mathewhe/aqua_rat huggingface dataset:
Question: A cyclist traveled for two days. On the second day the cyclist traveled 6 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling, what was her average speed on the second day?
(A) 5 mph
(B) 10 mph
(C) 20 mph
(D) 30 mph
(E) 40 mph
Rationale: SOLUTION:
D = 280 Mi
T = 12 hrs
Đây 1 time = T1
Dây 2 time = T2
T2 - T1 = 4 hrs ----- (I)
T1 + T2 = 12 hrs ----- (II)
Adding I and II, T2 = 8 hrs and T1 = 4 hrs
Dày 1 Rate = R1
Dây 2 Rate = R2
R1 - R2 = 10 mph
í.ẹ. R1 = 10 + R2
280 = 8R2 + 4R1
í.ẹ. 280 = 8R2 + 4 (10 + R2)
í.ẹ. R2 = 20 mph
ANSWER: A
Answer: (A) 5 mph
Question: If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?
(A) 77
(B) 78
(C) 79
(D) 80
(E) 81
Rationale: A two-digit number "cd" can be expressed algebraically as 10c+d.
The sum of A + B = (10c+d)+(10d+c)=11(c+d).
The only answer that is a multiple of 11 is 77.
The answer is A.
Answer: (A) 77
Question: The value of B+5B(BB)(2B)when B = 3 is:
(A) 900
(B) 810
(C) 809
(D) 803
(E) 813
Rationale: Solution:
B+5B(BB)(2B)
Put the value of B= 3 in the above expression we get,
3+ 15(33)(2 x 3)
= 3+ 15(3 Ã— 3)(2 Ã— 3)
= 3 + 810
=813
Answer : E
Answer: (E) 813
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5250. The monthly income of P is?
(A) A)Rs.4078
(B) B)Rs.4000
(C) C)Rs.4050
(D) D)Rs.4027
(E) E)Rs.4020
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10100 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10500 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv)
Subtracting (ii) from (iv), we get, P = 4050.
P's monthly income = Rs.4050.
Answer: C
Answer: (C) C)Rs.4050
Question: Timothy leaves home for school, riding his bicycle at a rate of 8 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 36 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
(A) 1/3
(B) 3
(C) 4
(D) 9
(E) 36/13
Rationale: In 15 mins, Timothy travels=8/4 miles.
Now, let his mother takes x hours to reach him, traveling at 36mph.
So, 36x=8x+8/4
x=1/13 hrs.
Thus, the distance traveled by his mother to reach= 36*1/13=36/13 miles. Ans E
Answer: (E) 36/13
Question: A teacher can divide her class into groups into groups of 5,13 and 17. What is the smallest possible strength of the class?
(A) 1387
(B) 1768
(C) 1105
(D) 1286
(E) 2812
Rationale: Explanation:
For smallest possible class strength, we consider LCM of the given numbers. So LCM (5, 13, 17) = 1105
Answer: C
Answer: (C) 1105
Question: is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, then how old is B?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 14
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 37
5x = 35 => x = 7
Hence, B's age = 2x = 14 years.
ANSWER:E
Answer: (E) 14
Question: If the cost of 6 erasers and 4 sharpeners is Rs.21/-. What will be the cost of 24 erasers and 16 sharpeners?
(A) Rs.62/-
(B) Rs.84/-
(C) Rs.64/-
(D) Rs.88/-
(E) Rs.99/-
Rationale: Explanation:
6 erasers + 4 sharpeners = Rs.21.
Multiply by 4
We get,
24 erasers + 16 sharpeners = Rs.21x4 = Rs.84/-.
Answer: Option B
Answer: (B) Rs.84/-
Question: The contents of two vessels containing copper and tin in the ratio 1:2 and 2:5 are mixed in the ratio 1:4. The resulting mixture will have copper and tin in the ratio?
