mathewhe/aqua_rat huggingface dataset:
Question: When 1/10 percent of 2,000 is subtracted from 1/10 of 2,000, the difference is
(A)  0
(B)  198
(C)  450
(D)  495
(E)  500
Rationale: We can break this problem into two parts:
1) What is 1/10 percent of 2,000?
2) What is 1/10 of 2,000?
To calculate 1/10 percent of 2,000 we must first remember to DIVIDE 1/10 BY 100.
So we have: (1/10)/(100)
To divide a number by 100 means to multiply it by 1/100, so we have:
1/10 x 1/100 = 1/1,000
Thus, 1/10 percent of 2,000 = 1/1,000 x 2,000 =2.
Now let's concentrate on part 2. We need to calculate 1/10 of 2,000. To do this we simply multiply 1/10 by 2,000.
1/10 x 2,000 = 200
The answer to part 1 is 2, and the answer to part 2 is 200. Their difference is 200 – 2 = 198.
Answer B.
Answer: (B)  198
Question: A corporation triples its annual bonus to 50 of its employees. What percent of the employees’ new bonus is the increase?
(A) 50%
(B) 662⁄3%
(C) 100%
(D) 200%
(E) 300%
Rationale: Let the annual bonus be X.
A corporation triples its annual bonus.
So new bonus = 3X.
Increase = 3X-X =2X
The increase is what percent of the employees’ new bonus
= (2X/3X)*100
= 66 2/3%
Hence B.
Answer: (B) 662⁄3%
Question: If 4-X < (2+5X)/3, which of the following is correct?
(A) X < -5.
(B) X > -5.
(C) X > 5/4.
(D) -5 < X < 0.
(E) 0 < X < 5.
Rationale: 4-X < (2+5X)/3
12-3X < 2+ 5X
10 < 8X
10/8<X
5/4<X
C is the answer
Answer: (C) X > 5/4.
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 13.5
II. 12.3
III. 9.3
(A) I only
(B) I and II only
(C) II only
(D) III only
(E) I and III only
Rationale: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
12.3 and 13.5 lies in the range of 2SD from mean
Answer: Option D
Answer: (D) III only
Question: If anangletis defined as 1 percent of 1 degree, then how many anglets are there in a quarter circle?
(A) 0.36
(B) 3.6
(C) 9000
(D) 3,600
(E) 36,000
Rationale: 1 degree * 1/100 = 1 anglet
So 1 degree = 100 anglets
=> 90 degrees = 9000 anglets
Answer - C
Answer: (C) 9000
Question: the hiker walking at a constant rate of 4 miles per hour is passed by a bike traveling in the same direction along the same path at 20 miles per hour. the bike stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the bike wait until the hiker catches up?
(A) 16
(B) 14
(C) 10
(D) 15
(E) 20
Rationale: After passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles/hour.
In those 5 mins the cyclist travels a distance of 5/3 miles.
In those 5 mins the hiker travels a distance of 1/3 miles.
So the hiker still has to cover 4/3 miles to meet the waiting cyclist.
The hiker will need 1/3 hours or 20 mins to cover the remaining 4/3 miles.
So the answer is E.
Answer: (E) 20
Question: A box contains eight bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
(A) 13/16
(B) 1/2
(C) 15/16
(D) 11/16
(E) 9/16
Rationale: Required probability
= 1 - 1/16
= 15/16
Answer: C
Answer: (C) 15/16
Question: A tap can fill a tank in 14 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 11 hrs 45 mins
(B) 12 hrs 45 mins
(C) 13 hrs 45 mins
(D) 14 hrs 45 mins
(E) 15 hrs 45 mins
Rationale: Time taken by one tap to fill the tank = 7 hrs.
Part filled by the taps in 1 hour = 4 * 1/14 = 2/7
Remaining part = 1 - 1/2 = 1/2
2/7 : 1/2 :: 1 : x
x = 1/2 * 1 * 7/2 = 7/4 = 105 mins = 1 hr 45 mins
So, total time taken = 15 hrs 45 mins
ANSWER: E
Answer: (E) 15 hrs 45 mins
Question: A and B invests Rs.1500 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) 9:5
(B) 9:8
(C) 9:2
(D) 9:9
(E) 9:16
Rationale: (1.5*6 + 3*6): (4*12)
27:48 =>
9:16
Answer:E
Answer: (E) 9:16
Question: In a factory there are three types of machine M1, M2 and M which produces 25%, 35% and 40% of the total products respectively. M1, M2 and M3 produces 2%, 4% and 5% defective products, respectively. what is the percentage of non-defective products ?
