divelab/Sys2Bench huggingface dataset:
Question: At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.80. What is the price of 2 doughnuts?
Options:
A)$ 0.55
B)$ 1.00
C)$ 1.10
D)$ 0.90
E)$ 1.80
Rationale: 3D + C = 2.25......(1)
2D + C = 1.8........(2)
(1) - (2) --> D = 0.45 --> 2D = 0.9
Answer: D
Answer: D
Question: Johnny makes $8.25 per hour at his work. If he works 2 hours, how much money will he earn?
Options:
A)$30.50
B)$16.50
C)$28.50
D)$12
E)$9.60
Rationale: 8.25*2=16.50. Answer is B.
Answer: B
Question: Find large number from below question The difference of two numbers is 1345. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1235
B)1345
C)1678
D)1767
E)1611
Rationale: Let the smaller number be x. Then larger number = (x + 1345).
x + 1345 = 6x + 15
5x = 1330
x = 266
Large number = 266+1345 = 1611
E
Answer: E
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,840,397 minutes earlier? (Assume standard time in one location.)
Options:
A)6:35
B)6:33
C)6:30
D)6:28
E)6:24
Rationale: 6:27 minus 2,840,397 in any way must end with 0.
The only answer choice which ends with 0 is C.
The answer is C.
Answer: C
Question: Find the odd man out
3, 5, 12, 39, 154, 772, 4634
Options:
A)39
B)154
C)5
D)3
E)12
Rationale: 3x1+2=5
5x2+2=12
12x3+2=38
38x4+2=154 .. and so on.
ANSWER:A
Answer: A
Question: Find the missing figures : ?% of 25 = 20125
Options:
A)4.5
B)6.5
C)2.5
D)7.5
E)8.5
Rationale: Let x% of 25 = 2.125. Then , (x/100)*25 = 2.125
X = (2.125 * 4) = 8.5.
Answer is E.
Answer: E
Question: If a and b are integers and (a*b)^5 = 64y, y could be:
Options:
A)16
B)32
C)64
D)128
E)256
Rationale: Distribute the exponent.
a^5 * b^5 = 64 y
Find the prime factorization of 64. This is 2^5 *2^1
We need 2^4 (or some other power of 2 that will give us a multiple of 2^5 as our second term).
2^4 = 16
The answer is A.
Answer: A
Question: If Leo gains 10 pounds, he will weigh 50% more than his sister Kendra. Currently their combined weight is 160 pounds. What is Leo's current weight?
Options:
A)80
B)86
C)92
D)98
E)104
Rationale: L+K = 160 and so K = 160-L
L+10 = 1.5K = 1.5(160-L)
2.5L = 230
L = 92
The answer is C.
Answer: C
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 140 pages?
Options:
A)10 hours 30 mins
B)8 hours
C)9 hours
D)7 hours
E)6 hours
Rationale: Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 140 pages when Anil and Suresh work together = 140 × 3 /40 = 21/2
= 10 1/2 hours = 10 hour 30 minutes
Answer is A.
Answer: A
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
A)140
B)146
C)152
D)162
E)170
Rationale: Number of newborns that can die in first month = 1/10 * 200 = 20
Survived = 180
Number of newborns that can die in second month = 1/10 * 180 = 18
Survived = 162
Number of newborns that can die in third month = 1/10 * 162 = 16
Survived = 146
Answer:B
Answer: B
Question: 54671 - 18456 - 33466 = ?
Options:
A)2749
B)5449
C)6749
D)6449
E)6468
Rationale: A
If we calculate we will get 2749
Answer: A
Question: TOM traveled the entire 20 miles trip. If he did the first 10miles of at a constant rate 12 miles per hour and the remaining trip of at a constant rate 10 miles per hour, what is the his average speed, in miles per hour?
