mathewhe/aqua_rat huggingface dataset:
Question: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 7 ?
(A) 3
(B) 1
(C) 4
(D) 0
(E) 2
Rationale: A number ending with 7 can never be a perfect square.
Answer: D
Answer: (D) 0
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 2 1/5
(B) 2 1/6
(C) 2 1/3
(D) 2 1/2
(E) 2 1/1
Rationale: Required time = (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer: D
Answer: (D) 2 1/2
Question: Each writer for the local newspaper is paid as follows: a dollars for each of the first t stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits t + a stories in a month earn than a writer who submits t + b stories?
(A) (a – b)( a + b + t)
(B) a – b
(C) a^2 – b^2
(D) t( a – b)
(E) at + bt – at
Rationale: total earned for t+a stories =a + a(a+b)
total earned for t+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
=(a+b)(a-b) =a^2-b^2
answer is C
Answer: (C) a^2 – b^2
Question: A trader bought a car at 20% discount on its original price. He sold it at a 60% increase on the price he bought it. What percent of profit did he make on the original price?
(A) A)10%
(B) B)12%
(C) C)14%
(D) D)20%
(E) E)28%
Rationale: Original price = 100
CP = 80
S = 80*(160/100) = 128
100 - 128 = 28%
E)
Answer: (E) E)28%
Question: If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 81 times in:
(A) 12 years
(B) 18 years
(C) 16 years
(D) 14 years
(E) 15 years
Rationale: Explanation:
The sum P becomes 3P in 4 years on compound interest
3P = P(1+R/100)4
⇒ 3 = (1+R/100)4
Let the sum P becomes 81P in n years
81P = P(1+R/100)n
⇒ 81 = (1+R/100)n
⇒ (3)4 = (1+R/100)n
⇒ ((1+R/100)4)4 = (1+R/100)n
⇒ (1+R/100)16 = (1+R/100)n
n=16
i.e, the sum will become 81 times in 16 years
Answer: Option C
Answer: (C) 16 years
Question: In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score O that Lindsey could have received on her midterm exam?
(A) 52%
(B) 64%
(C) 72%
(D) 76%
(E) 80%
Rationale: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Answer: (A) 52%
Question: In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 4:3:1, 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)  $675
(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 = 4x : 3x : x
Since we are told that the TOTAL amount allocated to these categories is $1,800 we can set up the equation:
4x + 3x + x = 1,800
8x = 1,800
x = 225
Thus, the total amount allocated to food is 3 x 225 = $675.
Answer C.
Answer: (C)  $675
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 130 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 65x+y
(B) 130x/y
(C) 130x+y
(D) 100x-y
(E) 130y/x
Rationale: A wheel covers 2πr distance in one revolution. where r= diameter/2
First wheel covers d feet in 130 rev. => d= 130* 2π * (x/2)
Second wheel covers d feet in let's say P revolutions; => d = P* 2π * (y/2)
comparing both equations:-
=> p= (130∗2π∗x/2)/(2π∗y/2)
=> 130x/y
Answer :- B
Answer: (B) 130x/y
Question: For a rectangular box, what is the product of the areas of the 3 adjacent faces that meet at a point?
(A) Volume of the box
(B) Twice the volume of the box
(C) Half of the volume of the box
(D) Square of the volume of the box
(E) None of these
Rationale: SOLUTION :
The area of the 3 adjacent faces of a rectangular box of length ‘l’, breadth ‘b’, and depth ‘h’ are ‘l*b’, ‘b*h’, and ‘l*h’.
Therefore, lb*bh*lh = l2b2h2 = (lbh) 2 = square of the volume of the box.
ANSWER IS D
Answer: (D) Square of the volume of the box
Question: Alex opened a shop investing Rs.10000. Samuel joined him 6 months later, investing Rs.15000. They earned a profit of Rs.3500 after completion of one year. What will be Alex and Samuel's profits respectively?
