3 men and 2 ladies?
Choose the correct option:
A) 40 B) 152 C) 175 D) 200 E) 212 | (3 men out 4) and (2 ladies out of 5) are to be chosen Required number of ways = (4C3 * 5C2) = 40 40nswer is 40
<result>A</result> | A | {
"A": "40",
"B": "152",
"C": "175",
"D": "200",
"E": "212"
} | In how many ways, a committee of 5 members can be selected from 4 men and 5 ladies, consisting of 3 men and 2 ladies? |
aqua_rat__f2A7QQq4fRuz5OxE | Rs.360 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins? Choose one.
A) 388 B) 266 C) 120 D) 299 E) 270 | 4x 5x 6x 100 50 25 400x + 250x + 150x = 36000 x = 45 6x = 270 Answer: 270
<result>E</result> | E | {
"A": "388",
"B": "266",
"C": "120",
"D": "299",
"E": "270"
} | Rs.360 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins? |
aqua_rat__NWEfGD6nn2FrhlgB | In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/5 . If the probability that a number 12 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 20 is drawn? Choose the correct choice from the following options.
A) 8/15 B) 1/6 C) 1/3 D) 1/2 E) 5/6 | You can simply use sets concept in this question. The formula Total = n(A) + n(B) - n(A and B) is applicable here too. Set 1: Number 12 or larger Set 2: Number 20 or smaller 1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both) 2/3 + P(Set 2) - 1/5 = 1 P(Set 2) = 8/15 8/15nswer (8/15)
<result>A</result> | A | {
"A": "8/15",
"B": "1/6",
"C": "1/3",
"D": "1/2",
"E": "5/6"
} | In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/5 . If the probability that a number 12 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 20 is drawn? |
aqua_rat__8WHrXie527whL7om | A car is purchased on hire-purchase. The cash price is $24 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment?
Options.
A) $503
B) $504
C) $555
D) $576
E) $587 | Explanation: Cash price = $24 000 $576eposit = 10% × $24 000 = $2400 Loan amount = $24000 − $2400 Number of payments = 60 = $21600 I=p*r*t/100 I=12960 Total amount = 21600 + 12960=
<gadget id="calculator">21600 + 12960</gadget>
<output>34_560</output>
$34560 Regular payment= total amount /number of payments=576 Answer: $576
<result>D</result> | D | {
"A": "$503",
"B": "$504",
"C": "$555",
"D": "$576",
"E": "$587"
} | A car is purchased on hire-purchase. The cash price is $24 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment? |
aqua_rat__Boh4rJ7xwn980EgD | A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? Choose the correct option
A) 600 B) 400 C) 500 D) 670 E) 800 | 800 25 = 800/(1000 - 800) * 100 1000 - 800 = 4800 1000 = 5800 => 800 = 200 1000 - 200=
<gadget id="calculator">1000 - 200</gadget>
<output>800</output>
800
<result>E</result> | E | {
"A": "600",
"B": "400",
"C": "500",
"D": "670",
"E": "800"
} | A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age? |
aqua_rat__DgQvVOJx6HgNPYrP | cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained? Choose the correct choice from the following choices:
A) 1002 B) 2899 C) 1000 D) 2807 E) 2800 | Along one edge, the number of small cubes that can be cut = 100/10=
<gadget id="calculator">100/10</gadget>
<output>10</output>
10 Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10=
<gadget id="calculator">10 * 10 * 10</gadget>
<output>1_000</output>
1000 Answer: 1000
<result>C</result> | C | {
"A": "1002",
"B": "2899",
"C": "1000",
"D": "2807",
"E": "2800"
} | cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained? |
aqua_rat__IGjd79gT2oegFWoh | On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 80 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Pick one: A) 20% B) 40% C) 60% D) 80% E) 100% | Let T be the total number of passengers. Let x be the number of people with round trip tickets. 0.2T had round trip tickets and took their cars. 0.2x had round trip tickets and took their cars. 0.2x = 0.2T x = T The answer is 100%.
<result>E</result> | E | {
"A": "20%",
"B": "40%",
"C": "60%",
"D": "80%",
"E": "100%"
} | On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 80 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets? |
aqua_rat__JmfByCsaeavAOyNQ | There are 15 boys and 10 girls in a class. If three students are selected at random, in how many ways that 1 girl and 2 boys are selected ? Choose the most appropriate option.