Options:
A)12.45 mph
B)11.25 mph
C)10.95 mph
D)10.91 mph
E)10.56 mph
Rationale: avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (10+10) / ((10/12)+(10/10) =120/11 = 10.91 mph D
Answer: D
Question: If x^2 – x = 2, then one possible value of x – 4 =
Options:
A)-9
B)-5
C)-3
D)-1
E)5
Rationale: x^2 –x = 2
i.e. x^2 – x - 2 = 0
i.e. x^2 +x -2x -2 = 0
i.e. (x-2)(x+1) = 0
i.e. x = 2 or -1
i.e. x-4 = 2-4 or -1-4
i.e. x-4 = -2 or -5
Answer: Option B
Answer: B
Question: Train X and train Y pass one another traveling in opposite directions. Thirty minutes later they are 100 miles apart. If train X’s constant speed is 40 miles per hour greater than train Y’s, how far does train X travel during that time?
Options:
A)28
B)40
C)60
D)72
E)80
Rationale: Let the rate of the Train Y be R
Then the rate of the Train X will be R+40 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+40) [add the rates] i.e. 2R+40
d=100 and t = 30 min i.e 30/60 hr
using RTD table, (2R+40) * 30/60 = 100 ==> R= 80 miles/hr
So the rate of train X is 120 miles/hr (since R+40)
The distance traveled by Train X in 30 min is R*T = 120 * 30/60 = 60 miles (C)
Answer: C
Question: 7 points are marked on a straight line and another 4 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
Options:
A)91
B)126
C)196
D)21
E)14
Rationale: getting the answer 126 which is not in the choices, what is the source of the problem?
7C2* 4C1 + 4C2* 7C1 = 126
B
Answer: B
Question: Which of the following is not the square of an integer?
Options:
A)275625
B)385641
C)426437
D)532900
E)318096
Rationale: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is C.
Answer: C
Question: Two marathoners begin their training run on the river bank at the same time. Sally Slow runs due south at 5 miles/hour, while Freddy Fast runs due North at 10 miles/hour. At this pace, how long before they have run 26.2 miles away from each other?
Options:
A)1.75 hours
B)1.634 hours
C)1.5 hours
D)3 hours
E)2.92 hours
Rationale: The runners run a combined pace of 15 miles per hour (10+5).
26.2 miles/ 15 miles/hour= 1.75 hours
Answer is A
Answer: A
Question: A portion of the 95% solution of dye was replaced with an equal amount of 20% solution of dye. As a result, 40% solution of dye resulted. What part of the original dye was replaced?
Options:
A)2/5
B)3/7
C)5/17
D)11/15
E)10/11
Rationale: This is a weighted average question. Say x% of the dye was replaced --> equate the amount of dye in the solution: 0.95(1-x)+0.2*x=0.4 --> x=11/15.
Answer: D.
Answer: D
Question: Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 8 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?
Options:
A)37.5 kilometers per hour
B)48 kilometers per hour
C)51.7 kilometers per hour
D)75 kilometers per hour
E)100 kilometers per hour
Rationale: Time taken to reach first 40 km is 40/60 = 2/3 hr
Time taken to reach next 40 km is 40/60 = 2/3 hr
Time taken to reach next 20 km is 20/60 = 1/3 hr
Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...
Each stop was of 8 min , so two 8min break = 2*2/15 => 4/15 hr
Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+4/15)= 29/15 hrs
So, Average speed is 100/(29/15) = 51.7 km/hour
Answer will be (C)
Answer: C
Question: A clock store sold a certain clock to a collector for 15 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 45 percent of what the collector had paid. The shop then sold the clock again at a profit of 85 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $80, for how much did the shop sell the clock the second time?
Options:
A)$168.58
B)$187.54
C)$158.74
D)$120.56
E)$200.84
Rationale: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 15% profit.
This means the clocks' selling price was C (1.15) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys it for 45% the price at which the collector bought it.
Thus, you get = 1.15*0.45*C = 0.5175 C
Furthermore, the store sells the clock for the second time for 85% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.85 = 1.85 * 0.5175 C
Finally given that C - 0.5175 C = 80 ----> C = 165.80$
Thus, the cost of the clock the second time around = 1.85*0.5175 C = 1.85 * 0.5175 * 165.80 = 158.74$. Hence C is the correct answer.
Answer: C
Question: If we have 17 people in a meeting, in how many ways they can sit around a table?
Options:
A)10*9!
B)11*12!
C)12*13!
D)16*15!
E)18*17!
Rationale: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=17
(n-1)!=16!=16*15!
Ans:D
Answer: D
Question: John can eat a quarter of a pizza in one minute. How long does it take John to eat one pizza and a half?