(A) 2000 and 1500
(B) 1500 and 2000
(C) 1800 and 1700
(D) 1700 and 1800
(E) 1000 and 2500
Rationale: SoL = ~s- So Alex's share = [4/7] x 3500= 2000
Samuel's share = [3/7] x 3500= 1500
Answer : A
Answer: (A) 2000 and 1500
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?
(A) 430
(B) 438
(C) 436
(D) 434
(E) 422
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 172 => 4x/10 = 172
=> 4x = 1720 => x = 430.
Answer:A
Answer: (A) 430
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
(A) 233
(B) 287
(C) 108
(D) 100
(E) 712
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: (D) 100
Question: Jerry, an electrician, worked 3 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 3? 12 months = 1 year
(A) 58.33%
(B) 25%
(C) 78.33%
(D) 88.33%
(E) 98.33%
Rationale: 1. Multiply the opposites
3 x 100 = 300
100=3/12
Divide by the remaining number
25%
correct answerB
Answer: (B) 25%
Question: If y = 2 + 2K and y≠0y≠0, then 7/y + 3/y + 1/y + 1/y = ?
(A) 1/(8+8k)
(B) 6/(1+k)
(C) 1/(8+k)
(D) 4/(8+k)
(E) 4/(1+k)
Rationale: 7/Y + 3/Y + 1/Y + 1/Y
= 12/Y
= 12/(2 + 2K)
= 6/(1 + K)
ANSWER:B
Answer: (B) 6/(1+k)
Question: A train covers a distance of 12 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
(A) 298 m
(B) 188 m
(C) 120 m
(D) 178 m
(E) 200 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 10
= 200 m.
Answer:E
Answer: (E) 200 m
Question: While out shopping for clothes you have a 20% off coupon, which must be applied before a 7% sales tax is added. What is the final percentage you will pay for the clothes relative to the un-adjusted price?
(A) 127.2%
(B) 74%
(C) 75.2%
(D) 84.8%
(E) 126%
Rationale: (100%-20%)*(100%+6%) = 0.80*1.06 = 84.8%
The Final Percentage you will pay of the un-adjusted price will be 84.8%
The Answer is D
Notice the answer is the same no mater which order you apply the tax and the discount.
(100%+6%)*(100%-20%) = 1.06*0.80 = 84.8%
Answer: (D) 84.8%
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 328
(B) 27
(C) 3
(D) 8
(E) 2
Rationale: 40*(40/100) = 16 --- 64
? --- 12 => Rs.3Answer: C
Answer: (C) 3
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 24
(B) 22
(C) 20
(D) 16
(E) 30
Rationale: B = 1/8 â€“ 1/2 = 1/24 => 24 days
ANSWER A
Answer: (A) 24
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there
(A) 109
(B) 128
(C) 138
(D) 209
(E) 176
Rationale: Explanation:
In a group of 6 boys and 4 girls, four children are to be selected such that
at least one boy should be there.
So we can have
(four boys) or (three boys and one girl) or (two boys and two girls) or (one boy and three gils)
This combination question can be solved as
(6C4)+(6C3∗4C1)++(6C2∗4C2)+(6C1∗4C3)
=[6×5/2×1]+[(6×5×4/3×2×1)×4]+[(6×5/2×1)(4×3/2×1)]+[6×4]
=15+80+90+24=209
Option D
Answer: (D) 209
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 99
(C) 88
(D) 77
(E) 21
Rationale: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer:A
Answer: (A) 40
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
(A) 18 1/2 years
(B) 12 1/8 years
(C) 16 1/2 years
(D) 12 1/2 years
(E) 12 1/5 years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 1/2 years
Answer: B
Answer: (B) 12 1/8 years
Question: The below sequence is a bit tricky. Can you solve it to find the next number?
4, 24, 324, 4324, ?
(A) 29816
(B) 38291
(C) 54324
(D) 38290
(E) 55291
Rationale: See the pattern. With every digit, the previous numbers are added after that digit
So the next number in the series is 54324
Answer : C
Answer: (C) 54324
Question: Which of these must the factor of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
(A) 1,2 only
(B) 2,3 only
(C) 1,2,3 only
(D) 1,2,3,4 only
(E) All of them
Rationale: 80 is not factor.... It has to have one 5.
