MU-NLPC/Calc-aqua_rat huggingface dataset:
The price ratio of oranges to lemons is 2:3. The price ratio of grapefruits to lemons is 3:5. What is the ratio, by price, of grapefruit to oranges?  Choose the most appropriate option:  A) 18:20  B) 10:9  C) 2:5  D) 5:2  E) 3:2

Solution: Let price of Lemons be 30 ( since that is common )   So, Price of Oranges = 20 & Price of Lemons is = 30   Further price of Grapefruit will be 6*3= 
6*3 = 18
18   Thus price, of grapefruit to oranges= 18 : 20   18:20NSWER:18:20
Answer: A
A hiker walked for 3 days. She walked 18 miles on the first day, walking 2 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?	Choose one.
A) 24
B) 44
C) 58
D) 69
E) 62

Solution: She walked 18 miles on the first day, walking 2 miles per hour i.e. total time of walk on Day-1 = 18/2= 
18/2 = 9
9 Hours   Second day time of walk= 9-1= 
9-1 = 8
8 hours and Speed= 2+1= 
2+1 = 3
3 miles per hour i.e. Distance walked on second day= 8*3= 
8*3 = 24
24 miles   Third day time of walk= 9 hours and Speed = 3 miles per hour i.e. 69istance walked on second day = 9*3= 
9*3 = 27
27 miles   Total 69istance travelled on three days= 18+24+27= 
18+24+27 = 69
69   Answer: Option 69
Answer: D
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? Choose one
A) 22 B) 13 C) 88 D) 77 E) 91

Solution: Explanation:   Let the required number of days be x.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   \inline {\color{13lue} \left.\begin{matrix} persons &30:39 \\ working\; hours/day & 6:5 \end{matrix}\right\}::12:x}   \inline {\color{13lue} \therefore } 30 x 6 x x = 39 x 5 x 12   => x= \inline {\color{13lue}\frac{39\times 5\times 12}{30\times 6}}   => x= 13   Answer: 13) 13
Answer: B
A foreign language club at Washington Middle School consists of n students, 1/2 of whom are boys. All of the students in the club study exactly one foreign language. 1/3 of the girls in the club study Spanish and 4/5 of the remaining girls study French. If the rest of the girls in the club study German, how many girls in the club, in terms of n, study German? Options:
A) 2n / 5 B) n / 3 C) n / 5 D) 2n / 15 E) n / 15

Solution: 1/2 of the students are boys, thus 1/2 of the students are girls.   1/3 of the girls in the club study Spanish and 4/5 of the remaining girls study French.   Thus 1/5 of 2/3 = 2/15 of the girls study German.   Since girls comprise 1/2 of the students, then 1/2*2/15 = 1/15 are girls who study German.   The answer is n / 15.
Answer: E
Jacob purchased a TV set for $ 12500 after getting a discount of 20% on the labelled price. He spent $ 125 on transport and $ 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?	Choose the correct choice from the following answers.
A) 14900	B) 12900	C) 15400	D) 17600	E) 14700

Solution: 17600   17600   Price at which the TV set is bought = $ 12,500   17600iscount offered = 20%   Marked Price = 12500 * 100/80= 
12500 * 100/80 = 15_625
$ 15625   The total amount spent on transport and installation= 125 + 250= 
125 + 250 = 375
$ 375\Total price of TV set= 15625 + 375= 
15625 + 375 = 16_000
$ 16000   The price at which the TV should be sold to get a profit of 10% if no discount was offered= 16000 * 110/100= 
16000 * 110/100 = 17_600
$ 17600
Answer: D
rahul played weel in this season.his current batting averagge is 51.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.
Choose the correct option:
A) 8
B) 10
C) 9
D) 6
E) 5

Solution: 51x+78=54(x+1)   =>3x=24   =>x=8   8NSWER:8
Answer: A
What approximate value should come in place of the question mark (?) in the following equation?
35% of 1478 + 29% of 3214 = ?  Choose the correct choice from the following answers.
A) 1600	B) 1250	C) 1300	D) 1450	E) 1500

