mathewhe/aqua_rat huggingface dataset:
Question: Farm Tax is levied on the 50% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. william. Mr. william paid only $ 480 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
(A) 15%
(B) 25%
(C) 0.125%
(D) 0.2083%
(E) none
Rationale: This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (480/3840)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/50) = 25%
The correct answer is (B).
Answer: (B) 25%
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.15 km and 0.6 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 42
(B) 9
(C) 7
(D) 67
(E) 15
Rationale: :
Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.15 + 0.6 = 1.75 km = 1750 m.
Required time = 1750 * 3/125
= 42 sec.
Answer: A
Answer: (A) 42
Question: In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
(A) 69.
(B) 73.
(C) 81
(D) 91
(E) 108
Rationale: Total students = 420
Boys = 312, Girls = 108
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 108 - 35 = 73.
Correct option: B
Answer: (B) 73.
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?
(A) 9%
(B) 10%
(C) 11%
(D) 12%
(E) 15%
Rationale: x discount on Pony jeans, (0.22 - x) discount on Fox jeans.
Set the equation: 3*15(0.22 - x) + 2*18x = 9 --> x = 0.1 = 10%.
Answer: B.
Answer: (B) 10%
Question: 4^15 is equal to which of the following?
(A) 1,073,751,828
(B) 1,073,751,824
(C) 1,073,751,842
(D) 1,073,751,806
(E) 1,073,751,821
Rationale: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 4^n has a cycle of 1.
4^1 = 4
4^2 = 16
4^3 = 64
Observe that the last digit of the resultant of 4^1 and 4^3 is 4. If we continue 4^n, the last digit follows the pattern 4, 6, 4, 6, 4, 6, .... So, all we need look for is the last digit in the pattern.
Cycle of 1, power of 15, last digit is 4.
Answer: B
Answer: (B) 1,073,751,824
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $468 per week. How much does she earn in dollars per hour?
(A) 2
(B) 8
(C) 9
(D) 11
(E) 13
Rationale: Explanation:
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 468. Hourly wage = 468 / 36 = 13
Answer: E
Answer: (E) 13
Question: The Shopkeeper increased the price of a product by 22% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
(A) A)12.5%
(B) B)12.2%
(C) C)13.15%
(D) D)14%
(E) E)15%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.22 = 0.854
Decrease in price = (0.122/1) × 100 = 12.2%
B)
Answer: (B) B)12.2%
Question: I sold a book at a profit of 10%. Had I sold it for $140 more, 15% would have been gained. Find the cost price?
(A) $2000
(B) $2500
(C) $3000
(D) $2800
(E) $1540
Rationale: 115% of cost - 110% of cost = $140
5% of cost = $140
cost = 140*100/5 = $2800
Answer is D
Answer: (D) $2800
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
(A) 720
(B) 127
(C) 137
(D) 129
(E) 112
Rationale: The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Answer: A
Answer: (A) 720
Question: In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
(A) 145m
(B) 829m
(C) 822m
(D) 929m
(E) 132mj
Rationale: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 - 855 = 145 m.
Answer:A
Answer: (A) 145m
Question: 0.009/x=0.05. find the value of X
(A) 0.00018
(B) 0.09
(C) 0.018
(D) 0.18
(E) 90
Rationale: x=0.009/0.18=0.05
ANSWER:D
Answer: (D) 0.18
Question: If a: b = 7: 5, b: c = 9: 11, find a: b: c?
(A) 63: 45: 58
(B) 63: 45: 55
(C) 63: 45: 53
(D) 63: 45: 59
(E) 63: 45: 58
Rationale: a: b = 7: 5
b: c = 9: 11
a: b: c = 63: 45: 55
Answer: B
Answer: (B) 63: 45: 55
Question: A man swims downstream 32 km and upstream 24 km taking 4 hours each time, what is the speed of the man in still water?