Answer is D
Answer: (D) 1,2,3,4 only
Question: If x is 30 percent more than y and y is 50 percent less than z, then x is what percent of z?
(A) 500%
(B) 250%
(C) 65%
(D) 125%
(E) 60%
Rationale: Z = 100 ; Y = 50 so X = 65
X as % of Z = 65/100 * 100 => 65%
Answer will be (C)
Answer: (C) 65%
Question: For how many integers k is k^3 = 3^k ?
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Rationale: 3^3=3^3
For k= 3 the above equality holds true.
B is the answer
Answer: (B) One
Question: It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to gate at least two socks of the same color?
(A) 2
(B) 3
(C) 48
(D) 25
(E) 26
Rationale: let
if first is red
and by luck if 2nd is not red then we u hav to take 3rd one.
which will be either red or blue.
but u will get 2 socks of same color,either red or blue.
ANSWER:B
Answer: (B) 3
Question: In wardrobe Marry has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens hiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
(A) 1/2
(B) 2/3
(C) 3/5
(D) 3/7
(E) 4/9
Rationale: Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
∴ Required probability = 2/3 x 3/4 = 1/2
A
Answer: (A) 1/2
Question: Tom went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 17
(B) 18
(C) 19.7
(D) 21.1
(E) 21.3
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
C)
Answer: (C) 19.7
Question: How many 3-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 121.
(A) 90
(B) 610
(C) 729
(D) 900
(E) 1000
Rationale: Take the task of building palindromes and break it intostages.
Stage 1: Select the hundreds digit
We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in9ways
Stage 2: Select the tens digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in10ways
IMPORTANT: At this point, the remaining digits are alreadylocked in.
Stage 3: Select the units digit
This digit must be the SAME as the thousands digit (which we already chose in stage 2)
So, we can complete this stage in1way.
By theFundamental Counting Principle(FCP), we can complete all 5 stages (and thus build a 3-digit palindrome) in(9)(10)(1)ways (= 900 ways)
Answer:A
Answer: (A) 90
Question: A trader bought a car at 40% discount on its original price. He sold it at a 80% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 8%
(B) 62%
(C) 2%
(D) 9%
(E) 22%
Rationale: Original price = 100
CP = 60
S = 60*(180/100) = 112
100 - 108 = 8%
Answer: A
Answer: (A) 8%
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 5 meters and a circumference of 4 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 10%
(B) 80%
(C) 100%
(D) 120%
(E) 125%
Rationale: For A, r=4/2pi. Its capacity = (2pi)^2 * 5= 20pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
A/B = 20pi/200pi = 0.1
A
Answer: (A) 10%
Question: Jasmine has a toaster with two slots that toasts one side of each piece of bread at a time, and it takes one minute to do so.
If she wants to make 3 pieces of toast, what is the least amount of time she needs to toast them on both sides?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 3 minutes. She puts two pieces in the toaster, toasting one side of each. Then she flips one of them, takes one out, and puts the completely untoasted piece into the toaster. Finally, she takes out the toasted piece and puts the two half-toasted pieces of bread into the toaster for a minute and she's done.
Answer: (C) 3
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
(A) 7 days
(B) 8 days
(C) 3 days
(D) 9 days
(E) 2 days
Rationale: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer:B
Answer: (B) 8 days
Question: A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 37 sec
(B) 89 sec
(C) 36 sec
(D) 87 sec
(E) 45 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 250 + 120 = 370 m.
Time taken = 370/10
=37 sec.
Answer: A
Answer: (A) 37 sec
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
(A) 675.5
(B) 635.5
(C) 635.28
(D) 635.98
(E) 635.03
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer:B
Answer: (B) 635.5
Question: Calculate the dividend from Moses's stock, if he invested Rs. 3000 at 72 to obtain an income of Rs. 210.