Solution: ? = 35% of 1478 + 29% of 3214   ≈ 35% of (1500 – 22) + (30% – 1%) of 3200   ≈ 35 × 15 – 8 + 30 × 32 – 32   = 525 + 960 – 40 = 525 + 920= 
525 + 920 = 1_445
1445 ≈ 1450   Answer 1450
Answer: D
The average (arithmetic mean) of 4 positive integers is 30. If the average of 2 of these integers is 15, what is the greatest possible value that one of the other 2 integers can have? Pick:
A) 55
B) 89
C) 100
D) 109
E) 115

Solution: a + b + c + d = 120   a + b = 30   c + d = 90   Greatest possible = 89 (Just less than 1)   Answer = 89
Answer: B
The population of a town is 10000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years? Choose the correct choice:
A) 6400	B) 4500	C) 5120	D) 5230	E) 5366

Solution: 10000 × 80/100 × 80/100 = 6400   6400nswer : 6400
Answer: A
If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 1 strokes ?  Choose the correct option.
A) 1/2  B) 7/8  C) 1/4  D) 1/8  E) 1/16

Solution: Left 1/2fter 1st stroke = 1/2   So removed = 1- 1/2 = 1/2
Answer: A
The maximum number of student amoung them 2010 pens and 1050 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Choose the most appropriate option
A) 90
B) 60
C) 30
D) 1911
E) None of these

Solution: Solution   Required number of student = H.C.F of 2010 and 1050 = 30. Answer 30
Answer: C
The average of temperatures at noontime from Monday to Friday is 25; the lowest one is 15, what is the possible maximum range of the temperatures?
Select the correct option:
A) 20  B) 25  C) 50  D) 45  E) 75

Solution: Average=25, Sum of temperatures=25*5= 
25*5 = 125
125   As the min temperature is 15, max would be   125-4*15= 
  125-4*15 = 65
65 --> The range=65(max)-15(min)=50   Answer: 50
Answer: C
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?  Choose the correct answer:
A) 25/42
B) 25/46
C) 25/41
D) 25/49
E) 25/23

Solution: Total fruits = 9   Since there must be at least two apples,   (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃ = 25/42.   25/42nswer:25/42
Answer: A
How many positive integers less than 80 are multiples of 4 but NOT multiples of 6? Select the correct option.
A) 4
B) 6
C) 8
D) 10
E) 12

Solution: The LCM of 4 and 6 is 12.   If x <80 and x is divisible by 4 not by 6 --> x is NOT divisible by 12.   From 1--> 80, we have 6 numbers which is divisible by 12: 12, 24, 36, 48, 60, 72.   From 1-->80, we have (72-4)/4 +1= 
(72-4)/4 +1 = 18
18 numbers divisible by 4.   Therefore, our answer is 18-6= 
18-6 = 12
12 numbers.   12
Answer: E
What is the total number of integers between 111 and 222 that are divisible by 9?
Select the correct option:
A) 12  B) 10  C) 11  D) 14  E) 13

Solution: 117, 126, 135, ..., 207,216   This is an equally spaced list; you can use the formula:   n = (largest - smallest) / ('space') + 1 = (216 - 117) / (9) + 1 = 99/9+ 1 = 11 + 1= 
11 + 1 = 12
12   12nswer is 12
Answer: A
The price of lunch for 15 people was $211.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity? Select:	A) $11.73	B) $12.78	C) $13.80	D) $14.00	E) $15.87

Solution: Take the initial price before the gratuity is 100   The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 211 is for 115 then we have to calculate for 100   for 115 211   for 100 x   so by cross multiplication we get 115x=100*211 => x=100*211/110 by simplifying we get x as 191.81 which is the price of lunch before gratuity so the gratuity is 19.19 so   as the question ask the average price person excluding gratuity is 191.81/15=12.78 so our answer is $12.78)
Answer: B
A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1400 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?	Choices
A) 12028  B) 12000  C) 20000  D) 12197  E) 12012