(A) 15:32
(B) 21:28
(C) 31:74
(D) 33:37
(E) 41:92
Rationale: The ratio of copper and tin the new vessel= (1/3*1/5 + 2/7*4/5) : (2/3*1/5 + 5/7*4/5)
= 31/105 : 74/105 = 31:74
Answer is C
Answer: (C) 31:74
Question: What will come in place of the question mark (?) in the following question?
112.36 + 225.05 + ? = 815.30
(A) 477.79
(B) 477.8
(C) 477.81
(D) 477.89
(E) 477.84
Rationale: Explanation:
815.30 - ( 112.36 + 225.05) = ?
= 477.89
ANSWER:D
Answer: (D) 477.89
Question: A wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 7 cm x 6 cm. The maximum number ofboxes that can be carried in the wooden box, is
(A) 9800000
(B) 1000000
(C) 7500000
(D) 2000000
(E) None of these
Rationale: Explanation: Number = (800*700*600)/8*7*6 = 2000000 Answer: D
Answer: (D) 2000000
Question: Two unbiased coins are tossed. What is the probability of getting at most one head?
(A) 1/2
(B) 1/4
(C) 2/3
(D) 3/4
(E) 5/7
Rationale: S = {HH, HT, TH, TT}
E = event of getting at most one head
E = {TT, HT, TH}
P(E) = 3/4
Answer is D
Answer: (D) 3/4
Question: Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 3 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
(A) 1.75
(B) 2.25
(C) 2.5
(D) 2.75
(E) 3.25
Rationale: Let the distance to the top be x, so the total distance traveled by Natasha is 2x.
The total time is 4 + 2 = 6 hours
The average speed = total distance/total time taken = 2x/6 = x/3
The average speed of the complete journey is 3 km/hour
x/3 = 3
x = 9 km
The average speed while climbing = distance/time = 9/4 = 2.25 km/h
The answer is B.
Answer: (B) 2.25
Question: What is the unit’s digit of 213 *212*347*468*778 ?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 3 × 2 = 6
6 × 7 = 42
2 × 8 = 16
6 × 8 = 48
So at units place 8 is present
thus ans is 8
ANSWER:D
Answer: (D) 8
Question: The product D of the first 10 prime numbers is closest to which of the following?
(A) 6.5 x 10^7
(B) 6.5 x 10^8
(C) 6.5 x 10^9
(D) 6.5 x 10^10
(E) 6.5 x 10^11
Rationale: The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.
# of different approximations are possible. For example:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667=D
2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.
Answer: C.
Answer: (C) 6.5 x 10^9
Question: On a sum of money ,the simple interest for 2 years is Rs. 660,while the compound interest is Rs. 696.30,the rate of interest being the same in both the cases.The rate of interest is :
(A) 10%
(B) 10.5%
(C) 12%
(D) None of these
(E) Cannot be determined
Rationale: Solution
Difference in C.I. and S.I. for 2 years = Rs.(696.30 - 660)= Rs. 36.30.
S.I. for one year = Rs. 330.
∴ S.I. on Rs. 330 for 1 year = Rs. 36.30.
∴ Rate (100x36.30/330x1)% = 11%. Answer D
Answer: (D) None of these
Question: How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 34% iodine solution?
(A) 35
(B) 49
(C) 100
(D) 105
(E) 136
Rationale: Solution 1:
Assume the iodine solution to be mixed = x lts.
Iodine = 0.4x lts, Water = 0.6x lts.
Solution 2: 35 liters of a 20% iodine solution
Iodine = 7 lts, Water = 28 lts.
Total iodine = 0.4x + 7
Total water = 0.6x + 28
The resultant is a 35% idoine solution.
Hence (0.4x + 7) / (x + 35) = 34/100
40x + 700 = 34x + 1220
6x = 820
x = 136 lts
Correct Option: E
Answer: (E) 136
Question: The duplicate ratio of 3:4 is?
