divelab/Sys2Bench huggingface dataset:
Question: The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Options:
A)8, 20, 28
B)16, 28, 36
C)20, 35, 45
D)18, 24, 32
E)None of these
Rationale: Explanation:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
Answer: B
Answer: B
Question: 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?
Options:
A)5
B)6
C)8
D)9
E)1
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8.Answer:C
Answer: C
Question: A number when divided by 128 gives a remainder 34, what remainder will be obtained by dividing the same number 19?
Options:
A)7
B)6
C)9
D)10
E)3
Rationale: Explanation:
128 + 34 = 162/19 = 10 (Remainder)
Answer: D
Answer: D
Question: If $ 5,000 is invested in an account that earns 8% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
Options:
A)$ 4
B)$ 8
C)$ 12
D)$ 16
E)$ 432
Rationale: Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.08/2)^2= 5408
Amount (SI) = P+PTR/100 = 5000+(5000*1*8/100)=5400
Difference = 5408-5400=8 $
ANSWER:B
Answer: B
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)11
B)10
C)17
D)16
E)18
Rationale: 4/12 + x/15 = 1
x = 10
Answer:B
Answer: B
Question: The average weight of 10 bags of sand is 20 pounds. Another bag of sand is added to the group and decreases the average weight by 1 pound. How much does the new bag of sand weigh?
Options:
A)7
B)21
C)29
D)9
E)19
Rationale: Total weight of 10 bags of sand = 10*20 = 200
Total weight of 11 bags of sand = 11*19 = 209
Weight of new bag = 209-200 = 9 pounds
Answer is D
Answer: D
Question: A, B and C rents a pasture for Rs.435. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?
Options:
A)180
B)227
C)268
D)198
E)176
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
12/29 * 435 = 180
Answer:A
Answer: A
Question: 30 carrots on a scale weigh 5.94 kg. When 3 carrots are removed from the scale, the average weight of the 27 carrots is 200 grams. What is the average weight (in grams) of the 3 carrots which were removed?
Options:
A)165
B)170
C)175
D)180
E)185
Rationale: 27*200=5400.
The other 3 carrots weigh a total of 540 grams.
The average weight is 540/3 = 180 grams.
The answer is D.
Answer: D
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age nine years back was?
Options:
A)10yr
B)15yr
C)20yr
D)25yr
E)30yr
Rationale: Let the son's present age be x years
Then, 38-x = x
x = 19
Son's age 9 years back = 19-9 = 10 years
Answer is A
Answer: A
Question: Find the probability that a number selected from numbers 1, 2, 3,..., 50 is a prime number, when each of the given numbers is equally likely to be selected?
Options:
A)10/50
B)15/50
C)8/50
D)3/50
E)7/50
Rationale: Let X be the event of selecting a prime number.
X = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}
n(X) = 15,
n(S) = 50
Hence, the required probability is 15/50.
ANSWER:B
Answer: B
Question: The fourth proportional to 12, 18 and 26 is?
Options:
A)21
B)66
C)39
D)88
E)61
Rationale: (18*26)/12
= 39
Answer:C
Answer: C
Question: Working simultaneously and independently at an identical constant rate, 4 machines of a certain type can produce a total of x units of product P in 6 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 2x units of product P in 6 days?
Options:
A)24
B)18
C)16
D)12
E)8
Rationale: 4 machines do x units in 6 days
we have x/6 => rate of the 4 machines
we know that we need to have 2x units in 4 days
therefore, we need to get to 2x/4 rate of the machines.
rate of one machine is x/6*1/4 = x/24.
now, we need to know how many machines need to work simultaneously, to get 2x done in 6 days.
2x/6 work needs to be done by machines that work at x/24 rate.
let's assign a constant Y for the number of machines:
(x/24)*y = 2x/6
y = 2x/6 * 24/x
cancel 6 with 24, and x with x and get -> 8. Answer choice E
Answer: E
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $2 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
Options:
A)1 : 4 : 400
B)1 : 4 : 100
C)20 : 4 : 1
D)100 : 4 : 1
E)400 : 4 : 1
Rationale: millionaire 20 cents = 1/5 dollar ..therefore 1 dollar M = 100 dollar of B
therefore 2 dollar M = 200 dollar of B also 1 dollar Y
Y:M:B = 1:2:200
= 1:2:200
E
Answer: E
Question: How many 1 1/2 foot pieces of cable can be cut out of a piece that is 30 feet long?