Solution: [1400 + (X-4000) * (2.5/100)] - X * (5/100)   = 600   X = 20000   Answer: 20000
Answer: C
45 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
Select the correct option:
A) 77 B) 66 C) 50 D) 55 E) 44

Solution: (45 * 8)/30 = (x * 6)/50 => x =100   100 – 45 = 55   Answer: 55
Answer: D
John sells his laptop to Mark at a loss of 20% who subsequently sells it to Kevin at a profit of 25%. Kevin after finding some defect in the laptop, returns it to Mark but could recover only Rs.4.50 for every Rs. 5 he had paid. Find the amount of Kevin’s loss if John had paid Rs. 1,75,000 for the laptop.	Choose the most appropriate option:  A) Rs. 13,500  B) Rs. 2,500  C) Rs. 17,500  D) Rs. 18,500  E) None of these

Solution: Let’s assume John bought the laptop for Rs. 100,   He then sells it to Mark for Rs. 80,   Who consequently sells it to Kevin for Rs. 100,   Then, Kevin sells it back to Mark for Rs. 90 (Rs.4.50 for every Rs. 5 that he had paid initially), so he suffers a loss of Rs. 10,   Therefore, for Rs 100 there is a loss of Rs. 10,   Then for Rs. 1,75,000 there will be a loss of Rs. 17,500   ANSWER:Rs. 17,500
Answer: C
A glass was filled with 10 ounces of water, and 0.05 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?	Select:
A) 0.002%
B) 0.02%
C) 0.2%
D) 2%
E) 10%

Solution: We are given that 0.05 ounces of water evaporated EACH DAY. Furthermore, we know that this process happened over a 20-DAY PERIOD. To calculate the total amount of water that evaporated during this time frame we need to multiply 0.05 by 20. This gives us:   0.05 x 20 = 1 ounces   Finally, we are asked for “What percent” of the original amount of water evaporated during this period. To determine this percentage, we have to make sure we translate the expression correctly. We can translate it to:   (Amount 10%vaporated/Original Amount) x 100%   (1/10) x 100%   (10/100) x 100% = 10%   Answer 10%
Answer: E
A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets $500 more than D, what is C's share? Answers:
A) $1200 B) $1600 C) $1800 D) $2000 E) $2400

Solution: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x respectively.   Then, 4x - 3x = 500   x = $500   C's share = 4x = 4*$500 = $2000   The answer is $2000.4* 500= 
4* 500 = 2_000
$2000   The answer is $2000.
Answer: D
In a sample of college students, 20 percent are third year students and 80 percent are not second-year students. What fraction of those students who are not third-year students are second-year students?	Choose the correct choice from the following options:
A) 1/4
B) 2/3
C) 4/7
D) 1/2
E) 3/7

Solution: = 20/80. = 1/4   my answer is 1/4 too
Answer: A
UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 6:4. If 60% of the Toyota bought and 40% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?
Select the correct option
A) 66%  B) 64%  C) 68%  D) 52%  E) 72%

Solution: let total no of Vehicles bought be 100, Toyota 60 and Honda 40, so total number of SUV's bought for Toyota and Honda respectively  60* 60/100= 
 60* 60/100 = 36
36 and   40* 40/100= 
  40* 40/100 = 16
16   so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52%   ANSWER:52%
Answer: D
A person decided to build a house in 100days. He employed 100men in the beginning and 100 more after 10 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?  Choose the most appropriate option:
A) 40	B) 80	C) 70	D) 60	E) 90

Solution: 200 men do the rest of the work in   100-10= 
  100-10 = 90
90days   100 men can do the rest of the work in 90*200/100= 
90*200/100 = 180
180 days   Required number of days= 180-90= 
180-90 = 90
90 days   Answer is 90
Answer: E
By selling a watch for Rs.400/-, a man loses 20% what is that watch cost price
Choose the correct choice from the following options.
A) s. 700/- B) s. 800/- C) s. 880/- D) s. 500/- E) s. 990/-