(A) 9
(B) 8
(C) 6
(D) 7
(E) 2
Rationale: 32 --- 4 DS = 8
? ---- 1
24 ---- 4 US = 6
? ---- 1 M = ?
M = (8 + 6)/2 = 7
Answer: D
Answer: (D) 7
Question: how many number of three digit numbers can be formed usingzs numbers 2,3,4,5 in which no repeatation..?
(A) 24
(B) 34
(C) 18
(D) 16
(E) 12
Rationale: 4*3*2=24
1 place of digit can be filled with 4 no
2 place of digit can be filled with 3 no (as 1 is already filled and not available)
3 place of digit can be filled with 2 no
so 24 ways
ANSWER:A
Answer: (A) 24
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 11
(B) 20
(C) 98
(D) 77
(E) 12
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: (B) 20
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 299
(B) 249
(C) 245
(D) 289
(E) 271
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: C
Answer: (C) 245
Question: Two trains 151 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.19
(B) 7.18
(C) 7.16
(D) 7.84
(E) 7.12
Rationale: T = (151 + 165)/ (80 + 65) * 18/5
T = 7.84
Answer: D
Answer: (D) 7.84
Question: To fill an art exhibit, the boys in an art course are assigned to create one piece of artwork each in the following distribution: 1/3 are sculptures, 1/8 are oil paintings, 1/2 are watercolors, and the remaining 10 pieces are mosaics. How many boys are in the art class?
(A) 80
(B) 120
(C) 240
(D) 320
(E) 400
Rationale: Let the total number of boys in the art class = s
Distribution of artwork is as
1/3 are sculptures
1/8 are oil paintings
1/2 are watercolors, and the remaining 10 pieces are mosaics
(1/3)s +(1/8)s +(1/2)s + 10 = s
Since remaining 10 pieces are mosaics , (1/24)s = 10
s = 240
Answer C
Answer: (C) 240
Question: Let Q represent a set of six distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?
(A) 1
(B) 2
(C) 5
(D) 3
(E) 7
Rationale: Q = p1+p2+p3+p4+p5+p6 = even (and all primes are distinct)
if the least prime is 2 then we have sum of Q = odd....hence 2 is not possible1 is not prime.
next least prime is 3, this satisfies the given condition that sum of Q = even.
Ans. D. 3
Answer: (D) 3
Question: If 20% of a = b, then b% of 20 is the same as:
(A) 4% of a
(B) 5% of a
(C) 20% of a
(D) None of these
(E) 8% of a
Rationale: Answer: Option A
20% of A=B= 20/100 A=B
B % OF 20= B/100*20=20/100 A *1/100*20=4/100A=4% OF A
Answer: (A) 4% of a
Question: An article costs Rs. 600. What should be the marked price of an article so that after 10% discount, the trader makes 20% profit?
(A) Rs. 802
(B) Rs. 800
(C) Rs. 8029
(D) Rs. 888
(E) Rs. 8128
Rationale: Explanation:
Cost price of article = Rs. 600
Profit % = 20%
Therefore,
selling price of article = 120% of C.P.
= (120 / 100) * 600 = Rs. 720
Marked price = ?
Discount % = 10%
S.P. = Rs. 720
90% of M.P. = S.P.
90/100 * M.P. = 720
M.P. = 720 * (100/90) = Rs. 800'
ANSWER: B
Answer: (B) Rs. 800
Question: The average expenditure of a man for the first five months is Rs.120 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
(A) Rs.140
(B) Rs.150
(C) Rs.160
(D) Rs.170
(E) none
Rationale: Explanation:
Total income = Rs.(120×5+130×7+290)=Rs.1800
Average monthly income
= Rs. (1800/12)=Rs.150
Correct Option: B
Answer: (B) Rs.150
Question: Total 100 members are writing exam. In the 48 members are writing first exam. 45 members are writing second exam. 38 members are writing third exam. 5 members are writing all the three exams. How many members are writing 2 exams?