Options:
A)a.10
B)b.16
C)c.17
D)d.18
E)e. 20
Rationale: Pretty Simple..the answer is choice (E) 20.
All that one has to do is :
1: Convert 1 1/2 into an improper fraction (3/2) or a decimal (1.5)
2: Divide 30 by 3/2 (or 1.5)
Answer =20 (E)
Answer: E
Question: T(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point T?
Options:
A)(1, 2).
B)(2, 0).
C)(0, -2).
D)(-2, 0).
E)(2, 2).
Rationale: A quick glance at the options, T(x, y) and we can see that A and E do not satisfy the circle equation. Now we are left with B, C and D. Now B and C do not satisfy the line equation. So we are just left with D. And thats the answer=D
Answer: D
Question: Three times the first of three consecutive odd integers is 5 more than twice the third. The third integer is:
Options:
A)9
B)11
C)13
D)15
E)17
Rationale: Let the three integers be x, x + 2 and x+ 4.
Then,
3x = 2(x + 4) + 5
x = 12
Third integer = x + 4 = 17.
ANSWER:E
Answer: E
Question: A can do a work in 9 days and B can do the same work in 27 days. If they work together, in how many days will they complete the work?
Options:
A)6 3/4 days
B)7 3/4 days
C)5 3/4 days
D)6 1/4 days
E)6 2/4 days
Rationale: One day's work of A and B = 1/9 + 1/27 = (3+1)/27 = 4/27 So, the time taken to complete the work is 6 3/4 days.
ANSWER:A
Answer: A
Question: Bhajan Singh purchased 120 reams of paper at Rs 80 per ream. He spent Rs 280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs 72 to the coolie. If he wants to have a gain of 8 %, what must be the selling price per ream?
Options:
A)90
B)22
C)28
D)27
E)92
Rationale: Explanation:
Total investment = Rs. (120 * 80 + 280 + (40/100) * 120 + 72).
= Rs. (9600 + 280+48 + 72) = Rs, 10000.
Sell price of 120 reams = 108% of Rs. 10000 = Rs. 10800.
Sell Price per ream = Rs. [10800/120] = Rs. 90.
Answer: A) 90
Answer: A
Question: If 20 typists can type 38 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
Options:
A)63
B)72
C)144
D)171
E)400
Rationale: 20 typists can type 38 letters, so 30 typists can type = 38*30/20
38*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 38*30*60/20*20= 171
D is the answer
Answer: D
Question: What is the greatest prime factor of 4^16 - 2^30?
Options:
A)2
B)3
C)5
D)7
E)11
Rationale: 4^16 - 2^30
=(2^2)^16 - 2^30
= 2^32 - 2^30
= 2^30 (2^2 -1)
= 2^30 * (4-1)
= 2^30 * 3
The greatest prime factor is 3.
The answer is B.
Answer: B
Question: A research team that must consists of 3 members is to be formed from a pool of 6 scientists. How many different teams are possible?
Options:
A)17
B)10
C)40
D)26
E)20
Rationale: Note that the team must consist of 3 members, not at least 3 members. Hence, all you have to do is 6C3 = 20
Answer (E)
Answer: E
Question: Rs 3000 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.
Options:
A)s 400
B)s 280
C)s 300
D)s 350
E)s 310
Rationale: Explanation :
Average rate = (144/3000)*100 = 4.8
Ratio = 2:18
So, first part = (2/20)*3000 = Rs 300.
Answer : C
Answer: C
Question: Of the 400 members at a health club, 260 use the weight room and 300 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
Options:
A)40 to 100
B)80 to 140
C)160 to 260
D)220 to 260
E)220 to 300
Rationale: 260-X+X+300-X+GT60 = 400
=>X = GT 620-400
=> X = GT 220
=> X >= 220 (Here GT means Greater than)
So Min value of X is 220 coming to options D/E
X's maximum value cannot exceed 260 as per the venn diagramsince 'W' circle cannot accomodate 'X' More than 260
ANSWER:D
Answer: D
Question: What annual payment will discharge a debt of Rs. 1030 due in 2 years at the rate of 5% compound interest?
Options:
A)553.94
B)551.25
C)534.33
D)543.33
E)646.33
Rationale: Explanation:
Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1030
820x + 1030 * 441
x = 553.94
So, value of each installment = Rs. 553.94
Answer: Option A
Answer: A
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Options:
A)100
B)110
C)120
D)130
E)150
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer: Option D
Answer: D
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ?