Options:
A)20 minutes.
B)17 minutes.
C)5 minutes.
D)12 minutes.
E)6 minutes.
Rationale: The above problem could also be solved by dividing the mixed number 1 and 1/2 by 1/4
1 (1/2) ? 1 / 4 = 3 / 2 ? 4 / 1 = 6 minutes.
correct answer E
Answer: E
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for five years, compounding done annually?
Options:
A)9688
B)9687
C)9685
D)9682
E)12884
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}5 = Rs.12884
Answer:E
Answer: E
Question: How many points (x, y) lie on the line segment between (32, 12 2/3) and (7, 17 2/3) such that x and y are both integers?
Options:
A)one
B)4
C)5
D)8
E)9
Rationale: slope = (17 2/3 - 12 2/3) / (7 - 32) = -1/5
y = mx + b => 12 2/3 = -22/3 + b => b = 19
y = -x/5 + 19
Only integer values work, and the only multiples of 5 between 7 and 32 for x values are 10, 15, 20, 25 and 30, thus 5 points.
C
Answer: C
Question: The price of pulses has fallen by 25%. How many quintals can be bought for the same amount which was sufficient to buy 22 quintals at the higher price?
Options:
A)20
B)22.5
C)29.3
D)28.5
E)32.5
Rationale: 80% of original price can buy = 22 quintals.
Therefore, he can buy ( 22 x 100 )/ 75 = 29.3 quintals at the lower price.
ANSWER:C
Answer: C
Question: There are 10 women and 15 men in an office. In how many ways can a person can be selected?
Options:
A)23
B)25
C)28
D)10
E)24
Rationale: The number of ways in which a person can be selected = 10 + 15 = 25
Answer is B
Answer: B
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 54 units per day, what is the value of n ?
Options:
A)30
B)18
C)10
D)9
E)7
Rationale: (average production for n days) * n = (total production for n days) --> 50n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 50n + 90 = 54 * (n+1) --> n=9.
Or as 40 extra units increased the average for n+1 days by 4 units per day then 40/(n+1)=4 --> n=9.
Answer D.
Answer: D
Question: If a/b = 1/2, b/c = 5, c/d = 2/3, d/e = 1/6 and e/f = 2/3, then what is the value of abc/def ?
Options:
A) 50/729
B) 20/456
C) 45/752
D) 13/452
E) 45/741
Rationale: Say a = 2. Then:
a/b = 1/2 --> b = 4;
b/c = 5 --> c = 4/5;
c/d = 2/3 --> d = 6/5;
d/e = 1/6 --> e = 36/5;
e/f = 2/3 --> f = 54/2.
abc/def = (2*4*4/5)/(6/5*36/5*54/5) = 50/729.
Answer: A.
Answer: A
Question: A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 127 in his diary to remember his PIN. He also wrote out the way to calculate 127 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 127".
Once, Prafull saw his diary in which Pinaki wrote this number 127. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?
Options:
A)670
B)770
C)870
D)970
E)470
Rationale: Explanation :
Let, the PIN is x.
According to the question,
The card number =996 and Remainder =127.
Thus, (996 × x)/997=127.
=>x= 870.
Answer : C
Answer: C
Question: In what time will a train 130 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5
B)3.25
C)4.5
D)5.25
E)6.25
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 130/40 = 3.25 sec.
Answer: Option B
Answer: B
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleble and there are 15 unsaleable mangoes in the crate then how msny mango are there in the crate?
Options:
A)100 mangoes
B)110 mangoes
C)120 mangoes
D)150 mangoes
E)125 mangoes
Rationale: 150 mangoes
ANSWER:D
Answer: D
Question: One week, a certain truck rental lot had a total of 24 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
Options:
A)24
B)16
C)12
D)8
E)4
Rationale: N - Not rented trucks; R - Rented trucks
N + R = 24
N + R/2 = 12
R =24
A
Answer: A
Question: A man saves Rs 350 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.
Options:
A)Rs 662
B)Rs 2262.01
C)Rs 1158.54
D)Rs 1662.54
E)None of these
Rationale: Explanation:
=[350(21/20×21/20×21/20)+350(21/20×21/20)+350(21/20)]=1158.54
Answer: C
Answer: C
Question: Larry, Michael, and Wilson have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
Options:
A) 21
B) 42
C) 120
D) 504
E) 5040
Rationale: Larry, Michael, and Wilson have five donuts to share to get the answer, see how can we get sum5with 3 numbers.