Solution: 80 % ------> 400 (80 * 5 = 400)   100 % ------>500 (100 * 5 = 500)   Cost price = Rs. 500/-   s. 500/-
Answer: D
The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 10 years ago ? (RBI Assistant 2015)	Choose the correct choice from the following:
A) 11	B) 18	C) 12	D) 15	E) 13

Solution: Let the present age of Viju be 7x years and that of Aju be 2x years.   Then, 4 years from now   7x + 4 / 2x + 4 = 5 / 2   or 4x = 12   or x = 3   Viju present age = 7 * 3= 
7 * 3 = 21
21 years   Viju age 10 years ago= 21 - 10= 
21 - 10 = 11
11 years   answer :11
Answer: A
Find the principle on a certain sum of money at 5% per annum for 3 years if the amount being Rs.1120? Options
A) 974
B) 1067
C) 1977
D) 1056
E) 1097

Solution: 1120 = P [1 + (5*3)/100]   P= 974   974nswer: 974
Answer: A
If x and y are integers and x divided by y is 19.15, then which of the following integers is a possible value for the remainder when x is divided by y? I. 15 II. 5 III. 3  Choose the most appropriate option:	A) I,III only	B) II only	C) I only	D) III only	E) II,III only

Solution: x=19.15y from which x = 19y + 15y/100 or x = 19y + 3y/20.   Since x and y are integers, 3y/20 must also be an integer. 3 is not divisible by 20, then y must be divisible by 20, and therefore, y/20 is an integer and 3y/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.   I,III onlynswer I,III only
Answer: A
At the beginning of the year, the ratio of juniors to seniors in high school X was 5 to 6. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 6 TO 7, how many juniors were there in high school X at the beginning of the year? Options:
A) 250 B) 100 C) 260 D) 110 E) 120

Solution: let the total number of juniors and seniors at the beginning of the year be 5x and 6x respectively.   now 10 juniors and 20 seniors are transferred to another school. thus no. of juniors and seniors students left in the school X are 5x-10 and 6x-20 respectively. the ratio of these juniors and seniors students = 6/7   thus we have (5x-10)/(6x-20) = 6/7   35x-70=36x-120   x=50   thus total no. of seniors at the beginning of the year =5(50)=250   250nswer:option 250
Answer: A
Which of the following is closer to (6!+4!)-(6!-4!)?
Choose the correct answer.
A) 28 B) 38 C) 48 D) 58 E) 68

Solution: 6!+4!)-(6!-4!)=720+24-720+24= 
720+24-720+24 = 48
48   Answer: 48
Answer: C
A sum was put a simple interest at a certain rate for 5 years. Had it been put at 2% higher rate, it would have fetched Rs. 250 more. The sum is: Choose the correct choice
A) s.2000	B) s.2500	C) s.3000	D) s.3500	E) s.4000

Solution: Explanation :   Let the sub be Rs.x and the initial rate be R%.Then   x Ã— (R+2) Ã— 5/100âˆ’xÃ—RÃ—5/100=250   â‡’x Ã— 2Ã—5/100=250   â‡’x Ã— 5 /100=125   â‡’5x=12500   â‡’x=2500   Answer : Option s.2500
Answer: B
The ratio of the radius of two circles is 2: 3, and then the ratio of their areas is?	Choose the correct answer
A) 1:7 B) 2:9 C) 4:9 D) 3:7 E) 3:4

Solution: r1: r2 = 2: 3   Î r1^2: Î r2^2   r1^2: r2^2 = 4:9   Answer: 4:9
Answer: C
If a/x = 3 and a/y = 4, then (x + y) in terms of a  Select the correct option:
A) a/4	B) 5a/7	C) 7a/12	D) 6a/13	E) 11a/17

Solution: Ratio 1:   x= a/3   Ratio 2:   y = a/4   x+y = a/3+a/4 = 7a/12   Answer is 7a/12
Answer: C
Two taps can separately fill a cistern 10 minutes and 12 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?	Choose the correct choice from the following:	A) 7	B) 7.8	C) 6	D) 9	E) 5