Options:
A)0.5906
B)0.5904
C)0.5902
D)0.5901
E)0.5932
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904.
Answer: B
Answer: B
Question: 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 10.
Options:
A)150
B)152
C)154
D)163
E)144
Rationale: D = d * Q + R
D = 17 * 9 + 10
D = 153 + 10
D = 163
ANSWER D
Answer: D
Question: A furniture dealer purchased a desk for $140 and then set the selling price equal to the purchase price plus a markup that was 30% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
Options:
A)$40
B)$60
C)$80
D)$90
E)$100
Rationale: Purchase price = 140
Selling price = x
140 + 0.3*x = x
0.7*x = 140
x = 200
Profit = 200 - 140 = 60
ANSWER:B
Answer: B
Question: Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 10 more photos than Claire. How many photos has Claire taken?
Options:
A)5
B)8
C)11
D)12
E)14
Rationale: L = R
L = 3C
R = C + 10
3C = C + 10
C = 5
The answer is A.
Answer: A
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
Options:
A)50 Km
B)55 Km
C)45 Km
D)35 Km
E)40 Km
Rationale: Let the actual distance travelled be x km.
Then,	x /10=x + 20 / 14
14x = 10x + 200
4x = 200
x = 50 km.
ANSWER : A
Answer: A
Question: Abhay's age after six years will be three -seven of his father 's age . TTen years ago, the ratio of heir ages was 1 : 5. What is Abhay's fathers age at present ?
Options:
A)45 years
B)48 years
C)49 years
D)50 years
E)52 years
Rationale: Explanation :
Sol. Let the ages of Abhay and his father 10 years ago be xand5xxand5x years respectively . Then
Abhay's age after 6 years = (x+10)+6 =(x+16)(x+10)+6 =(x+16) years
Father's age after 6 years = (5x+10) +6=(5x+16)(5x+10) +6=(5x+16) years
âˆ´âˆ´ (x+16)=37(5x+16)(x+16)=37(5x+16)
â‡” 7(x+16)=3(5x+16
â‡” 7x+112=15x+48
â‡” 8x=64
â‡” x=8
Hence , Abhay's father's present age = (5x+10)(5x+10) = 50 years
ANSWER IS D
Answer: D
Question: In a group of ducks and cows, the total number of legs are 22 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)11
B)12
C)13
D)15
E)16
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 22
=> 2x = 22 => x = 11
A
Answer: A
Question: A certain restaurant offers 5 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
Options:
A)8
B)12
C)15
D)21
E)20
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 5C2*2C2=10*1=10
B. 1 kind of cheese and 1 kind of fruit --> 5C1*2C1=5*2=10
A+B=10+10=20
Answer: E.
Answer: E
Question: Tom, working alone, can paint a room in 16 hours. Peter and John, working independently, can paint the same room in 8 hours and 4 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?
Options:
A)4/7
B)5/7
C)2/7
D)1/7
E)3/7
Rationale: Let the time when all three were working together be t hours. Then:
Tom worked for t+4 hour and has done 1/16*(t+4) part of the job;
Peter worked for t+2 hour and has done 1/8*(t+2) part of the job;
John worked for t hours and has done 1/4*t part of the job:
1/16*(t+4)+1/8*(t+2)+1/4*t=1 --> multiply by 16 --> (t+4)+(2t+2)+4t=16 --> t=10/7;
Hence Peter has done 1/8*(10/7+2)=1/8 *24/7=3/7
Answer: E
Answer: E
Question: Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn’t know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.
Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?
Options:
A)$30
B)$20
C)$10
D)$40
E)$50
Rationale: There is no missing dollar. A dollar only goes "missing" because the statement "each man paid $9 for the room" is wrong - each of three men paid out a total of $9, but that $9 included both the room charge and the bellboy's tip. All in all, each man paid out a total of $9 and had $1 left over, completely accounting for the $30 they started with.. Hotel - $25 Bellhop - $2 Customers - $1 each $25 + $2 + $3 = $30
Answer A
Answer: A
Question: If X is to be chosen at random from the integers between 1 to 6, inclusive, and Y is to be chosen at random from the integers between 7 and 10, inclusive, what is the probability that X + Y will be even?
Options:
A)1/2
B)2/3
C)3/4
D)4/5
E)5/6
Rationale: X+Y will be even if X and Y are both even or both odd.
P(X and Y are both even) = 3/6*2/4 = 1/4
P(X and Y are both odd) = 3/6*2/4 = 1/4
P(X+Y is even) = 1/4 + 1/4 = 1/2
The answer is A.