1) 0,0,5 = 3 combinations or 3! /2!
2) 0,1,4 = 6 combinations or 3!
similarly
3) 0,2,3 = 6 combinations
4) 1,1,3 = 3 combination
5) 2,2,1 = 3 combination
total =21=A
Answer: A
Question: What is the sum of the different positive prime factors of 1050?
Options:
A)8
B)10
C)12
D)14
E)17
Rationale: I think answer is E: 17
1050 = 2*3*5*5*7
Sum of theDIFFERENTpositive prime factors = 2 + 3 + 5 + 7 = 17
Answer: E
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they take to finish the work, if all the three work together?
Options:
A)4
B)9
C)2
D)11
E)None
Rationale: 1/7 + 1/14 + 1/28 = 7/28 = 1/4
All three can finish the work in 4 days
Answer: A
Answer: A
Question: For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(18)/h(10) ?
Options:
A)1.8
B)3
C)6
D)18
E)60
Rationale: Mean = Median =(First+Last)/2
and Sum = Mean*Number of terms
h(18) = [(2+18)/2]*9 = 90
h(10) = (2+10)/2]*5 = 30
h(18)/h(10) = (90) / (30) = 3
ANSWER:B
Answer: B
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Options:
A)26
B)72
C)25
D)82
E)27
Rationale: Explanation:
D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer: Option C
Answer: C
Question: Kamal started a business investing Rs 9000. After five months, Sameer joined with a capital of Rs 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?
Options:
A)Rs 2380
B)Rs 2300
C)Rs 2280
D)Rs 2260
E)None of these
Rationale: Solution: Now as per question, Kamal invested for 12 months and Sameer invested for 7 months.
So Kamal: Sameer = (9000*12):(8000*7)
= 108 : 56
= 27 : 14
Sameer Ratio in profit will be =(6970*14/41)=Rs 2380.
Answer: Option A
Answer: A
Question: Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 16 hours. If all the pipes are open, in how many hours will the tank be filled ?
Options:
A)2.5 hours
B)2 hours
C)3.5 hours
D)2.3 hours
E)None of these
Rationale: Explanation:
Part filled by A in 1 hour = 1/4
Part filled by B in 1 hour = 1/8
Part filled by C in 1 hour = 1/16
Part filled by (A+B+C) in 1 hour =
1/4+1/8+1/16=7/16
So all pipes will fill the tank in 2.3 hours.
Option D
Answer: D
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 100 meters, how long will it take to cross a railway platform 120 meters long
Options:
A)6 sec
B)7 ½ sec
C)8 sec
D)8 ½ sec
E)9 sec
Rationale: Explanation:
Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (100 + 120) m = 220 m.
Time taken =220 ×(3/110) sec =6 sec
Answer: Option A
Answer: A
Question: Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.2,70,000 earned at the end of 3 years from the start of the business in 1999?
Options:
A)Rs 45000
B)Rs 50000
C)Rs 90000
D)Rs 75000
E)None
Rationale: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(270000×2/6) = Rs.90000.
Answer C
Answer: C
Question: At a loading dock, each worker on the night crew loaded 2/3 as many boxes as each worker on the day crew. If the night crew has 5/6 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
Options:
A)6/11
B)7/12
C)8/13
D)9/14
E)11/15
Rationale: Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (5x/6)(2y/3) = 5xy/9
The total number of boxes is xy + 5xy/9 = 14xy/9
The fraction loaded by the day crew is xy / (14xy/9) = 9/14
The answer is D.
Answer: D
Question: When positive integer N is divided by positive integer J, the remainder is 12. If N/J = 134.02, what is value of J?
Options:
A)300
B)600
C)500
D)112
E)620
Rationale: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.02, the decimal part of the decimal quotient, must equal the remainder, 12, divided by the divisor J.
0.02 = 12/J
0.02*J = 12
J = 12/0.02 = 1200/2 = 600/1 = 600
So J = 600, answer = B.