(A) 3
(B) 9
(C) 3
(D) 4
(E) 5.04
Rationale: By investing Rs.3000, income = Rs.210
By investing Rs.72, income = 210Ã—72/3000=5.04
ie, dividend = 5.04%
Answer is E.
Answer: (E) 5.04
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 187
(B) 178
(C) 375
(D) 167
(E) 619
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Answer: (C) 375
Question: The value of a machine depreciates at 22% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
(A) $255260
(B) $435260
(C) $125260
(D) $115260
(E) $155260
Rationale: The value of the machine after two years = 0.78 * 0.78 * 1,50,000 = $91,260
SP such that a profit of $24,000 is made = 91,260 + 24,000 = $1,15,260
D
Answer: (D) $115260
Question: The ratio of the present ages of a man and his wife is 3 : 2. Which of the following can't be a possible ratio of their ages 25 years ago?
(A) 1: 3
(B) 2: 3
(C) 3:3
(D) 4: 3
(E) 5: 4
Rationale: 3x-25/2x-25 = 4/3
Therefore x=-25
Age cannot be negative.
Answer: D
Answer: (D) 4: 3
Question: A farmer had d animals, all of which the farmer bought for the same price. The farmer decided to sell the animals. 18 of the animals were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, the farmer made neither a profit nor a loss. Which of the following is equal to d?
(A) 21
(B) 24
(C) 27
(D) 32
(E) 36
Rationale: Let P be the price the farmer paid for each animal.
The total profit on the 18 animals is 18*0.1*P.
The total loss on the other (d-18) animals is (d-18)*0.2*P.
(d-18)*0.2*P = 18*0.1*P
0.2*d = 1.8 + 3.6
d = 27
The answer is C.
Answer: (C) 27
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)
(A) Rs. 8167
(B) Rs. 4261
(C) Rs. 4269
(D) Rs. 4266
(E) Rs. 4262
Rationale: Explanation:
CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266
Answer:D
Answer: (D) Rs. 4266
Question: If x and y are positive integers and 9 + x + y + xy = 23, what is the value of x + y?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Try each answer choices.
For A: 9 + 3 + xy = 23; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3)
For B: 9 + 5 + xy = 23; xy = 9 (no combination of xy = 9 and x + y = 5)
For C: 9 + 6 + xy = 23; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2)
For D: 9 + 8 + xy = 23; xy = 6 (no combination of xy = 6 and x + y = 8)
For E: 9 + 9 + xy = 23; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9)
Therefore, answer C.
Answer: (C) 6
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 27 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
(A) 20
(B) 10
(C) 30
(D) 50
(E) 40
Rationale: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+27) and number of girls were 5x
Hence, 2(5x) = x + 27
=> 10x = x + 27
=> x = 3
Number of girls in the beginning = (5x + 15) = (5×3 + 15) = 30
Answer is C.
Answer: (C) 30
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
(A) 394 cm
(B) 384 cm
(C) 380 cm
(D) 364 cm
(E) 382 cm
Rationale: Explanation:
Area of a parallelogram = base * height = 24 * 16 = 384 cm
Answer: Option B
Answer: (B) 384 cm
Question: I have 300 friends on facebook and 300 on twitter. When I posted pictures of my birthday party, 50 percent of the facebook friends and 42 percent of the twitter friends "liked" my post; what percent of the total number of friends on both social media platform liked my post ?
(A)  35.5%
(B)  40.0%
(C)  46.0%
(D)  49.5%
(E)  51.0%
Rationale: Facebook : 50% of 300 friends liked my post, hence 0.50*300 = 150 friends liked.
Twitter : 42% of 300 friends liked my post, hence 0.42*300 = 126 seeds germinated.
Thus (friends who liked my post) /(total) = (150 + 126)/(400 + 300) = 276/600 = 46% seeds germinated.
Answer: C.
Answer: (C)  46.0%
Question: Find the odd man out. 16,20,24,72,80
(A) 16
(B) 20
(C) 24
(D) 72
(E) 80
Rationale: All except 20 are multiples of 8
Answer is B
Answer: (B) 20
Question: The ratio of the present age of Sandy to that of Molly is 7:2. Sixteen years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago?