(A) 9:15
(B) 9:10
(C) 9:16
(D) 9:13
(E) 9:11
Rationale: 32: 42 = 9:16
Answer: C
Answer: (C) 9:16
Question: Which of the following is NOT a factor of 5! ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 120=5*4*3*2 and we dont have 6
ANSWER IS E
Answer: (E) 6
Question: A number consists of two digits whose sum is 11. If 27 is added to the number, then the digits change their places. What is the number ?
(A) 47
(B) 65
(C) 83
(D) 92
(E) 98
Rationale: Explanation:
Let the ten's digit be x. Then, unit's digit = (11 - x).
So, number = 10x + (11 - x) = 9x + 11.
Therefore (9x + 11) + 27 = 10 (11 - x) + x 9x + 38 = 110 - 9x 18x = 72 x = 4.
Thus, ten's digit = 4 and unit's digit = 7.
Hence, required number = 47.
Answer: Option A
Answer: (A) 47
Question: solve the following quadratic equation by factoring.
u^2-5u-14=0
(A) (5,7)
(B) (8,9)
(C) (3,2)
(D) (5,3)
(E) (-2,7)
Rationale: We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
(u+2)(u-7)=0
u=-2, u=7
Therefore the two solutions are :(-2,7)
Ans: E
Answer: (E) (-2,7)
Question: What is the smallest prime number with two sevens in it?
(A) 77
(B) 177
(C) 277
(D) 377
(E) 108794769
Rationale: The smallest positive integers with two sevens are 77, 177, 277, . . . . The first
integer with two sevens that does not end with two sevens is 707.
77 = 7 11, and 177 is divisible by 3 because the sum of its digits is. So now you just need to
check that 277 is prime. There is no particular shortcut to see this – test divisibility by 2, 3, 5,
7, 11, and 13.
correct answer C
Answer: (C) 277
Question: If neha is 10
Both Sonali and priyanka is 15
Both sadaf and tanu is 10.
how much is prinka by the same system ?
(A) 8
(B) 11
(C) 10
(D) 15
(E) 6
Rationale: C
prinka is 10, in a system that awards five for each vowel.
Answer: (C) 10
Question: Look at this series: 53, 53, 41, 41, 29, 29, ... What number should come next?
(A) A)12
(B) B)14
(C) C)27
(D) D)53
(E) E)17
Rationale: In this series, each number is repeated, then 12 is subtracted to arrive at the next number.
Answer: E
Answer: (E) E)17
Question: If X boxes of grape juice cost 200 cents, how much will Y boxes cost in dollars?
(A) Y*3/x
(B) Y*4/x
(C) Y*2/x
(D) Y*6/x
(E) Y*8/x
Rationale: X boxes of grape juice cost 200 cents or 2 dollars.
cost of grape juice = 2/x
Cost of Y grape juices = Y*2/x
Hence Answer : C
Answer: (C) Y*2/x
Question: √3 percent of 3√3 =
(A) 5.2
(B) 1.0
(C) 0.1
(D) 2.0
(E) 5.0
Rationale: The other solutions are great, but here's one more approach.
First, we scan the answer choices to see that they are quite spread apart. This means we can also use someAPPROXIMATION
All test-takers must memorize the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
So, √3 percent of 3√3 ≈ 1.7 percent of (3)(1.7)
≈ (1.7/100)(5.1)
≈ 8.67/100
≈ 0.08
Check the answer choices to see that C is the only answer that's close.
Answer: C
Answer: (C) 0.1
Question: Jill is dividing her 16-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
(A) 10
(B) 25
(C) 1260
(D) 2520
(E) 6435
Rationale: With 16 players, the process of figuring out how many groups of 8 can be formed is pretty straight-forward....
16C8 = 16!/(8!8!) = 12870 possible groups of 8
Once forming that first group of 8, the remaining 8 players would all be placed on the second team by default.
The 'twist' is that the two teams of 8 canshow upin either order:
E
Answer: (E) 6435
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 12 inclusive?