Solution: 1/10 + 1/12 - 1/x = 1/18   x = 180/23 = 7.8   Answer: 7.8
Answer: B
Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father and mother respectively when his brother was born ? Choices.
A) 32 years, 23 years	B) 32 years, 29 years	C) 35 years, 29 years	D) 35 years, 33 years	E) 36 years, 33 years

Solution: Explanation:   When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years.   Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32.   Ravi's age = (y - 26) years.   Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years.   Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.   32 years, 23 yearsnswer: 32 years, 23 years) 32 years, 23 years
Answer: A
If 40% of a certain number is 160, then what is 50% of that number?  Answers:	A) 270	B) 380	C) 200	D) 360	E) 290

Solution: Explanation:   40% = 40*4= 
40*4 = 160
160   50%= 50*4= 
50*4 = 200
200   Answer: Option 200
Answer: C
Every student at Parcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Parcy School?
Select:	A) 63	B) 69	C) 74	D) 82	E) 86

Solution: the total number of students at Parcy School The answer is 86 or any multiple of 43.86
Answer: E
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 200 resolutions.	Choose the correct choice from the following choices: A) 271.34 m B) 281.34 m C) 291.34 m D) 301.34 m E) 311.34 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 200 resolutions.   = 200 * 2 * 22/7 * 22.4   = 28134 cm   = 281.34 m   Answer: 281.34 m
Answer: B
Hanks Manufacturing recently conducted a survey of its employees. The results showed that of the n people who work at the company, 1/3 drink decaffeinated coffee, and the remainder drink regular coffee. Of those who do not drink decaf, 2/5 add cream to their coffee. Which of the expressions below accurately represents the number of employees who do not drink regular coffee with cream. Choose the correct choice from the following answers.
A) 2n/3  B) n/8  C) 4n/15  D) 11n/15  E) 13n/15

Solution: Decaffeinated coffee = 1/3   Regular coffee = 2/3   "Of those who do not drink decaf, 2/5 add cream to their coffee."   means 'of the regular drinkers, i.e. of the 2/3, 2/5 add cream'   Regular coffee drinkers who add cream = 2/5 * 2/3 = 4/15   The fraction that drinks "regular coffee with cream" = 4/15   The fraction that does not drink "regular coffee with cream" is the rest = 1 - 4/15 = 11/15   Number of people = 11n/15   ANSWER:11n/15
Answer: D
The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 87, and the average of the female students’ grades was 92, how many female students took the test?	Pick one
A) 8 B) 9 C) 10 D) 11 E) 12

Solution: Total Marks of male = M   Total Marks of female = F   Number of males = 8   Number of females = f   Given: (M+F)/(8+f) = 90 -------------1   Also given, M/8 = 87 Thus M = 696 ---------2   Also, F/f = 92 thus F = 92 F - --------3   Put 2 and 3 in 1: we get   (696+92f)/(8+f) = 90   solving this we get f = 12   Answer: 12
Answer: E
If the sum of four consecutive positive integers is A, then the sum of the next four consecutive integers in terms of A is:  Answers:  A) A+4  B) A+16  C) 2A  D) 2A + 4  E) 4A

Solution: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median   I.e. Median = A/4 = Mean = Average of Second and Third Integer   First Integer = A/4 - 1.5   Second Integer = A/4 - .5   Third Integer = A/4 + .5   Fourth Integer = A/4 + 1.5   i.e.   Fifth Integer = A/4 + 2.5   Sixth Integer = A/4 + 3.5   Seventh Integer = A/4 + 4.5   Eighth Integer = A/4 + 5.5   Now Mean of next 4 Integers = Median = A/4 + 4   i.e. Sum of Next 4 integers = (A/4 + 4)*4 = A+16   Answer: option A+16
Answer: B
What is the area of a square field whose diagonal of length 12 m?	Pick one:
A) 288
B) 72
C) 200
D) 112
E) 178