A) 950
B) 1050
C) 2150
D) 2050
E) 1000 | n(s) = sample space = 25C3 = 2300 E = event that 1 girl and 2 boys are selected n(E) = we have to select 2 boys from 15 and 1 girl from 10 = 15C2 * 10C1 = 1050 Ans - 1050
<result>B</result> | B | {
"A": "950",
"B": "1050",
"C": "2150",
"D": "2050",
"E": "1000"
} | There are 15 boys and 10 girls in a class. If three students are selected at random, in how many ways that 1 girl and 2 boys are selected ? |
aqua_rat__Cll40axH5MLQB7e6 | consider the sequence 1,-2,3,-4,5,6.....what is the average of the first 200 terms of the sequence? Choose the correct option: A) -1/2 B) -3/2 C) 0 D) 1/2 E) 3/2 | suppose n=2 => avg is (1+-2)/2= -1/2, when n=4 => avg is -1/2 , similarly for n=200 avg will be -1/2. -1/2NSWER:-1/2
<result>A</result> | A | {
"A": "-1/2",
"B": "-3/2",
"C": "0",
"D": "1/2",
"E": "3/2"
} | consider the sequence 1,-2,3,-4,5,6.....what is the average of the first 200 terms of the sequence? |
aqua_rat__ERsib8KsGAJkLDSH | 3 balls are drawn randomly from a bag contains 3 black, 5 red and 4 blue balls. What is the probability that the balls drawn contain balls of different colors?
Choose the correct choice from the following options.
A) 1/3 B) 1/2 C) 2/11 D) 3/11 E) 11/13 | Total number of balls = 3 + 5 + 4=
<gadget id="calculator">3 + 5 + 4</gadget>
<output>12</output>
12 Let S be the sample space. n(S)= Total number of ways of drawing 3 balls out of 12 = 12C3 Let E = Event of drawing 3 different coloured balls To get 3 different coloured balls,we need to select one black ball from 3 black balls, one red ball from 5 red balls, one blue ball from 4 blue balls Number of ways in which this can be done = 3C1 × 5C1 × 4C1 i.e., n(E) = 3C1 × 5C1 × 4C1 P(E) = n(E)/n(S)=3C1×5C1×4C1/12C3 =3×5×4/(12×11×10/3×2×1)=3×5×4/2×11×10=3×4/2×11×2=3/11 ANSWER:3/11
<result>D</result> | D | {
"A": "1/3",
"B": "1/2",
"C": "2/11",
"D": "3/11",
"E": "11/13"
} | 3 balls are drawn randomly from a bag contains 3 black, 5 red and 4 blue balls. What is the probability that the balls drawn contain balls of different colors? |
aqua_rat__J3FhbTwa9bKMDnps | Of the four numbers, whose average is 40, the first is one-fourth of the sum of the last three. The first number is ? Pick one: A) 28 B) 29 C) 11 D) 32 E) 10 | Explanation: Let the first number be x, Then, sum of the four numbers = x + 4x = 5x. so, 5x/4 = 40 or x = (40 * 4) / 5=
<gadget id="calculator">(40 * 4) / 5</gadget>
<output>32</output>
32 Answer: 32
<result>D</result> | D | {
"A": "28",
"B": "29",
"C": "11",
"D": "32",
"E": "10"
} | Of the four numbers, whose average is 40, the first is one-fourth of the sum of the last three. The first number is ? |
aqua_rat__ErnACDeRVeBn97Dl | In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ? Choose the correct answer.
A) 6
B) 10
C) 8
D) 12
E) 14 | Explanation: Let the number of buffaoes be x and number of ducks be y. Then 4x + 2y = 2(x + y) + 24 => 2x = 24 => x = 12. Answer: 12
<result>D</result> | D | {
"A": "6",
"B": "10",
"C": "8",
"D": "12",
"E": "14"
} | In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ? |
aqua_rat__36hrGog7lSmZz9Re | A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at: Choose the correct choice from the following
A) 6 %
B) 6.1 %
C) 6.2 %
D) 6.3 %
E) 6.4 % | Income from $ 4000 at 5 % in one year = $ 4000 of 5 %. = $ 4000 × 5/100. = $ 4000 × 0.05. = $ 200. Income from $ 3500 at 4 % in one year = $ 3500 of 4 %. = $ 3500 × 4/100. = $ 3500 × 0.04. = $ 140. Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340. Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340. = $ 160. Total invested amount = $ 4000 + $ 3500 = $7500. Remaining invest amount = $ 10000 - $ 7500 = $ 2500. We know that, Interest = Principal × Rate × Time Interest = $ 160, Principal = $ 2500, Rate = r [we need to find the value of r], Time = 1 year. 160 = 2500 × r × 1. 160 = 2500r 160/2500 = 2500r/2500 [divide both sides by 2500] 0.064 = r r = 0.064 Change it to a percent by moving the decimal to the right two places r = 6.4 % Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year. Correct Answer: 6.4 %)6.4 %
<result>E</result> | E | {
"A": "6 %",
"B": "6.1 %",
"C": "6.2 %",
"D": "6.3 %",
"E": "6.4 %"
} | A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at: |
aqua_rat__BFGzeioRbEwgwQ6Z | he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg. What might be the weight of the new person ?