Answer: A
Question: If X is invested in a bank at a rate of simple interest of y% p.a. for two years, then the interest earned is 800. if X is invested at y% p.a., for two years when the interest is compounded annually, the interest is 820. What is the value of X?
Options:
A)8000
B)6000
C)5000
D)4000
E)3000
Rationale: Simple way to solve this question is to use options.
From SI, we know that X*y=40,000.
Now, put the value of X = 8000, we will have y = 5%
To calculate CI,
Now, we know 1st year Amount= 8000+5% of 8000= 8400.
2nd year, Amount = 8400 + 5% of 8400 = 8820.
We can see after 2 years Interest = 8820-8000= 820. hence, it satisfies the question. Hence A is the correct answer
Answer: A
Question: Rob also compared the Empire State Building and the Petronas
Towers. What is the height difference between the two if the Empire
State Building is 356m tall and the Petronas Towers is 370m tall?
Options:
A)14
B)17
C)23
D)45
E)12
Rationale: 370-356=14.Answer is A.
Answer: A
Question: In the third grade of Windblown School there are 90 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
Options:
A)0.
B)6.
C)8.
D)10.
E)12.
Rationale: Total = 90
failed in math = 90/3=30
failed in literature=90/6=15
the least failed in both can be 0
while max can be 15
Answer A
Answer: A
Question: Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 20% profit?
Options:
A)15.12
B)16.33
C)16.35
D)16.3
E)16.32
Rationale: C.P. of 50 kg wheat = (30 * 11.50 + 20 * 14.25) = Rs. 630.
S.P. of 50 kg wheat = 120% of Rs. 630 = 120/100 * 630 = Rs. 756
S.P. per kg = 756/50 = Rs. 15.12
Answer: A
Answer: A
Question: An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 6 industrial stocks, 5 transportation stocks, and 4 utility stocks, how many different combinations of 6 stocks are possible?
Options:
A)1200
B)900
C)600
D)180
E)720
Rationale: 6C2 * 5C2 * 4C2 = 15*10*6 = 900.
Answer: C
Answer: C
Question: If the LCM and HCF of 8 and another number is 24 and 4 respectively. Find the other number ?
Options:
A)11
B)12
C)14
D)15
E)16
Rationale: HCF x LCM = Product of Numbers
4 x 24 = 8 x the other number
other number = (4 x 24) / 8
other number = 12
ANSWER : B
Answer: B
Question: 544, 509, 474, 439, ... ?
Options:
A)404
B)302
C)108
D)115
E)210
Rationale: Each number is 35 less than the previous number.
544
544-35=509
509-35=474
474-35=439
439-35=404
ANSWER:A
Answer: A
Question: A big container is 30% full with water. If 45 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
Options:
A)36 liters
B)40 liters
C)45 liters
D)54 liters
E)100 liters
Rationale: A big container is 30% full with water and after 45 liters of water is added, the container becomes 75% full. Hence these 45 liters account for 45% of the container, which means that the capacity of it is 45/0.45=100 liters.
OR: if the capacity of the container is x liters then: 0.3x+45=0.75x --> x=100 liters.
Answer:E.
Answer: E
Question: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 61 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Options:
A)96 degrees
B)64 degrees
C)65 degrees
D)66 degrees
E)67 degrees
Rationale: Explanation:
Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (61 * 4) = 244 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 12 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 12 or x = 12. Answer: A
Temperature on the 5th day = 8x = 96 degrees.
Answer: A
Question: A call center has two teams. Each member of Team A was able to process 3/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B?
Options:
A)3/2
B)3/4
C)8/11
D)1/2
E)1/5
Rationale: Let team B has 8 agents, so team A has 5 agents
Let each agent of team B picked up 5 calls, so total calls by team B = 40
So, each agent in Team A picked up 3 calls, so total calls for team A = 15
Fraction for team B = 40/(40+15) =8/11 = Answer = C
Answer: C
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Options:
A)16.80 × 4.50 + 4.4
B)1600 ÷ 40 + 16 × 2
C)5.5 × 8.4 + 34.6
D)1620 ÷ 20 – 1
E)1856.95 – 1680.65 – 96.3
Rationale: Others equal 80 whereas (c) equals 80.8.
Answer C
Answer: C
Question: If |u+v|=|u-v|, then u*v must be equal to:
Options:
A)2
B)0
C)-3
D)3
E)-2
Rationale: Solution 1: Distance perspective
|u-v| = |u+s| ==> The distance of u and v is equal to the distance of u and -v.