(A) 89%
(B) 97.1%
(C) 96.1%
(D) 86.1%
(E) None of these
Rationale: Solution: Non-defective products,
{[(25*0.98)+(35*0.96)+(40*0.95)]/100}*100
= 96.1%.
Answer: Option C
Answer: (C) 96.1%
Question: A fruit juice is composed of pineapple, strawberry juice, and cherry juice. How many ml of cherry juice is required to make 6 liters of fruit juice containing twice as much pineapple juice as strawberry juice and three times as much strawberry juice as cherry juice? (1L=1000ml)
(A) 1800 ml
(B) 600 ml
(C) 1000 ml
(D) 200 ml
(E) 50 ml
Rationale: 1L=1000ml
6L=6000ml
pineapple=2 strawberry
strawberry=3 cherry
pineapple+strawberry+cherry=6,000
2 strawberry+strawberry+1/3 strawberry=6,000
10 strawberry=18,000
strawberry=18,00 ml
Answer A
Answer: (A) 1800 ml
Question: Find the number of square tiles to cover the floor of a room measuring 6.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 422
(B) 476
(C) 429
(D) 864
(E) 413
Rationale: Floor area to be covered by tiles = 6 * 9 = 54
tiles area = 0.25 * 0.25 =0.0625
No. of tiles = 54/0.0625 = 864
Answer : D
Answer: (D) 864
Question: The average of nine numbers is 14. The average of first four numbers is 11.5 and the average of last four numbers is 16.5. What is the middle number?
(A) 14
(B) 16
(C) 15
(D) 18
(E) 17
Rationale: The total of nine numbers = 9X14 = 126
The total of first 4 and last 4 numbers is = 4 X 11.5+4 X 16.5 = 112
So, the middle number is (126 - 112 ) = 14
A
Answer: (A) 14
Question: There are 8 balls in a bucket, 4 balls are blue and 4 balls are red. If two ball chosen randomly , how many chances there are at least one blue ball will present?
(A) 21
(B) 25
(C) 16
(D) 22
(E) 20
Rationale: Two ball will be chosen. At least 1 blue ball
Total ways = 8C2 = 28
Total without any blue ball = 4C2 = 6
Hence ways in which at least one blue will be present = 28 - 6 = 22
Correct option: D
Answer: (D) 22
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $16, what was the price before the first discount?
(A) $28.44
(B) $18.44
(C) $48.44
(D) $38.44
(E) $68.44
Rationale: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 16
(x - 25%x) - 25%(x - 25%x) = 16
Solve for x
x = $28.44
correct answer A
Answer: (A) $28.44
Question: A salt manufacturing company produced a total of 4000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 5520
(B) 2789
(C) 5550
(D) 2889
(E) 4550
Rationale: Total production of salt by the company in that year = 4000 + 4100 + 4200 + .... + 5100 = 54600.
Average monthly production of salt for that year = 54600/12 = 4550.
Answer: E
Answer: (E) 4550
Question: A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
(A) 11 2/3 days
(B) 11 3/7 days
(C) 8 days
(D) 6 days
(E) 5 days
Rationale: A's 1 day's work =1/15
B's 1 day's work =1/20
5 days before the completion of the work, A leaves=X-5/15
(x â€“ 5)/15 + x/20 = 1
x = 11 3/7 days
Answer: Option B
Answer: (B) 11 3/7 days
Question: A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5km on foot. His total journey is?
(A) 130
(B) 152
(C) 225
(D) 260
(E) 180
Rationale: Let the total journey be x km
then, (3x/5)+(7x/20)+6.5 = x
12x+7x+20*6.5 = 20x
x = 130km
Answer is A
Answer: (A) 130
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $30, what was the final price of the sweater?
(A) $25.75
(B) $35.75
(C) $15.75
(D) $ 45.75
(E) $15.75
Rationale: The price with 30% off
30 - 30% of 30 = 30 - (30 / 100) *30 = 30 - 9 = 21
The price with another 25% off
21 - 25% of 21 = 21 - (25/100)* 21
= 21 - (525 / 100) = 21 - 5.25 = $15.75
correct answer C
Answer: (C) $15.75
Question: What is the perimeter of a square field whose diagonal is 4√2?
(A) 16 m
(B) 32 m
(C) 27 m
(D) 26 m
(E) 76 m
Rationale: 4a
= 16 m
Answer: A
Answer: (A) 16 m
Question: What percent of 120 are 90?