Choose the correct answer.
A) 75 kg
B) 55 kg
C) 45 kg
D) 85 kg
E) 90 kg | Explanation: Total weight increased = (8 x 3.5) kg = 28 kg. Weight of new person = (62 + 28)=
<gadget id="calculator">(62 + 28)</gadget>
<output>90</output>
90 kg. Answer: 90 kg
<result>E</result> | E | {
"A": "75 kg",
"B": "55 kg",
"C": "45 kg",
"D": "85 kg",
"E": "90 kg"
} | he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg. What might be the weight of the new person ? |
aqua_rat__O1iZ5YgFxjsCWzya | 7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.5 ounces and a standard deviation of 0.2 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean? Choose the correct choice.
A) Four B) Five C) Nine D) Ten E) Eleven | Mean = 8.5 Standard Deviation = 0.2 within 1.5 standard deviation of the mean i.e. 1.5 standard deviation AFiveOVE the mean = 8.5+1.5*0.2=
<gadget id="calculator">8.5+1.5*0.2</gadget>
<output>8.8</output>
8.8 and 1.5 standard deviation FiveELOW the mean= 8.5-1.5*0.2=
<gadget id="calculator">8.5-1.5*0.2</gadget>
<output>8.2</output>
8.2 hence, 5 values fall within 1.5 SD from Mean Answer: Option Five
<result>B</result> | B | {
"A": "Four",
"B": "Five",
"C": "Nine",
"D": "Ten",
"E": "Eleven"
} | 7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.5 ounces and a standard deviation of 0.2 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean? |
aqua_rat__EavXVatVYoGD30zH | Vinoth can complete a painting work in 20 days. Prakash can do the same work in 25 days. They start the work together but Vinoth quit after 3 days of work. How many days are required to complete the remaining painting work by Prakash.
Choose the correct choice from the following answers: A) 15.25 days B) 16.25 days C) 17.25 days D) 18.25 days E) 19.25 days | Vinoth can complete the painting work in one day is 1/20 Prakash can complete the same work in one day is 1/25 Both of them can complete the work in 1/20+ days=9/100( 1/20+1/25) they must have completed in three days=9/100*3=27/100 Remaining work to be done is by Prakash =1-27/100=73/100 For one work, Prakash can do in 25 days For 73/100 work, he can do in 73/100*25=73/4days or 18.25 days ANSWER:18.25 days
<result>D</result> | D | {
"A": "15.25 days",
"B": "16.25 days",
"C": "17.25 days",
"D": "18.25 days",
"E": "19.25 days"
} | Vinoth can complete a painting work in 20 days. Prakash can do the same work in 25 days. They start the work together but Vinoth quit after 3 days of work. How many days are required to complete the remaining painting work by Prakash. |
aqua_rat__L0aUG7HNKTJfkF6O | A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good
Choose the correct choice from the following choices.