Solution: d2/2 = (12 * 12)/2= 
(12 * 12)/2 = 72
72   Answer: 72
Answer: B
A boat goes 6 km up stream and 7 km down stream in 5 hours. It goes 3 km up stream and 6 km down stream in 3 hours. The speed of the boat in still water is:
Choose the correct choice from the following.
A) 2 km/hr	B) 5.4 km/hr	C) 4.8 km/hr	D) 3.33 km/hr	E) None of these

Solution: Explanation:   Let speed of the boat in still water be x km/hr   speed of the stream be y km/hr   then, speed of upstream = (x-y) km/hr   speed of down stream = (x+y) km/hr   6/(x-y) + 7/(x+y) = 5   3/(x-y) + 6/(x+y) = 3   Take 1/(x-y) = a & 1/(x+y) = b   6a + 7b = 5 ---(1)   3a + 6b = 3 ----(2)   (1) -------> 6a + 7b = 5   (2) x 2 ---> 6a + 12b = 6   ------------------------   -5b = -1   b = 1/5   3a + (6/5) = 3   3a = 3 - 6/5   3a = (15 - 6)/5 = 9/5   a = 3/5   3/5 = 1/(x-y)   1/5 = 1/(x+y)   3x - 3y = 5 ---->(iii)   x + y = 5 ----> (iv)   (iv) x 3 ----> 3x + 3y = 15   (iii) -------> 3x - 3y = 5   -----------   6x = 20   x = 20/6 = 10/3 = 3.33   Answer: Option 3.33 km/hr
Answer: D
1, 6, 16, 31, 51, (....)
Choices.
A) 61  B) 66  C) 76  D) 86  E) 83

Solution: Explanation:   The pattern is 5, 10, 15, 20, 25, etc   Hence 25=66   Answer : 66
Answer: B
(69842 x 69842 - 30158 x 30158) / (69842 - 30158) = ?	Choices.
A) 100000
B) 69842
C) 39684
D) 30158
E) None

Solution: 100000nswer   Given expression = [(69842)2 - (30158)2] / [(69842 - 30158)]   = [ (69842 - 30158) (69842 + 30158) ] / (60842 - 30158)   = 100000   Correct Option: 100000
Answer: A
If x = 32 * 64 * 27 / 8, Find the tenth place of x,	Choose the correct choice:
A) 1
B) 2
C) 5
D) 4
E) 3

Solution: x = 32 * 64 * 27 / 8   x = 2^5 * 4^3 * 3*3 / 2^3   x = 2^2 * 12*3   x = 6912   1ns: 1
Answer: A
If p - q = 3 and
p2+q2=29
, find the value of pq. Choose the correct option.
A) 7 B) 8 C) 9 D) 10 E) 11

Solution: Explanation:   We know   2ab=(a2+b2)−(a−b)2   2pq=29−9=20   =>pq=10   Option 10
Answer: D
Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.90 at the candy store. What is John’s weekly allowance?	Answers: A) $2.40 B) $3.00 C) $3.40 D) $3.60 E) $4.80

Solution: Total allowance=X   Amount spent at the arcade=3/5X   Amount Remaining=2/5X   Amount Spent at the toy store=2/5*1/3X=2/15X   Amount Remaining=2/5X-2/15X=4/15X   Now, 4/15X=$0.9   Therefore, X=$3.40. Answer $3.40
Answer: C
If a and b are different positive integers and a + b = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b Pick.
A) I only
B) II only
C) III only
D) I and II
E) I and III

Solution: a+b=a(a+b)a+b=a(a+b) --> a(a+b)−(a+b)=0a(a+b)−(a+b)=0 --> (a+b)(a−1)=0(a+b)(a−1)=0 --> as aa and bb are positive the a+b≠0a+b≠0, so a−1=0a−1=0 --> a=1a=1. Also as aa and bb are different positive integers then bb must be more than a=1a=1 --> a<ba<b (bb can not be equal to aa as they are different and bb can not be less than aa as bb is positive integer and thus can not be less than 1).   So we have that: a=1a=1 and a<ba<b.   I. a = 1 --> true;   II. b = 1 --> not true;   III. a < b --> true.   Answer: I and III (I and II only).
Answer: E