(A) 420
(B) 840
(C) 1260
(D) 2520
(E) 27,720
Rationale: We have to find the LCM of 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, and 2^2*3.
The LCM is 1*2^3*3^2*5*7*11= 27,720
The answer is E.
Answer: (E) 27,720
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 310,000 cells two hours ago, approximately how many cells will be populating the colony ten hours from now?
(A) 77,500
(B) 1,860,000
(C) 12,480,000
(D) 19,840,000
(E) 24,960,000
Rationale: 310,000 × 2 × 2×2×2×2×2 = 310,000 × 64 = D
Answer: (D) 19,840,000
Question: Two trains of equal are running on parallel lines in the same direction at 50 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 70 m
(B) 72 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 50 - 36 = 14 km/hr.
= 14 * 5/18 =35/9 m/sec.
2x/36 =35/9 => x = 70.
ANSWER:A
Answer: (A) 70 m
Question: The greatest ratio out of 2:1, 5:8, 3:2, 8:9 and 8:5 is?
(A) 2:1
(B) 3:2
(C) 5:8
(D) 8:5
(E) 8:9
Rationale: 2/1=2
5/8=0.625
3/2=1.5
8/9=0.888
8/5=1.6
ANSWER:A
Answer: (A) 2:1
Question: How many numbers from 10 to 40 are exactly divisible by 3?
(A) 13
(B) 15
(C) 16
(D) 10
(E) 18
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39.
10 Numbers.
10/3 = 3 and 40/3 = 13 ==> 13 - 3 = 10. Therefore 10 digits
D)
Answer: (D) 10
Question: Each of the following equations Q has at least one solution EXCEPT
(A) Q=–2^n = (–2)^-n
(B) Q=2^-n = (–2)^n
(C) 2^n = (–2)^-n
(D) (–2)^n = –2^n
(E) (–2)^-n = –2^-n
Rationale: While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.
Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.
In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.
If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
Answer: (A) Q=–2^n = (–2)^-n
Question: A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is
(A) 10√2 m
(B) 100 m
(C) 100√2 m
(D) 200 m
(E) None
Rationale: Solution
Let the altitude of the triangle be hïand base of each be b.
Then , (½ ×b× h1) where h2 = 100 m.
= h1 = 2h2
= ( 2 x 100) m
= 200 m.
Answer D
Answer: (D) 200 m
Question: The length and breadth of the floor of the room are 20 feet and 10 feet respectively. Square tiles of 2 feet length of different colours are to be laid on the floor. Black tiles are laid in the first row on all sides. If white tiles are laid in the one-third of the remaining and blue tiles in the rest, how many blue tiles will be there?
(A) 16
(B) 24
(C) 32
(D) 48
(E) None of these
Rationale: Area left after laying black tiles
= [(20 – 4) × (10 – 4)] sq. ft. = 96 sq. ft.
Area under white tiles = (1⁄3 × 96) sq. ft = 32 sq. ft.
Area under blue tiles = (96 – 32) sq. ft = 64 sq. ft.
Number of blue tiles = 64/2×2=16.
Answer A
Answer: (A) 16
Question: A bag contains 70 black balls and 60 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 2/5
(B) 5/7
(C) 1/2
(D) 1/4
(E) 6/13
Rationale: Total number of balls = 70+60 = 130
no. of white balls = 60
probability of drawing a white ball = 60/130 = 6/13
Answer is E
Answer: (E) 6/13
Question: If 20 men can build a wall 66 metres long in 8 days, what length of a similar can be built by 86 men in 8 days?
(A) 283.8 mtrs
(B) 378.4 mtrs
(C) 478.4 mtrs
(D) 488.4 mtrs
(E) 578.4 mtrs
Rationale: If 20 men can build a wall 66 metres long in 8 days,
length of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(8*20) = 283.8 mtrs
ANSWER:A
Answer: (A) 283.8 mtrs
Question: How many multiples of 6 are there between 30 and 140, 30 and 140 inclusive ?