(A) 12
(B) 33
(C) 75
(D) 88
(E) 11
Rationale: (?% /100) * 120 = 90
? = 75%
Answer:C
Answer: (C) 75
Question: Mr. Zimmer has 237 papers to hand out to his class. The class consists of 30 students, and each student will need 8 papers. How many more papers will he need to be able to give 8 papers to each 30 student?
(A) 3
(B) 7
(C) 21
(D) 78
(E) 4
Rationale: 8*30=240, not 237.
Therefore 3 papers will need to be added in order for 30 students to get 8 papers each.
Therefore A is correct
Answer: (A) 3
Question: |-4| (|-25|-|5|)= ??
Source: Preparation Material MBA Center
(A) 80
(B) 100
(C) 160
(D) 175
(E) 200
Rationale: Absolute value will turn negatives into their positive 'equivalents', and will leave positives unchanged, so |-4| = 4, |-25| = 25, and |5| = 5. Getting rid of our absolute values we have:
|-4| (|-25|-|5|) = (4) (25 - 5) = 4*20 = 80
Answer: (A) 80
Question: x is what percent of y percent of z, in terms of x, y and z? p be the value expressed in terms of x,y and z.
(A) xyz
(B) 1/xyz
(C) 10,000x/yz
(D) 1000*xyz
(E) 100x/yz
Rationale: Algebraically, y% of z is just (y/100)*z, or yz/100. So we want to answer the question: x is what percent of yz/100? Say x is equal to p% of yz/100; then we have:
x = (p/100)*(yz/100)
10,000x/yz = p
C
Answer: (C) 10,000x/yz
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
(A) 33.8
(B) 32.3
(C) 33.6
(D) 33.3
(E) 31.3
Rationale: Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer: C
Answer: (C) 33.6
Question: A company wants to manufacture computer models of x% of a list of 10,000 models from the market. After a budget cut, the company finds it must reduce this selection by (x − 6)%. In terms of x, how many computer model will the group be able to manufacture?
(A) x*x – 6x
(B) (x)(106 – x)
(C) (100)(106 – x)
(D) (100)(94 – x)
(E) (x-6)/100
Rationale: Based on the answer choices and the question, this question begs the use of x=6 as a sample number.
Initial = 6%*10000 = 600
Reduction = 6-6=0%, so no math required here to calculate the reduction; just make sure that you can calculate 600 in your answer.
A. x*x – 6x = 0; No
B. (x)(106 – x) = 600; Winner!
C. (100)(106 – x) > 600; No
D. (100)(94 – x) > 600; No
E. (x-6)/100 = 0; No
B
Answer: (B) (x)(106 – x)
Question: If 10 typists can type 30 letters in 30 minutes, then how many letters will 40 typists working at the same rate complete in 1 hour?
(A) 200
(B) 210
(C) 205
(D) 225
(E) 240
Rationale: No. of letters typing by 10 typists in 30 minutes = 30
No. of letters typing by 10 typists in 60 minutes = 30*2 = 60
No. of letters typing by 40 typists in 60 minutes = 60/10*40 = 240
Answer : E
Answer: (E) 240
Question: Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are queen?
(A) 4/26
(B) 55/221
(C) 56/221
(D) 55/220
(E) 57/220
Rationale: Probability of taking 2 from 52 cards = 52C2 = 52 * 51/2*1 = 1326
There r 26 black cards
There r 4 queens
prob that both r black cards P(A)= 26C2/1326 = 26 * 25/2 * 1 = 325/1326
prob that both r queens P(B)= 4C2/1326 = 4 * 3/2 * 1 = 6/1326
P(A n B) = 2C2/1326 = 1/1326
P(A U B) = P(A) + P(B) - P(A n B) = 325/1326 + 6/1326 - 1/1326
=> 55/221
ANSWER:B
Answer: (B) 55/221
Question: workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.50 lacs . How many workers were they?
(A) 220
(B) 230
(C) 500
(D) 560
(E) 1000
Rationale: N * 50 = (350000 - 300000) = 50000
N = 50000 / 50
= 1000
E
Answer: (E) 1000
Question: A Cuban cigar would cost 5 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
(A) 92.7$.
(B) 23$.
(C) 25.5$.
(D) 12.7$.
(E) 37.4$.
Rationale: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.
From the given data we know French cigar < Cuban cigar < Arabic cigar
and each is more expensive 1.5 times. Therefore eliminate options C,A,E straightaway . Since French cigar is at least 1.5 times cheaper we know B cannot be the answer.
Therefore D is the answer.
Answer: (D) 12.7$.