(A) 66
(B) 21
(C) 88
(D) 719
(E) 011
Rationale: otal number of exams written by 100 students = 48 + 45 + 38 = 131
Now let us say x members are writing only 1 exam, y members are writing only 2 exams, z members are writing only 3 exams.
Therefore, x + 2y + 3z = 131 also x + y + z = 100.
Given that z = 5. So x + 2y = 116 and x + y = 95.
Solving we get y = 21.
So 21 members are writing exactly 2 exams.
Answer:B
Answer: (B) 21
Question: Evaluate: (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100)
(A) 7/100
(B) 8/100
(C) 9/100
(D) 6/100
(E) 3/100
Rationale: (1 - 1/10)(1 - 1/11)(1 - 1/12)...(1 - 1/99)(1 - 1/100)
= (9/10)(10/11)(11/12)...(98/99)(99/100)
= 9/100 : simplify
correct answer C
Answer: (C) 9/100
Question: A man’s speed with the current is 17 km/hr and the speed of the current is 2.5 km/hr. the man’s speed against the current is :
(A) 8.5 km/hr
(B) 12 km/hr
(C) 10 km/hr
(D) 12.5 km/hr
(E) None of these
Rationale: Solution
Man's rate in still water = (17-2.5) km/hr = 14.5 km/hr.
Man's rate against the current = (14.5-2.5) km/hr = 12 km/hr Answer B
Answer: (B) 12 km/hr
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?
(A) 22 minutes
(B) 88 minutes
(C) 70 minutes
(D) 77 minutes
(E) 48 minutes
Rationale: 1/20 - 1/28 = 1/70
70 minutes
Answer:C
Answer: (C) 70 minutes
Question: Shopkeeper rise price by 34% and gives successive discount of 10% and 15%. What is overall % gain or loss?
(A) 2.51%
(B) 4.51%
(C) 3.51%
(D) 6.51%
(E) 7.51%
Rationale: Let d initial price be 100
34 % rise
now price = 134/100*100 = 134
10% discount
Then price = 134 * 90/100 = 120.6
15 % discount
Then price = 120.6 * 85/100 = 102.51
So Gain = 102.51 - 100 = 2.51
Gain % = Gain * 100 /CP
==> 2.51 * 100 /100 = 2.51%
ANSWER:A
Answer: (A) 2.51%
Question: On a test, students receive 5 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?
(A) -6
(B) -1
(C) 0
(D) 1
(E) 6
Rationale: For the minimum possible score, let us take the worst case scenario
Suppose, he gets all of the last 3 qs wrong whose correct answer options are B and one of the first 3 qs wrong whose correct option is C
In that case, he will get only 2 out of the first 3 qs right.
Therefore, minimum possible score=(5*2)-(4*1)=6
Answer E
Answer: (E) 6
Question: The ratio of the present ages of a son and his father is 1 : 5 and that of his mother and father is 4 : 5. After 2 years the ratio of the age of the son to that of his mother becomes 3 : 10. What is the present age of the father?
(A) 30 years
(B) 28 years
(C) 37 years
(D) Data inadequate
(E) None of these
Rationale: S⁄F = 1⁄5 ⇒ F = 5S
M⁄F = 4⁄5 ⇒ M = 4⁄5 F
S+2/M+2=310
10S + 20 = 30 M + 6 = 3 × 4⁄5 5S + 6 = 12S + 6
\ 2 S = 14 ⇒ S = 7 years
\ F = 5S = 35 years
Answer E
Answer: (E) None of these
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 9:6
(B) 9:8
(C) 9:0
(D) 9:3
(E) 9:2
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer:B
Answer: (B) 9:8
Question: The difference of two numbers is 11. One third of their sum is 7. What are the two numbers?
(A) 21,10
(B) 16,5
(C) 3,14
(D) 11,10
(E) 7,14
Rationale: Let the two numbers be x and y.