A) 125/126
B) 125/129
C) 125/128
D) 125/124
E) 125/121 | Required probability = 1 - 1/126 = 125/126.125/126nswer:125/126
<result>A</result> | A | {
"A": "125/126",
"B": "125/129",
"C": "125/128",
"D": "125/124",
"E": "125/121"
} | A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good |
aqua_rat__XBywrRheJUwLHG6o | If 180/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer. Choose the correct choice: A) I, II, and III B) III only C) I and II only D) II and III only E) I only | The largest possible value of x is 36 (the greatest common factor of 180 and 108), and if x=36 then III only
<result>B</result> | B | {
"A": "I, II, and III",
"B": "III only",
"C": "I and II only",
"D": "II and III only",
"E": "I only"
} | If 180/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer. |
aqua_rat__E32SLOZxHPHoUPSM | A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choose the correct choice from the following answers
A) 120 m
B) 225 m
C) 300 m
D) 360 m
E) 280 m | Speed = 54 x 5/18 m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/35 = 15 x + 300 = 525 x = 225 m.Answer: Option 225 m
<result>B</result> | B | {
"A": "120 m",
"B": "225 m",
"C": "300 m",
"D": "360 m",
"E": "280 m"
} | A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? |
aqua_rat__KICDywfYEVoSmFFg | Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: Choose the correct choice from the following options: A) 4 B) 5 C) 6 D) 8 E) 9 | Explanation: N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 )=
<gadget id="calculator">( 1 + 1 + 2 + 0 )</gadget>
<output>4</output>
4 4NSWER IS 4
<result>A</result> | A | {
"A": "4",
"B": "5",
"C": "6",
"D": "8",
"E": "9"
} | Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is: |
aqua_rat__HaRSiiQGz50EU6T6 | In a simultaneous throw of two coins, the probability of getting at least one head is Choose one:
A) 1/2 B) 1/3 C) 2/3 D) 3/4 E) 3/5 | Here S={HH, HT, TH, TT} Let E = event of getting at least one head = {HT, TH, HH} Therefore P(E) = n(E)/n(S) = 3/4 Answer 3/4.
<result>D</result> | D | {
"A": "1/2",
"B": "1/3",
"C": "2/3",
"D": "3/4",
"E": "3/5"
} | In a simultaneous throw of two coins, the probability of getting at least one head is |
aqua_rat__isO9eukQrghvfIKD | Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 20000 at the end of the year, what should be the share of Narendra? Pick one: A) A)Rs.7000 B) B)Rs.8000 C) C)Rs.8500 D) D)Rs.8600 E) E)Rs.16000 | The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1. :. Narendra’s share on profit of Rs.20000 = 20000 × 4/5 = Rs.16000. Rs.16000)
<result>E</result> | E | {
"A": "A)Rs.7000",
"B": "B)Rs.8000",
"C": "C)Rs.8500",
"D": "D)Rs.8600",
"E": "E)Rs.16000"
} | Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 20000 at the end of the year, what should be the share of Narendra? |
aqua_rat__JC0bbyULKgnQ2reo | A train 120 m long crosses a platform 120 m long in 6 sec; find the speed of the train?
Select
A) 144 kmph B) 58 kmph C) 54 kmph D) 94 kmph E) 59 kmph | D = 120 + 120=
<gadget id="calculator">120 + 120</gadget>
<output>240</output>
240 T= 6 S = 240/6 * 18/5=
<gadget id="calculator">240/6 * 18/5</gadget>
<output>144</output>
144 kmph 144 kmphnswer: 144 kmph
<result>A</result> | A | {
"A": "144 kmph",
"B": "58 kmph",
"C": "54 kmph",
"D": "94 kmph",
"E": "59 kmph"
} | A train 120 m long crosses a platform 120 m long in 6 sec; find the speed of the train? |
aqua_rat__lrlxZLhoPNwJimb7 | Find the largest number of four digits which is exactly divisible by 27,18,12,15 Pick.
A) 9700 B) 9710 C) 9720 D) 9730 E) None of these | Explanation: LCM of 27-18-12-15 is 540. After dividing 9999 by 540 we get 279 remainder. So answer will be 9999-279=
<gadget id="calculator">9999-279</gadget>
<output>9_720</output>
9720 Answer: Option 9720
<result>C</result> | C | {
"A": "9700",
"B": "9710",
"C": "9720",
"D": "9730",
"E": "None of these"
} | Find the largest number of four digits which is exactly divisible by 27,18,12,15 |
aqua_rat__Spn5AuJMMmmLznjy | Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was: Choices: A) three times as much B) twice as much C) a third as much D) half as much E) the same | et speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr. We know that Speed = Distance/Time. Or, Time = Distance/Speed. So, times taken to covered a distance of 50 miles on his first trip = 50/x hr. And times taken to covered a distance of 300 miles on his later trip = 300/3x hr. = 100/x hr. So we can clearly see that his new time compared with the old time was: twice as much.
<result>B</result> | B | {
"A": "three times as much",
"B": "twice as much",
"C": "a third as much",
"D": "half as much",
"E": "the same"
} | Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was: |
aqua_rat__WVsS9na9m1M7Bh8j | The contents of a certain box consist of 24 oranges and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be oranges? Choose the correct choice from the following answers
A) 24
B) 26
C) 30
D) 46
E) 50 | oranges = (oranges + kiwi + x)*0.3 24 = (30 + 24 + x)*0.3 x = 26. Answer: 26.