(A) 18
(B) 16
(C) 17
(D) 19
(E) 15
Rationale: 6 multiples are ...30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,...
,...,
the answer is =19
Answer is D
Answer: (D) 19
Question: The average height of 50 pupils in a class is 160 cm. Five of them whose height is 146 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ?
(A) 287 cm
(B) 151 cm
(C) 276 cm
(D) 287 cm
(E) 161 cm
Rationale: Total height = 160 * 50 = 8000 cm.
New average = [8000 - 5 * 146 + 5 * 156 ] / 50
= 161 cm.
Answer:E
Answer: (E) 161 cm
Question: How many 5 digit ( digit = 0 - 9 ) zip codes can exist in which at least one digit is repeated ?
(A) 39760
(B) 49760
(C) 59760
(D) 69760
(E) 70000
Rationale: Zip codes with 5 digits (all five digits can be repeated): 10^5=100,000
Zip codes with no digit being repeated: 10*9*8*7*6=30,240
Zip codes with at least one digit being repeated: 100,000-30,240=69,760
= 69760
ANS:D
Answer: (D) 69760
Question: Express of the following as a fraction:
56%
(A) 14/25
(B) 13/25
(C) 11/25
(D) 17/25
(E) None of them
Rationale: 56% = 56/100= 14/25.
Answer is A.
Answer: (A) 14/25
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, x
(A) 23
(B) 26
(C) 41
(D) 35
(E) 29
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 30 + 5 = 35.
Answer: (D) 35
Question: Two trains each 210m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 90km/h while the other travels at 85km/h. how long will it take for them to pass each other completely.
(A) 3 sec
(B) 2.6 sec
(C) 3.6 sec
(D) 8.6 sec
(E) 7.6 sec
Rationale: Explanation:
D = 210 m +210 m = 420 m
RS = 90 + 85 = 175 * 5/18 = 243/5
T = 420 * 5/243 = 8.6 sec
Answer: Option D
Answer: (D) 8.6 sec
Question: A can do in 6 day and B can do in 8 and C can do in 12 days but b left after working for 6 days for how many no of day A and C shluld work ?
(A) 2 days
(B) 1 day
(C) 3 days
(D) 4 days
(E) 5 days
Rationale: B for one day work is 1/8
he worked for 6 days, so 6*1/8=3/4 work will be completed.
remaining work is 1-3/4=1/4
A and C can complete the work in 4 days
but there is only 1/4 work that is to be completed, so A and C can complete 1/4 work in 1 day..
ANSWER:B
Answer: (B) 1 day
Question: A sum of money becomes double itself in 4 years at simple interest. How many times will it become 10 years at the same rate?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: P ---- 2P ---- 4 years5P ---- 10 years Answer: E
Answer: (E) 5
Question: Kim finds a 6-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
(A) 7/5
(B) 1/2
(C) 8/15
(D) 2/5
(E) 3/5
Rationale: 3 pieces of 1/5 length and two piece each of 1/15 and 2/15 lengths. removing one piece each from pieces of each kind of lengths the all that will remain will be
2 pieces of 1/5 i.e 2/5, 1 piece of 1/15, and 1 piece of 2/15
Which gives us 2/5 + 1/15 + 2/15 -----> 3/5
Answer is E
Answer: (E) 3/5
Question: Mahesh can do a piece of work in 60days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work?
(A) 45
(B) 25
(C) 37
(D) 41
(E) 30
Rationale: Work done by Mahesh in 60days = 20*1/60 = 1/3
Remaining work = 1 - 1/3 = 2/3
2/3 work is done by Rajesh in 30days
Whole work will be done by Rajesh is 30*3/2 = 45days
Answer is A
Answer: (A) 45
Question: Anne bought doughnuts for a class breakfast party. She bought 12 chocolate doughnuts, 6 coconut doughnuts, and 8 jam-filled doughnuts. How many doughnuts did Anne buy in all?