<=======(-v)=======0=======(v)======>
Only 0 is the value that has a distance equal to v and -v.
Solution 2:
|u-v| = |u+v| (square both)
u^2 -2uv + v^2 = u^2 + 2uv + v^2
4uv = 0
uv = 0
Answer: B
Answer: B
Question: What positive number, when squared, is equal to the cube of the positive square root of 12?
Options:
A)64
B)32
C)8
D)4
E)2
Rationale: Let the positive number be x
x^2 = ((12)^(1/2))^3
=>x^2 = 4^3 = 16
=> x = 4
Answer D
Answer: D
Question: Evaluate
3.6×0.48×2.50 / 0.12×0.09×0.5
Options:
A)80
B)800
C)8000
D)80000
E)None of these
Rationale: Explanation:
3.6×0.48×2.50 / 0.12×0.09×0.5
=36×48×250 / 12×9×5=800
Option B
Answer: B
Question: An aircraft company has 20 planes in its fleet. Every year it retires 5 of its planes and replaces then with 6 newer planes. How many years will it take the company, starting from 2010, to reduce the number of it s old planes to less than half of its fleet?
Options:
A)2
B)1
C)3
D)4
E)5
Rationale: Total fleet--20
End of year 2010 -- (retires 5 and buys 6) total fleet--21(15 old 6 new).
End of year 2011 -- (retires 5 and buys 6) total fleet--22(10 old 12 new).
End of year 2012 -- (retires 5 and buys 6) total fleet--23(5 old 18 new).
Answer is A--after 2 years the company has a total of 22 planes (10 old 12 new).
Answer: A
Question: Mario and Nina each have a bag of marbles, each of which contains 4 blue marbles, 10 red marbles, and 6 white marbles. If Mario and Nina each select one marble from their respective bags, what is the probability that either Mario or Nina select a red marble?
Options:
A)3/4
B)2/4
C)1/4
D)1/8
E)1/16
Rationale: Mario and Nina each select one marble from their respective bags.
Probability that either Mario or Nina select a red marble = Probability that Mario selects a red marble + Probability that Nina selects a red marble
Probability that either Mario or Nina select a red marble = (10/20)*(10/20) + (10/20)*(10/20) = 2*(1/4)
Probability that either Mario or Nina select a red marble = 1/2
Answer would be B.
Answer: B
Question: A can do a piece of work 40 days. B can do work in 60 days. In how many days they will complete the work together?
Options:
A)15 days
B)16 days
C)19 days
D)17 days
E)24 days
Rationale: LCM = 120, Ratio= 40:60=2:3
No of days= 120/(2 + 3) = 90/5 = 24 days
ANSWER:E
Answer: E
Question: If mn > 0, which of the following must be negative?
Options:
A)m +n
B)|m| + n
C)m^2
D)-m/n
E)mn
Rationale: Given mn> 0 So both will be the positive integers. If both are positive, then A,B,C,E also positive.
Answer :D
Answer: D
Question: If it takes 4 identical printing presses exactly 4 hours to print 6,000 newspapers, how long would it take 2 of these presses to print 5,000 newspapers?
Options:
A)6 hrs 50 mins
B)6 hrs 40 mins
C)6 hrs 30 mins
D)6 hrs 20 mins
E)6 hrs 10 mins
Rationale: 4 presses - 6,000 newspapers - 4 hours ;
2 presses - 3,000 newspapers - 4 hours ; (240 mins)
2 presses - 5,000 newspapers - 240/3000*5000 = 400 mins = 6 hrs 40 mins
Answer : B
Answer: B
Question: What will be the fraction of 6%
Options:
A)1/20
B)3/50
C)1/75
D)1/25
E)None of these
Rationale: Explanation:
6*1/100 = 3/50.
Option B
Answer: B
Question: How many times in a day the hands of a clock are straight?
Options:
A)21
B)27
C)24
D)22
E)25
Rationale: In 12 hours, the hands coincide or are in oppesite direction 22 times.
In 24 hours, they are at right angles 22 times.
Answer is D.
Answer: D
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 152. If the ratio of his marks in English and Maths is 1:5, find his marks in Science?
Options:
A)8
B)77
C)66
D)55
E)31
Rationale: S:E = 1:3
E:M = 1:5
------------
S:E:M = 1:3:15
1/19 * 152 = 8
Answer: A
Answer: A