<result>B</result> | B | {
"A": "24",
"B": "26",
"C": "30",
"D": "46",
"E": "50"
} | The contents of a certain box consist of 24 oranges and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be oranges? |
aqua_rat__KLKhESv1QAR3bKFT | A train 250 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? Options:
A) 32 B) 28 C) 29 D) 44 E) 21 | S = (250 + 300)/45 = 550/45 * 18/5=
<gadget id="calculator">550/45 * 18/5</gadget>
<output>44</output>
44 Answer: 44
<result>D</result> | D | {
"A": "32",
"B": "28",
"C": "29",
"D": "44",
"E": "21"
} | A train 250 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is? |
aqua_rat__ITF9yWWxjfjwBhtp | A side of an equilateral triangle is tripled. If the previous parameter is 3x, what is the length of one of the sides before it was tripled? Pick.
A) 4x B) 3x C) 1x D) 2x E) 6x | If the parameter before it was tripled 3x, one of the sides must have been 3x/3. This reduces to 1x. Answer option 1x.
<result>C</result> | C | {
"A": "4x",
"B": "3x",
"C": "1x",
"D": "2x",
"E": "6x"
} | A side of an equilateral triangle is tripled. If the previous parameter is 3x, what is the length of one of the sides before it was tripled? |
aqua_rat__Opr66vl29dO24Cu8 | If 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursday, bow much coal will be required for 8 engines, each running 13hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type? Choose the correct choice.
A) 22 B) 24 C) 26 D) 28 E) None of them | Let 3 engines of former type consume 1 unit in 1 hour. Then, 4 engines of latter type consume 1 unit in 1 hour. Therefore 1 engine of former type consumes(1/3) unit in 1 hour. 1 engine of latter type consumes(1/4) unit in 1 hour. Let the required consumption of coal be x units. Less engines, Less coal consumed (direct proportion) More working hours, More coal consumed (direct proportion) Less rate of consumption, Less coal consumed(direct prportion) Number of engines 9: 8 Working hours 8 : 13 } :: 24 : x Rate of consumption (1/3):(1/4) [ 9 x 8 x (1/3) x x) = (8 x 13 x (1/4) x 24 ) = 24x = 624 = x = 26. Hence, the required consumption of coal = 26 metric tonnes. Answer is 26.
<result>C</result> | C | {
"A": "22",
"B": "24",
"C": "26",
"D": "28",
"E": "None of them"
} | If 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursday, bow much coal will be required for 8 engines, each running 13hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type? |
aqua_rat__U5yO83shMchCyeRP | An individual deposited 20% of 25% of 30% of what he had into his account with a bank. If he deposited Rs.750, how much was he having initially with him before depositing? Choose the correct choice from the following answers:
A) Rs.500000 B) Rs.50000 C) Rs.5000 D) Rs.15000 E) Rs.6000 | let x amount he has then 20% of 25% of 30% of x=750 so x=50000 ANSWER:Rs.50000
<result>B</result> | B | {
"A": "Rs.500000",
"B": "Rs.50000",
"C": "Rs.5000",
"D": "Rs.15000",
"E": "Rs.6000"
} | An individual deposited 20% of 25% of 30% of what he had into his account with a bank. If he deposited Rs.750, how much was he having initially with him before depositing? |
aqua_rat__a8BFQJjyThtQxmbY | At what angle the hands of a clock are inclined at 15 minutes past 5? Select
A) 117/2°
B) 64°
C) 135/2°
D) 145/2°
E) 155/2° | Apply the formula: 30h-11/2m=Angle 30*5-11/2*15 150-165/2=135/2 ANSWER:135/2°
<result>C</result> | C | {
"A": "117/2°",
"B": "64°",
"C": "135/2°",
"D": "145/2°",
"E": "155/2°"
} | At what angle the hands of a clock are inclined at 15 minutes past 5? |
aqua_rat__5Ou0upUgm5YmFtWH | A man walks a certain distance and rides back in 6 1⁄4h. He can walk both ways in 7 3⁄4h. How long it would take to ride both ways ? Choose the correct choice from the following