Question: Two trains of equal length, running with the speeds of 60 and 20 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?
(A) 12.5
(B) 8.01
(C) 7.5
(D) 26
(E) 22
Rationale: RS = 60 -40 = 20 * 5/18 = 100/18
T = 50
D = 50 * 100/18 = 2500/9
RS = 60 + 20 = 80 * 5/18
T = 2500/9 * 18/400= 12.5 sec.Answer: A
Answer: (A) 12.5
Question: In an entrance test, Deepika came across a mathematical patter problem.
If
6 / 7 = 2,
3 / 9 = 7,
8 / 2 = 6,
Then
4 / 5 = ?
She was able to solve it in less than a minute. Can you?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Solution:
The answer is 0.
As
6 / 7 = 42 but the answer is written as 2
3 / 9 = 27 but the answer is written as 7
8 / 2 = 16 but the answer is written as 6
If we look at the answers, the second digit has been used in the problem.
Now, as
4 / 5 = 20 and the second digit is 0, the answer is 0.
Answer A
Answer: (A) 0
Question: How many numbers from 9 to 79 are exactly divisible by 11?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 12
Rationale: 9/11 = 0 and 79/11 = 7 ==> 7 - 0 = 7 Numbers
Answer : B
Answer: (B) 7
Question: A ship sails 4 degrees north, then 14 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) None of these
Rationale: Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 14 + 17 - 19 = -11
And x = 1.
Answer B
Answer: (B) 1
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 46 hats in this group, how many of these hats are not blue?
(A) 28
(B) 22
(C) 48
(D) 64
(E) 76
Rationale: B:G:P = 7:4:12 --> total of 23 parts.
Not blue = (G + P)/(total)*92 = 16/23*46 = 32.
Answer: B.
Answer: (B) 22
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench?
(A) 5040
(B) 710
(C) 720
(D) 730
(E) 740
Rationale: npn = n!
7p7 = 7 X 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 5040
A
Answer: (A) 5040
Question: Two trains start from p and q respectively and travel towards each other at a speed of 50km/hr and 40km/hr respectively. By the time they meet, the first train has travelled 1ookm more than the second. The distance between p and q is
(A) 500km
(B) 600km
(C) 700km
(D) 900km
(E) 400km
Rationale: Explanation:
At the time of meeting, let the distance travelled by the second train be x km
Then, distance covered by the first train is (x+100)km
=> x/40 = (x+100)/50 => 50x = 40x+4000 => x=400km
so, distance between p and q = (x+x+100)km = 900km
Answer: Option D
Answer: (D) 900km
Question: If x⁄2 + 5⁄4 = 5⁄4, what is the value of x?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
Rationale: x⁄2 + 5⁄4 = 5⁄4
Let's multiply both sides by 4.
2x + 5 = 5
2x = 0
x = 0
The answer is C.
Answer: (C) 0
Question: At 3:00 pm, a car has driven 20 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?
(A) a) 10
(B) b) 11
(C) c) 12
(D) d) 15
(E) e) 14
Rationale: 0.8 minutes --> 1 mile
1 minute --> 1/0.8 = 10/8 = 1.25 miles/minute
Distance covered in 40 minutes = 1.25 * 40 = 12.5 * 4 = 50 miles
Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
20 + x = 50 - x
2x = 30
x = 15
Answer: D
Answer: (D) d) 15
Question: Lucy deposited $31250 in an investment fund that provided 16 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $2550?
(A) 0.5
(B) 2
(C) 12/4
(D) 12/2
(E) 6.1
Rationale: A = P + I = 31250 + 2550 = 33800
33800 = 31250(1 + 16/4*100)^(4t)
(676/625) = (104/100)^(4t)
(26/25)^2 = (26/25)^4t
t = 1/2 yrs = 12/2 months
Answer: D
Answer: (D) 12/2
Question: What number comes next in this Number series.
5 5 3 4 4 6 9 ?
*Hint: check calender
(A) 7
(B) 8
(C) 6
(D) 1
(E) 8
Rationale: A
7 (the number of letters in the month October)
March : 5 letters
April : 5 letters
May : 3 letters
June : 4 letters
July : 4 letters
August: 6 letters
September : 9 letters
Answer: (A) 7
Question: If 2 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture?
(A) (2x + 2y)/5
(B) (2x + 2y)/(x + y)
(C) (2x + 2y)/(xy)
(D) 5(2x + 2y)
(E) 2x + 2y
Rationale: Total Cost = Weight(in pounds) * Price/pound;
To find Total cost/pound, Divide by total pounds.