Answer: B
Question: A train running at the speed of 54 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)288
B)279
C)135
D)272
E)150
Rationale: Speed = 54 * 5/18 = 15 m/sec
Length of the train = speed * time = 15 * 9
= 135 m
Answer: C
Answer: C
Question: Two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. Approximately what percent of the combined five-quart mixture is water?
Options:
A)40%
B)45%
C)50%
D)55%
E)60%
Rationale: Since we are asking of water in the end, lets concentrate on water only..
A solution has 2 quarts with fraction of water =2/3, almost 67%..
B solution has 3 quarts with fraction of water =3/8 almost 37%..
so the ratio A:B=2:3...
the average will therefore be closer to B % and will be 2/(2+3) of {67-37} away from B..
2/(2+3) of {67-37}= 2/5 * 30 =12..
so 37 +12 =49 nearly 50%
ANSWER:C
Answer: C
Question: The letters of the word 'SUBITI' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SUBITI'
Options:
A)- 246
B)- 245
C)- 237
D)- 315
E)- 275
Rationale: Total Number of Words = 6!/2! = 360 [(number of characters)/(repeating group )!]
After S, we have T and U.
Number of words starting with T = 5!/2! = 60
Number of words starting with U = 5!/2! = 60
So any word starting with S will have rank < 360 - 60(for Us) - 60(for Ts) = 240
Only option A < 240, so Answer is C.
Answer: C
Question: If xy=1, x/y=36, for positive numbers x and y, y=?
Options:
A)1/2
B)2
C)1/3
D)3
E)1/6
Rationale: Very easy question. 2 variables and 2 easy equations.
xy=1 ---> x=1/y - (i)
x/y=36 ---> replacing (i) here ---> 1/(y^2)=36 ---> y^2=1/36 ---> y=1/6 or -1/6
The question states that x and y are positive integers. Therefore, y=1/6 is the answer.
Answer E.
Answer: E
Question: 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?
Options:
A)5 days
B)4 days
C)3 days
D)6 days
E)9 days
Rationale: Explanation:
1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
answer B
Answer: B
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $864 in total compensation, how many total hours did he work that week?
Options:
A)36
B)40
C)44
D)48
E)52
Rationale: For 40 hrs = 40*16=640
Excess = 864-640=224
For extra hours =.75(16)=12+16=28
Number of extra hrs =224/28=56/7=8
Total hrs =40+8=48
Answer D 48
Answer: D
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Options:
A)1378
B)1800
C)2738
D)2778
E)1928
Rationale: Explanation:
Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
machines & 6:10\\ time(in\; minutes) &1:4 \end{matrix}\right\}::270:x}
6 x 1 x x = 10 x 4 x 270
{10\times 4\times 270}{6}}
=> x= 1800
Answer: B
Answer: B
Question: A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?
Options:
A)48 min. past 12.
B)20 min. past 12.
C)28 min. past 12.
D)18 min. past 12.
E)42 min. past 12.
Rationale: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
hrs of this clock = 24 hours of the correct clock.
29 hours of this clock =(24 x 6/145 x 29) hrs of the correct clock
= 28 hrs 48 min of the correct clock.
Therefore, the correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.
Answer A
Answer: A
Question: Of the integers between 100 and 799, inclusive, how many do not have digit 3 and 6?
Options:
A) 310
B) 520
C) 410
D) 420
E) 320
Rationale: Options for the first digit 7-2(2 and 5)=5;
Options for the second digit 10-2=8;
Options for the third digit 10-2=8;
Total numbers possible 5*8*8=320.
Answer: E
Answer: E
Question: How many different ways can you select a pilot and a co pilot if you have 70 people to choose from?
Options:
A) 199
B) 200
C) 398
D) 4830
E) 9900
Rationale: You are not just choosing two from 70. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (70C2) x 2 = 4830.
Ans D
Answer: D
Question: During one year, the population of town increased by 5% . If the total population is 9975 at the end of the second year , then what was the population size in the beginning of the first year ?
Options:
A)50000
B)10000
C)90000
D)70000
E)120000
Rationale: Population in the beginning of the first year
= 9975/[1+(5/100)]*[1-(5/100)]
= [9975*(20/21)*(20/19)]
=10000.
Answer is B.
Answer: B