A) 5 hours B) 4 1⁄2 hours C) 4 3⁄4 hours D) 6 hours E) None of these | We know that, the relation in time taken with two different modes of transport is twalk both + tride both = 2 (twalk + tride) 31⁄4 + tride both = 2 × 25⁄4 ⇒ tride both = 25⁄2 - 31⁄4 = 19⁄4 = 43⁄4 hours Answer 4 3⁄4 hours
<result>C</result> | C | {
"A": "5 hours",
"B": "4 1⁄2 hours",
"C": "4 3⁄4 hours",
"D": "6 hours",
"E": "None of these"
} | A man walks a certain distance and rides back in 6 1⁄4h. He can walk both ways in 7 3⁄4h. How long it would take to ride both ways ? |
aqua_rat__TTXU0jLEzsfKkqG0 | It is only in the second option we find the sentence A in continuation with the opening sentence D. Sentence A alone explains, why the fear has such enormous effect on the human beings. Choose one:
A) 28 B) 99 C) 728 D) 27 E) 271 | Answer:99
<result>B</result> | B | {
"A": "28",
"B": "99",
"C": "728",
"D": "27",
"E": "271"
} | It is only in the second option we find the sentence A in continuation with the opening sentence D. Sentence A alone explains, why the fear has such enormous effect on the human beings. |
aqua_rat__txJY1FCBbUx5RdpO | What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent? Select: A) 266 B) 500 C) 287 D) 26 E) 281 | 70 = (P*4*7/2)/100 P = 500 Answer: 500
<result>B</result> | B | {
"A": "266",
"B": "500",
"C": "287",
"D": "26",
"E": "281"
} | What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent? |
aqua_rat__iBE92ki5JIHd8AXJ | If x > 1, which of the following decreases as x decreases?
I. x + x^2
II. 1/(2x^2 − x)
III. 1/(x + 1) Options:
A) I only B) II only C) III only D) I and II only E) II and III only | let x= 4 and 3 b old and new values ST1: x= 4 -> 4+16 = 20 x=3-> 3+9 = 12 ...decreased ST2:x= 4-> 2*16-4 = 1/28 x=3->2*9-3 = 1/15 increased St3: x=4-> 1/4 = .25 x=3->1/3 = .33 I onlyns: I only
<result>A</result> | A | {
"A": "I only",
"B": "II only",
"C": "III only",
"D": "I and II only",
"E": "II and III only"
} | If x > 1, which of the following decreases as x decreases?
I. x + x^2
II. 1/(2x^2 − x)
III. 1/(x + 1) |
aqua_rat__9AL0R3G9hhvRMUHY | the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? Choose the correct choice from the following options: A) 10 B) 15 C) 20 D) 25 E) 30 | For the 5 minutes the cyclist continues to overtake the hiker, she is going at 21 miles per hour faster than the hiker. Once the cyclist stops, the hiker is going at 7 miles per hour while the cyclist is at rest So the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds. 21/7 * 5 or 15 minutes Answer is (15)
<result>B</result> | B | {
"A": "10",
"B": "15",
"C": "20",
"D": "25",
"E": "30"
} | the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? |
aqua_rat__4bAiwdBMwzIUApes | Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 12 meters, and the interior of tank B has a height of 12 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
Choose the correct choice from the following answers:
A) 80%
B) 90%
C) 100%
D) 110%
E) 120% | The radius of tank A is 12/(2*pi). The capacity of tank A is 10*pi*144 / (4*pi^2) = 360 / (pi) The radius of tank B is 10 / (2*pi). The capacity of tank B is 12*pi*100 / (4*pi^2) = 300 / (pi) Tank A / Tank B = 360/300 = 12/10 = 120% The answer is 120%.
<result>E</result> | E | {
"A": "80%",
"B": "90%",
"C": "100%",
"D": "110%",
"E": "120%"
} | Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 12 meters, and the interior of tank B has a height of 12 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? |
aqua_rat__n2z8xIEmzzroD47E | The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? Pick.