Cost of Dried apricots = 2x;
Cost of prunes = 2y;
Cost per pound = (2x + 2y)/5;
Ans is (A).
Answer: (A) (2x + 2y)/5
Question: AA is two digit number then m times its cube of AA has 1 in its tens place then what is m.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: when AA=11
7*(11)^3= 7*1331= 9317
m=7
ANSWER:E
Answer: (E) 7
Question: If the line L passes through the point (3,n) and (n,3), where n is not equal to 3, which of the following must be true?
1. The slope of L is negative
2.Line L must passes through the first quadrant
3. Line L does pass the origin.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: Slope of the given line= 3-n/n-3
Given information is that n is not equal to 3, that means n <3 or n>3. In both these conditions the slope will be negative.
1) n<3 (n=2)
3-2/2-3= -1
2) n<3 (n= 0)
3-0/0-3= -1
3) n<3 (n=-3)
3+3/ -3-3= -2/3
4) n>3
3-4/4-3= -1
Answer A
Answer: (A) I only
Question: In a certain sequence of 7 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Non - Negative ( zero to positive infinity )
Solution to the question :
-5,-4,-3,-2,-1,0 , 1
Hence ans is 1 ..option B
Answer: (B) One
Question: Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $75 per month and Plan B costs $250 per month per customer. If the company’s average revenue per customer per month is $200, then what percent of the company's revenue comes from customers with Plan A?
(A) 10.7%
(B) 30%
(C) 37.5%
(D) 56.25%
(E) 75%
Rationale: If there are A customers with plan A, and B customers with plan B, then the total revenue is $75A + $250B.
Since the average customer pays $100, we know that
$200 = ($75A + $250B) / (A + B)
$200(A + B) = ($75A + $250B)
$200A + $200B = $75A + $250B
$125A = $50B
A = 2/5*B.
Since there are 2/5 times as many $75 clients as $250 clients, for every $250 received from Plan B customers, 2/5*($75) = $30 is received from Plan A customers, and the percent of revenue from customers with Plan A is:
$30/($30 + $250) = $30/$280 = 10.7%.
The correct answer is choice (A).
Answer: (A) 10.7%
Question: In Town X, 64 percent of the population are employed, and 50 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 22%
(C) 32%
(D) 40%
(E) 52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 50 are employed males, hence 14% are employed females.
(employed females)/(total employed people)=14/64=22%
Answer: B.
Answer: (B) 22%
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 12?
(A) 6
(B) 8
(C) 4
(D) 3
(E) 2
Rationale: You should consider the worst case scenario: if you pick numbers 0, 1, 2, 3, 4,5 and 6 then no two numbers out of these 7 add up to 12.
Now, the next, 8th number whatever it'll be (7, 8, or 9) will guarantee that two number WILL add up to 12. So, 8 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 12.
Answer: B
Answer: (B) 8
Question: If k and y are integers, and 10k + y is odd, which of the following must be true?
(A) k is odd
(B) k is even
(C) y is odd
(D) y is even
(E) both k and y are odd
Rationale: 10k will be always even as 10 has 2 as one of its factors
if 10k+y is odd, then the only possible explanation is that y is odd
correct answer C
Answer: (C) y is odd
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
(A) 3/5
(B) 3/7
(C) 4/7
(D) 4/9
(E) 5/3
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
C)
Answer: (C) 4/7
Question: A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 30% impurities to the product. Find the net profit percentage of the dealer?
(A) 44%
(B) 40%
(C) 50%
(D) 56.25%
(E) 37.5%
Rationale: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.
It means that he is selling $4 worth of product for $5.
The dealer then further added 30% impurities to the product.
It means that he is selling $5 worth of product for $5.5.
So his profit is $5.5-$4 = $1.5
and his profit percent is
(1.5/4)*100 = 37.5%
Answer:- E
Answer: (E) 37.5%
Question: A basketball coach will select the members of a five-player team from among 11 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter?
(A) 1/9
(B) 1/6
(C) 2/11
(D) 5/18
(E) 1/3
Rationale: straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 9c3
total number of ways of selecting 5 players out of 11 = 11c5
probability = 9c3/11c5 =2/11
C
Answer: (C) 2/11
Question: A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
(A) 15
(B) 14
(C) 18
(D) 19
(E) 20
Rationale: Let the average after the 16th inning be P.
So, the average after the 15th inning will be
(P-3) Hence, 15(P-30) + 64 = 16P => P = 19.
Answer:D
Answer: (D) 19