mathewhe/aqua_rat huggingface dataset:
Question: A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
(A) 6 %
(B) 6.1 %
(C) 6.2 %
(D) 6.3 %
(E) 6.4 %
Rationale: Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Correct Answer: E)6.4 %
Answer: (E) 6.4 %
Question: he average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 62 kg. What might be the weight of the new person ?
(A) 75 kg
(B) 55 kg
(C) 45 kg
(D) 85 kg
(E) 90 kg
Rationale: Explanation:
Total weight increased = (8 x 3.5) kg = 28 kg.
Weight of new person = (62 + 28) kg = 90 kg.
Answer: E
Answer: (E) 90 kg
Question: 7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.5 ounces and a standard deviation of 0.2 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
(A) Four
(B) Five
(C) Nine
(D) Ten
(E) Eleven
Rationale: Mean = 8.5
Standard Deviation = 0.2
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 8.5+1.5*0.2 = 8.8
and 1.5 standard deviation BELOW the mean = 8.5-1.5*0.2 = 8.2
hence, 5 values fall within 1.5 SD from Mean
Answer: Option B
Answer: (B) Five
Question: Vinoth can complete a painting work in 20 days. Prakash can do the same work in 25 days. They start the work together but Vinoth quit after 3 days of work. How many days are required to complete the remaining painting work by Prakash.
(A) 15.25 days
(B) 16.25 days
(C) 17.25 days
(D) 18.25 days
(E) 19.25 days
Rationale: Vinoth can complete the painting work in one day is 1/20
Prakash can complete the same work in one day is 1/25
Both of them can complete the work in 1/20+ days=9/100( 1/20+1/25)
they must have completed in three days=9/100*3=27/100
Remaining work to be done is by Prakash =1-27/100=73/100
For one work, Prakash can do in 25 days
For 73/100 work, he can do in 73/100*25=73/4days or 18.25 days
ANSWER:D
Answer: (D) 18.25 days
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good
(A) 125/126
(B) 125/129
(C) 125/128
(D) 125/124
(E) 125/121
Rationale: Required probability = 1 - 1/126 = 125/126.Answer:A
Answer: (A) 125/126
Question: If 180/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.
(A) I, II, and III
(B) III only
(C) I and II only
(D) II and III only
(E) I only
Rationale: The largest possible value of x is 36 (the greatest common factor of 180 and 108), and if x=36 then
B
Answer: (B) III only
Question: A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 120 m
(B) 225 m
(C) 300 m
(D) 360 m
(E) 280 m
Rationale: Speed = 54 x	5/18	m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then,	(x + 300)/35	= 15
x + 300 = 525
x = 225 m.Answer: Option B
Answer: (B) 225 m
Question: Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= H.C.F. of 3360, 2240 and 5600 = 1120.
Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
ANSWER IS A
Answer: (A) 4
Question: In a simultaneous throw of two coins, the probability of getting at least one head is
(A) 1/2
(B) 1/3
(C) 2/3
(D) 3/4
(E) 3/5
Rationale: Here S={HH, HT, TH, TT}
Let E = event of getting at least one head = {HT, TH, HH}
Therefore P(E) = n(E)/n(S) = 3/4
Answer D.
Answer: (D) 3/4
Question: Narendra started a business, investing 30000. Six months later, Chandan joined him with 15000. If they make a profit of 20000 at the end of the year, what should be the share of Narendra?
(A) A)Rs.7000
(B) B)Rs.8000
(C) C)Rs.8500
(D) D)Rs.8600
(E) E)Rs.16000
Rationale: The ratio of their investments = 30000 × 12 : 15000 × 6 = 4 : 1.
:. Narendra’s share on profit of Rs.20000 = 20000 × 4/5 = Rs.16000.
E)
Answer: (E) E)Rs.16000
Question: A train 120 m long crosses a platform 120 m long in 6 sec; find the speed of the train?
(A) 144 kmph
(B) 58 kmph
(C) 54 kmph
(D) 94 kmph
(E) 59 kmph
Rationale: D = 120 + 120 = 240
T = 6
S = 240/6 * 18/5 = 144 kmph
Answer: A
Answer: (A) 144 kmph
Question: Find the largest number of four digits which is exactly divisible by 27,18,12,15
(A) 9700
(B) 9710
(C) 9720
(D) 9730
(E) None of these
Rationale: Explanation:
LCM of 27-18-12-15 is 540.
After dividing 9999 by 540 we get 279 remainder.
So answer will be 9999-279 = 9720
Answer: Option C
Answer: (C) 9720
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
(A) three times as much
(B) twice as much
(C) a third as much
(D) half as much
(E) the same
Rationale: et speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer: (B) twice as much
Question: The contents of a certain box consist of 24 oranges and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be oranges?