A) 140 sq.units B) 186 sq.units C) 176 sq.units D) 865 sq.units E) 143 sq.units | Given that the area of the square = 1225 sq.units => Side of square = √1225 = 35 units The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35=
<gadget id="calculator">2/5 * 35</gadget>
<output>14</output>
14 units Given that breadth= 10 units 140 sq.unitsrea of the rectangle = lb = 14 * 10=
<gadget id="calculator">14 * 10</gadget>
<output>140</output>
140 sq.units 140 sq.unitsnswer:140 sq.units
<result>A</result> | A | {
"A": "140 sq.units",
"B": "186 sq.units",
"C": "176 sq.units",
"D": "865 sq.units",
"E": "143 sq.units"
} | The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? |
aqua_rat__0zwsnNdGI6l3JPtu | Which of the following is a prime number ? Options: A) 33 B) 81 C) 93 D) 97 E) 95 | Explanation: Clearly, 97 is a prime number. ANSWER IS 97
<result>D</result> | D | {
"A": "33",
"B": "81",
"C": "93",
"D": "97",
"E": "95"
} | Which of the following is a prime number ? |
aqua_rat__wlcrN6cP9wYu1iKL | A man buys an article for $10. and sells it for $30. Find the gain percent? Pick one
A) 25% B) 50% C) 20% D) 150% E) 300% | C.P. = $10 S.P. = $30 Gain = $20 Gain% = 20/10 *100 = 300% Answer is 300%
<result>E</result> | E | {
"A": "25%",
"B": "50%",
"C": "20%",
"D": "150%",
"E": "300%"
} | A man buys an article for $10. and sells it for $30. Find the gain percent? |
aqua_rat__Nj71DEoTl0dRYHEJ | The average age of 19 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is? Answers
A) 9 B) 71 C) 85 D) 92 E) 90 | Age of the 15th student = 19*15 - (14*5+16*9) = 285-214=
<gadget id="calculator">285-214</gadget>
<output>71</output>
71 years Answer is 71
<result>B</result> | B | {
"A": "9",
"B": "71",
"C": "85",
"D": "92",
"E": "90"
} | The average age of 19 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is? |
aqua_rat__fFrIoDsVrzP93TrP | Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. Answers.
A) 208 km B) 637 km C) 342 km D) 300 kilometre E) 543 km | Let the distance travelled be x km. Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11 => x = 300 km Answer:300 kilometre
<result>D</result> | D | {
"A": "208 km",
"B": "637 km",
"C": "342 km",
"D": "300 kilometre",
"E": "543 km"
} | Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan. |
aqua_rat__LtD1OKAfLv5mxeNn | What is the probability of getting a sum of 12 when rolling 3 dice simultaneously?
Choose the correct choice from the following choices:
A) 10/216
B) 12/216
C) 21/216
D) 23/216
E) 25/216 | Sum of 12 can be achieved in following ways 6,5,1---Total cases = 3! = 6 6,4,2---Total cases = 3!= 6 6,3,3---Total cases = 3!/2! = 3 5,5,2---Total cases = 3!/2! = 3 5,4,3---Total cases = 3! = 6 4,4,4---Total cases = 3!/3! = 1 Total cases 3 /3=
<gadget id="calculator">3 /3</gadget>
<output>1</output>
1 Total cases= 25 Probability = 25 * (1/6 * 1/6 * 1/6) = 25/216 ANSW25/216R:25/216
<result>E</result> | E | {
"A": "10/216",
"B": "12/216",
"C": "21/216",
"D": "23/216",
"E": "25/216"
} | What is the probability of getting a sum of 12 when rolling 3 dice simultaneously? |
aqua_rat__FxzuCaWxHX3LKrHa | A sum of Rs.7000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. Choose the correct answer:
A) A)282 B) B)4550 C) C)8383 D) D)8383 E) E)3284 | Let A be the amount received at the end of the three years. A = 7000[1 + 10/100][1 + 20/100][1 + 25/100] A = 7000 * 1.65 A = Rs.11550 So the interest = 11550 - 7000 = Rs.4550 Answer: 4550
<result>B</result> | B | {
"A": "A)282",
"B": "B)4550",
"C": "C)8383",
"D": "D)8383",
"E": "E)3284"
} | A sum of Rs.7000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years. |
aqua_rat__X7PhXBGFyF1M4Lx9 | In how many ways can the letters of the word ASTERIX be arranged in a row so that the vowels appear in alphabetic order? Choose the correct choice from the following choices
A) 800
B) 820
C) 880
D) 960
E) 840 eight hundred forty | three letters can be arranged in 3! ways. only one combination AEI is required. 7 letters can be arranged in 7! ways. thus 7!/ 3! * 1 = 840.