Equation (i): x - y = 11
Equation (ii): (x + y)/3 = 7
Solve system of equations:
x + y = 21
x - y = 11
(add equations together) --- 2x = 32 --- x=16
16 - y = 11 --- y=5
Since x=16 and y=5, answer B (16,5) is correct.
Answer: (B) 16,5
Question: A shade of paint is made by evenly mixing m gallons of white paint, costing $12 a gallon, with n gallons of blue paint, costing $30. What is the cost, in dollars per gallon, of the resulting mixture?
(A) 12m +30n
(B) 42(12m +30n)
(C) (12m +30n)/42
(D) (12m +30n)/(M+ N)
(E) 42(M+ N)/(12m +30n)
Rationale: M gallons of white paint and N gallons of blue paint are combined to form a new mixture. The total number of gallons in the new mixture will be M + N gallons
M gallons of white paint cost $12, so the cost of adding this mixture is 12M
N gallons of blue paint cost $30, so the cost of adding this mixture is 30N
The cost per gallon of the new mixture is equal to the total cost of all the paint used divided by the total number of gallons used to produce it:
cost of new mixture: 12M + 30N
total gallons used: M+N
cost per gallon = total cost/total gallons used = (12M + 30N)/(M+N)
ANSWER:D
Answer: (D) (12m +30n)/(M+ N)
Question: If the population of a certain country increases at the rate of one person every 20 seconds, by how many persons does the population increase in 30 minutes?
(A) 55
(B) 20
(C) 96
(D) 90
(E) 40
Rationale: Answer = 3 * 30 = 90
Answer = D
Answer: (D) 90
Question: The smallest 3 digit prime number is:
(A) 250
(B) 365
(C) 789
(D) 412
(E) 101
Rationale: Explanation:
The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
ANSWER E
Answer: (E) 101
Question: By selling a watch for Rs.560/-, a man loses 20% what is that watch cost price?
(A) s. 600/-
(B) s. 700/-
(C) s. 800/-
(D) s. 850/-
(E) s. 900/-
Rationale: 80 % ------> 560 (80 * 7 = 640)
100 % ------>700 (100 * 7 = 700)
Cost price = Rs. 700/-
B)
Answer: (B) s. 700/-
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient?
(A) 0
(B) 12
(C) 13
(D) 20
(E) 22
Rationale: Number = (12 * 35) = 420
Correct quotient = 420/21 = 20
ANSWER:D
Answer: (D) 20
Question: A person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all the three cases. The money invested at 4% is?
(A) 3888
(B) 2799
(C) 2799
(D) 1200
(E) 2771
Rationale: Let the parts be x, y and [2600 - (x + y)].
Then,
(x * 4 * 1)/100 = (y * 6 * 1)/100 = {[2600 - (x + y)] * 8 * 1}/100
y/x = 4/6 = 2/3 or y = 2/3 x
So, (x * 4 * 1)/100 = [(2600 - 5/3 x) * 80/100
52x = (7800 * 8) => x = 1200
Money invested at 4% = Rs. 1200.Answer:D
Answer: (D) 1200
Question: If the area of circle is 452 sq cm then its circumference?
(A) 21
(B) 88
(C) 75
(D) 78
(E) 12
Rationale: 22/7 r2 = 452 => r = 12
2 * 22/7 * 12 = 75
Answer: C
Answer: (C) 75
Question: The diameter of a wheel is 0.7 m. How far will it travel in 200 revolutions
(A) 4.4 m
(B) 220 m
(C) 440 m
(D) 560
(E) 650
Rationale: Diameter(d) = 0.7 m
Circumference of the wheel,
= 2 * pi *R = d * pi
= 0.7 * 3.14 = 2.198 m.
In one revolution, wheel will covered = 2.198 m,
So, in 200 revolution, it will cover = 200 *2.198 = 4.396 m = 440 m (Approx).