(A) 66
(B) 70
(C) 74
(D) 78
(E) 82
Rationale: Let the present age of Sandy be 7x years and that of Molly be 2x years.
(7x + 16) / (2x + 16) = 5 / 2
4x = 48
x = 12
Six years ago, Sandy's age was 7(12) - 6 = 78
The answer is D.
Answer: (D) 78
Question: The value of 4.12 is :
(A) 4(11 / 90)
(B) 4(11 / 99)
(C) 371 / 900
(D) 4(3/25)
(E) None
Rationale: 4.12 can be written as 412/100=103/25
this can be written as 4(3/25)
ANSWER:D
Answer: (D) 4(3/25)
Question: In the game of Dubblefud, yellow chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many yellow chips are in the selection?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: this is equivalent to :-
2x * 4y * 5z = 16000
y = z (given)
2x * 4y * 5y = 16000
2x * y^2 = 16000/20
2x * y^2 = 800
now from options given we will figure out which number will divide 800 and gives us a perfect square :-
which gives us x = 4 as
2* 4 * y^2 =800
y^2 = 100
y =10
Number of yellow chips = 4 hence D
Answer: (D) 4
Question: A man rides at the rate of 30km/hr. But stops 20minutes to change horses at the end of every 60th kilometer. How long will he take to go a distance of 180 kilometers?
(A) 5hr
(B) 6hr 30min
(C) 6hr 40min
(D) 7hr 20min
(E) 9hr
Rationale: speed of man = 60km/hr
number of rests = (180/60)-1 = 2
time taken for the man = (180/30)+2*(20/60) = 6 hr 40 min
Answer is C
Answer: (C) 6hr 40min
Question: The sum of 3 hours 45 minutes and 3 hours 55 minutes is approximately what percent of a day?
(A) 35%
(B) 34%
(C) 33%
(D) 32%
(E) 31%
Rationale: Since the question is asking for an approximate percentage
3:45+3:55 ~ 8 hours
% of day = 8*100/24 ~ 8*100/25= 32%
Answer is D.
Answer: (D) 32%
Question: The last digit of 12^12+13^13–14^14×15^15 =
(A) 0
(B) 1
(C) 5
(D) 8
(E) 9
Rationale: 12^12+13^13–14^14∗15^15
=12^12+13^13–(14^14∗15^15)
Note that the answer would be -ve for this question
So, Just for the sake of last digit, I'm re-arranging the term as below
(14^14∗15^15)−(12^12+13^13)
(14^14∗15^15) >> As 4 & 5 are at the units place, the units place would be 0 of the product. No need of further calculation
12^12>> Cyclicity is 2, 4, 8, 6... units digit = 6
13^13 >> Cyclicity is 3, 9, 7, 1... units digit = 3
0 - (6+3)
= 0 - 9 = 1 at the units place
Answer = 1 = B
Answer: (B) 1
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time W will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did?
(A) 2 minute and 12 seconds.
(B) two minutes.
(C) 44 seconds.
(D) 20 seconds.
(E) 12 seconds.
Rationale: Tom is running alone for 20 seconds.
So he will cover a distance of 20*2.5 = 50 m in 20 seconds=W
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side
D is the answer
Answer: (D) 20 seconds.
Question: What comes next in the series?
1 2 6 24 120 720 ___
(A) 2290
(B) 2020
(C) 5040
(D) 4028
(E) 3920
Rationale: C
5040
Multiply each number by 2, 3, 4, 5 and 6 and (finally) 7.
Answer: (C) 5040
Question: Q:Robert purchased $1000 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
(A) 10
(B) 12
(C) 17
(D) 20
(E) 30
Rationale: I started off with looking at the answer choices... 10-12-17-20 are in a tight range, so my guess was to look and rule out the bigger numbers.
The total amount is $1000. So with 30 bonds, each $50 = $1500 , we already exceed the $1000 limit. Hence E is the answer.
Answer: (E) 30