<result>E</result> | E | {
"A": "800",
"B": "820",
"C": "880",
"D": "960",
"E": "840 eight hundred forty"
} | In how many ways can the letters of the word ASTERIX be arranged in a row so that the vowels appear in alphabetic order? |
aqua_rat__YZO850qYiBVq2mhJ | There are 3 numbers A, B and C. If A:B = 3/5, B:C = 5/4, C:D = 4/8, then A:D will be? Choose the most appropriate option: A) 1 : 2 B) 3 : 5 C) 5 : 7 D) 6 : 11 E) 3:8 | Sol. A : B = 3 : 5, B : C = 5 : 4, C : D = 4 : 8 ∴A∶B∶C∶D= 3 : 5:4 : 8 Thus, A : D = 3 : 8 3:8
<result>E</result> | E | {
"A": "1 : 2",
"B": "3 : 5",
"C": "5 : 7",
"D": "6 : 11",
"E": "3:8"
} | There are 3 numbers A, B and C. If A:B = 3/5, B:C = 5/4, C:D = 4/8, then A:D will be? |
aqua_rat__eYGcmB4YozFhiST3 | If y exceeds x by 28%, then x is less than y by? Choose the correct choice from the following answers:
A) 16 2/8% B) 16 8/3% C) 21 7/8% D) 76 2/3% E) 17 2/3% | X=100 y=128 128------28 100-------? => 21 7/8% Answer:21 7/8%
<result>C</result> | C | {
"A": "16 2/8%",
"B": "16 8/3%",
"C": "21 7/8%",
"D": "76 2/3%",
"E": "17 2/3%"
} | If y exceeds x by 28%, then x is less than y by? |
aqua_rat__WGEois3tULe8j5th | If 14 men do a work in 80 days, in how many days will 20 men do it?
Choose the correct choice from the following choices
A) 18 days B) 38 days C) 42 days D) 48 days E) 56 days | 14 * 80 = 20 * x x = 56 days ANSW56 daysR:56 days
<result>E</result> | E | {
"A": "18 days",
"B": "38 days",
"C": "42 days",
"D": "48 days",
"E": "56 days"
} | If 14 men do a work in 80 days, in how many days will 20 men do it? |
aqua_rat__1wpdeDMowTNi7StE | A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.1446 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
Select the correct option
A) 32200 B) 41897 C) 58799 D) 60000 E) 62782 | P(11/10)^4 - P(6/5)^2 = 1446 P = 60000 Answer: 60000
<result>D</result> | D | {
"A": "32200",
"B": "41897",
"C": "58799",
"D": "60000",
"E": "62782"
} | A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.1446 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum. |
aqua_rat__nG2G5zxAhFTekGrC | A soccer team played 160 games and won 65 percent of them. How many games did it win? Choose the correct choice from the following answers:
A) 84
B) 94
C) 104
D) 114
E) 124 | 65% of 160 =x 0.65*160=
<gadget id="calculator">0.65*160</gadget>
<output>104</output>
x 104=x answer :104
<result>C</result> | C | {
"A": "84",
"B": "94",
"C": "104",
"D": "114",
"E": "124"
} | A soccer team played 160 games and won 65 percent of them. How many games did it win? |
aqua_rat__GEhiIhFonVK9512W | If the numerator of a fraction be increased by 15% and its denominator be diminished by 8%, the value of the fraction is 15/16. Find the original fraction ? Select the correct option.
A) 1/2 B) 3/5 C) 5/7 D) 9/11 E) 3/4 | Let the original fraction be x/y Then, 115% of x/92% of y = 15/16 115x/92y = 15/16 x/y = 3/4 Answer is 3/4
<result>E</result> | E | {
"A": "1/2",
"B": "3/5",
"C": "5/7",
"D": "9/11",
"E": "3/4"
} | If the numerator of a fraction be increased by 15% and its denominator be diminished by 8%, the value of the fraction is 15/16. Find the original fraction ? |
aqua_rat__36sTDpkJsDVSpTK8 | A driver goes on a trip of 50 kilometers, the first 25 kilometers at 66 kilometers per hour and the remaining distance at 33 kilometers per hour. What is the average speed of the entire trip in kilometers per hour? Choose the correct choice from the following options
A) 38 B) 40 C) 44 D) 45 E) 48 | The time for the first part of the trip was 25/66 hours. The time for the second part of the trip was 25/33 hours. The total time fro the trip was 25/66 + 25/33 = 75/66 = 25/22 hours. The average speed for the trip was 50 / (25/22)=
<gadget id="calculator"> 50 / (25/22)</gadget>
<output>44</output>
44 kph The answer is 44.
<result>C</result> | C | {
"A": "38",
"B": "40",
"C": "44",
"D": "45",
"E": "48"
} | A driver goes on a trip of 50 kilometers, the first 25 kilometers at 66 kilometers per hour and the remaining distance at 33 kilometers per hour. What is the average speed of the entire trip in kilometers per hour? |
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