Answer: Option C
Answer: (C) 440 m
Question: John left home and drove at the rate of 35 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive?
(A) 235 miles.
(B) 245 miles.
(C) 255 miles.
(D) 265 miles.
(E) 275 miles.
Rationale: The total distance D traveled by John is given by
D = 35 * 2 + 3 * 55 = 235 miles.
Answer A
Answer: (A) 235 miles.
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 199
(C) 676
(D) 156
(E) 122
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Answer: (A) 270
Question: 40% of a number is more than 20% of 650 by 190. Find the number?
(A) 288
(B) 282
(C) 800
(D) 277
(E) 232
Rationale: (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Answer:C
Answer: (C) 800
Question: Machine A working alone can complete a job in 9 hours. Machine B working alone can do the same job in 12 hours. How long will it take both machines working together at their respective constant rates to complete the job?
(A) 21/8
(B) 27/5
(C) 12/7
(D) 36/7
(E) 15/7
Rationale: Machines ( A ) ( B ) (A+B)
---Time - 9 - ( 12 ) -
---Rate 4 --- 3 --- 7
--Work 36 ---36 --36
A+B = (36/7)
D
Answer: (D) 36/7
Question: In how many ways, a committee of 5 members can be selected from
6 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 200
(B) 400
(C) 300
(D) 500
(E) 430
Rationale: Sol. (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1] = 200.
ANSWER A
Answer: (A) 200
Question: If A is to be chosen at random from the set {56,85,41} and B is to be chosen at random from the set {1,2,3,4,5}, what is the probability that AB will be odd?
(A) 4/15
(B) 13/15
(C) 56/15
(D) 6/15
(E) 8/15
Rationale: Method-1
AB will be odd when
1) A is odd and B is even, Probability of A odd is (2/3) and Probability of B even is (2/5), so Probability of Case(1) = (2/3)*(2/5) = (4/15)
2) A is even and B is odd, Probability of A even is (1/3) and Probability of B odd is (3/5), so Probability of Case(2) = (1/3)*(3/5) = (3/15)
3) A is odd and B is odd, Probability of A odd is (2/3) and Probability of B odd is (3/5), so Probability of Case(1) = (2/3)*(3/5) = (6/15)
Total Favorable Probability = (4/15)+(3/15)+(6/15) = (13/15)
Answer: option B
Answer: (B) 13/15
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 seconds. What is the length of the fast train?
(A) 23 m
(B) 23 (2/9)m
(C) 38 (8/9)m
(D) 29 m
(E) 28 m
Rationale: Relative speed = (40 - 20) km/hr =	(20 x(5/18))m/sec =	(50/9)m/sec.
Therefore Length of faster train =	((50/9)	x 7) m =	(350/9)m = 38	(8/9)	m.
C
Answer: (C) 38 (8/9)m
Question: Johnny travels a total of one hour to and from school. On the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 21 miles per hour. How far is it to the school?
(A) 2 miles
(B) 4 miles
(C) 6.5 miles
(D) 8 miles
(E) 10 miles
Rationale: Answer: C) 6.5 miles.
Average speed for round trip = 2*a*b/(a+b), where a,b are speeds
so, average speed was = 2*5*21/(5+21) = 6.5m/hr
the distance between schoolhome should be half of that. ie. 6.5 miles
Answer C
Answer: (C) 6.5 miles
Question: Rs. 800 becomes Rs. 956 in 3 years at a rate of S.I. If the rate of interest is increased by 4%, what amount will Rs. 800 become in 3 years?
(A) 2889
(B) 2798
(C) 1052
(D) 2789
(E) 2878
Rationale: S.I. = (956 - 800) = Rs. 156.
Rate = (100 * 156) / (800 * 3) = 6 1/2 %
Now rate = (6 1/2 + 4) = 10 1/2 %
New S.I. = (800 * 21/2 * 3/100) = Rs. 252
New amount = (800 + 252)
= Rs.1052.