(A) 25
(B) 26
(C) 39
(D) 21
(E) 11
Rationale: Add the numbers of doughnuts.
12 + 6 + 8 =26.
Answer is B.
Answer: (B) 26
Question: In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 5:3:1, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?
(A)  $900
(B)  $720
(C)  $600
(D)  $450
(E)  $225
Rationale: To solve this question, it will be best to first express the given ratio using variable multipliers. Thus, we have:
Household Expenses : Food : Miscellaneous = 5x : 3x : x
Since we are told that the TOTAL amount allocated to these categories is $1,800 we can set up the equation:
5x + 3x + x = 1,800
9x = 1,800
x = 200
Thus, the total amount allocated to food is 3 x 200 = $600.
Answer C.
Answer: (C)  $600
Question: If 20 men can build a wall 66 metres long in 6 days, what length of a similar can be built by 86 men in 8 days?
(A) 278.4 mtrs
(B) 378.4 mtrs
(C) 478.4 mtrs
(D) 488.4 mtrs
(E) 578.4 mtrs
Rationale: If 20 men can build a wall 66 metres long in 6 days,
length of a similar wall that can be built by 86 men in 8 days = (66*86*8)/(6*20) = 11*172/5 = 1892/5 mtrs = 378.4 mtrs
ANSWER:B
Answer: (B) 378.4 mtrs
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 22
(B) 44
(C) 276
(D) 29
(E) 12
Rationale: Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer:B
Answer: (B) 44
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
(A) 12
(B) 6
(C) 15
(D) 8
(E) 14
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
ANSWER A
Answer: (A) 12
Question: Suppose 10 monkeys take 20 minutes to eat 10 bananas. How many monkeys would it take to eat 80 bananas in 80 minutes?
(A) 9
(B) 10
(C) 11
(D) 20
(E) 13
Rationale: One monkey takes 20 min to eat 1 banana , so in 80 mins 1 monkey will eat 4 bananas , so for 80 bananas in 80 min we need 80/4 =20 monkeys
ANSWER:D
Answer: (D) 20
Question: 10 men do a work in 10days. How many men are needed to finish the work in 2days?
(A) 50
(B) 20
(C) 30
(D) 10
(E) 15
Rationale: men required to finish the work in 2days = 10*10/2 = 50
Answer is A
Answer: (A) 50
Question: A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is?
(A) 25 years
(B) 65 years
(C) 45 years
(D) 75 years
(E) 95 years
Rationale: Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.
Then, woman's age = (10X + y) years; husband's age = (10y + x) years.
Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)
(9y-9x) = (1/11)(11y + 11x) = (x + y) 10x = 8y x = (4/5)y
Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age = 10x + y = 45 years.
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Answer:C
Answer: (C) 45 years
Question: A certain telephone number has seven digits. If the telephone number has the digit zero exactly 3 times, and the number 1 is not used at all, what is the probability that the phone number contains one or more prime digits.
(A) 1/24
(B) 1/16
(C) 1/2
(D) 15/16
(E) 23/24
Rationale: First step of getting rid of 3 digits of containing zeros is right: we are left with 4 digit number each of which can be one of 8 digit (2,3,4,5,6,7,8,9 as 0 is already used in first three and 1 is not used).
Next step:
total number of combinations possible 8^,
combinations with NO PRIME 4^4,
P(no prime)=4^4/8^4=1/2^4
P(p>=1)=1-1/2^4=15/16
Answer D.
Answer: (D) 15/16
Question: Look at this series: 2, 6, 18, 54, ... What number should come next?
(A) 108
(B) 148
(C) 162
(D) 216
(E) None
Rationale: Explanation: This is a simple multiplication series. Each number is 3 times more than the previous number.
Answer: Option C
Answer: (C) 162
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.4
(B) 1.8
(C) 1.2
(D) 1.5
(E) 1.9
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer:D
Answer: (D) 1.5