Answer: C
Answer: (C) 1052
Question: If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
(A) None
(B) I only
(C) II only
(D) III only
(E) I and II
Rationale: given 2x/y is prime and greater than 2.
=> 2x/y could be any of the following
3,5,7....
=> 2x/y is odd and prime (as 2 is the only even prime number and its not in this set)
1. x = y , can't be true
if x=y , 2x/y = 2 which is not odd and prime.
2. y=1. can't be true.
if y=1,2x/y = 2x = even which is not odd & prime.
3. x and y are prime integers, need not be true.
lets say 2x/y = 3 and say y=2 prime
=>x = 6/2 = 3 prime
satisfies the given condition here.
but when 2x/y = 3 and y=5 prime
=> x = 15/2 not prime
My Answer is A
Answer: (A) None
Question: In the list 3, 4, 5, 5, 5, 5, 7, 11, 21, what fraction of the data is less than the mode?
(A) 2/9
(B) 1/3
(C) 2/5
(D) 2/3
(E) 7/9
Rationale: highest frequent term in the set is 5 (with frequency 4) hence
Mode = 5
two terms (3, 4) out of a total of 9 terms are less than mode of the set.
Fraction of set that are less than Mode of set = 2/9
Answer: Option A
Answer: (A) 2/9
Question: Eleven books consisting of 4 financial management, 3 marketing management and 4 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.
(A) 1/1455
(B) 1/1355
(C) 1/2255
(D) 1/5040
(E) 1/1155
Rationale: Since the denominator will be 11! . And there is no way to divide 11 from numerator and denominator. Use a multiple of 11 in the denominator only answer
E
Answer: (E) 1/1155
Question: In the year 2011, Shantanu gets a total of Rs. 3832.5 as his pocket allowance. Find his pocket allowance per day.?
(A) Rs. 9.5
(B) Rs. 10.5
(C) Rs. 12.5
(D) Rs. 11.5
(E) None of these
Rationale: Answer
Allowance per day = 3832.5 / 365 = Rs. 10.50
Correct Option: B
Answer: (B) Rs. 10.5
Question: Three numbers are in the ratio 3:5:7. The largest number is 56. What is the difference between smallest and largest number?
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: The three numbers are 3x, 5x, and 7x.
The largest number is 56 = 7*8, so x = 8.
The smallest number is 3*8 = 24.
56 - 24 = 32
The answer is D.
Answer: (D) 32
Question: A and B can do a piece of work in 40 days and 50 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
(A) 28 days
(B) 60 days
(C) 20 days
(D) 30 days
(E) 40 days
Rationale: Explanation:
(A+B)’s 10 days work = 10[1/40+1/50]=10[5+4/200]= 9/20
A complete remaining work in 9/20*40 = 18
Total work = 10+18 = 28days
Answer: Option A
Answer: (A) 28 days
Question: I had 30 donuts when I left home this morning but only 9 when I came back home. What percentage of the donuts are missing?
(A) 70
(B) 65
(C) 55
(D) 75
(E) 60
Rationale: 30 - 9 = 21
21/30 or 7/10
7/10 = 70/100 = 70%
Answer is A
Answer: (A) 70
Question: The average salary of 20 people in the shipping department at a certain firm is $1000. The salary of 10 of the employees is $600 each and the salary of 6 of the employees is $200 each. What is the average salary of the remaining employees?
(A) $2500
(B) $3200
(C) $4500
(D) $5000
(E) $5200
Rationale: total salary... 20*1000=20000
10 emp @ 600 =6000
6 emp @ 200 =1200
remaing 4 emp salary = 20000-6000-1200 =12800
average=12800/4 = 3200
Answer is B
Answer: (B) $3200
Question: A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.
or 137 + x = 144 o144 - 137 = 7.
Answer: B
Answer: (B) 7