(A)  24
(B)  26
(C)  30
(D)  46
(E)  50
Rationale: oranges = (oranges + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B.
Answer: (B)  26
Question: A train 250 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 32
(B) 28
(C) 29
(D) 44
(E) 21
Rationale: S = (250 + 300)/45 = 550/45 * 18/5 =44
Answer: D
Answer: (D) 44
Question: A side of an equilateral triangle is tripled. If the previous parameter is 3x, what is the length of one of the sides before it was tripled?
(A) 4x
(B) 3x
(C) 1x
(D) 2x
(E) 6x
Rationale: If the parameter before it was tripled 3x, one of the sides must have been 3x/3. This reduces to 1x. Answer option C.
Answer: (C) 1x
Question: If 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursday, bow much coal will be required for 8 engines, each running 13hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?
(A) 22
(B) 24
(C) 26
(D) 28
(E) None of them
Rationale: Let 3 engines of former type consume 1 unit in 1 hour.
Then, 4 engines of latter type consume 1 unit in 1 hour.
Therefore 1 engine of former type consumes(1/3) unit in 1 hour.
1 engine of latter type consumes(1/4) unit in 1 hour.
Let the required consumption of coal be x units.
Less engines, Less coal consumed (direct proportion)
More working hours, More coal consumed (direct proportion)
Less rate of consumption, Less coal consumed(direct prportion)
Number of engines 9: 8
Working hours	8 : 13 } :: 24 : x
Rate of consumption (1/3):(1/4)
[ 9 x 8 x (1/3) x x) = (8 x 13 x (1/4) x 24 ) = 24x = 624 = x = 26.
Hence, the required consumption of coal = 26 metric tonnes.
Answer is C.
Answer: (C) 26
Question: An individual deposited 20% of 25% of 30% of what he had into his account with a bank. If he deposited Rs.750, how much was he having initially with him before depositing?
(A) Rs.500000
(B) Rs.50000
(C) Rs.5000
(D) Rs.15000
(E) Rs.6000
Rationale: let x amount he has then 20% of 25% of 30% of x=750
so x=50000
ANSWER:B
Answer: (B) Rs.50000
Question: At what angle the hands of a clock are inclined at 15 minutes past 5?
(A) 117/2Â°
(B) 64Â°
(C) 135/2Â°
(D) 145/2Â°
(E) 155/2Â°
Rationale: Apply the formula:
30h-11/2m=Angle
30*5-11/2*15
150-165/2=135/2
ANSWER:C
Answer: (C) 135/2Â°
Question: A man walks a certain distance and rides back in 6 1⁄4h. He can walk both ways in 7 3⁄4h. How long it would take to ride both ways ?
(A) 5 hours
(B) 4 1⁄2 hours
(C) 4 3⁄4 hours
(D) 6 hours
(E) None of these
Rationale: We know that, the relation in time taken with two different modes of transport is
twalk both + tride both = 2 (twalk + tride)
31⁄4 + tride both = 2 × 25⁄4
⇒ tride both = 25⁄2 - 31⁄4 = 19⁄4 = 43⁄4 hours
Answer C
Answer: (C) 4 3⁄4 hours
Question: It is only in the second option we find the sentence A in continuation with the opening sentence D. Sentence A alone explains, why the fear has such enormous effect on the human beings.
(A) 28
(B) 99
(C) 728
(D) 27
(E) 271
Rationale: Answer:B
Answer: (B) 99
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
(A) 266
(B) 500
(C) 287
(D) 26
(E) 281
Rationale: 70 = (P*4*7/2)/100
P = 500
Answer: B
Answer: (B) 500
Question: If x > 1, which of the following decreases as x decreases?
I. x + x^2
II. 1/(2x^2 − x)
III. 1/(x + 1)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: let x= 4 and 3 b old and new values
ST1: x= 4 -> 4+16 = 20
x=3-> 3+9 = 12 ...decreased
ST2:x= 4-> 2*16-4 = 1/28
x=3->2*9-3 = 1/15
increased
St3: x=4-> 1/4 = .25
x=3->1/3 = .33
Ans: A
Answer: (A) I only
Question: the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour. the cyclist 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 cyclist wait until the hiker catches up?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: For the 5 minutes the cyclist continues to overtake the hiker, she is going at 21 miles per hour faster than the hiker.
Once the cyclist stops, the hiker is going at 7 miles per hour while the cyclist is at rest
So the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds. 21/7 * 5 or 15 minutes
Answer is (B)
Answer: (B) 15
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 12 meters, and the interior of tank B has a height of 12 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 80%
(B) 90%
(C) 100%
(D) 110%
(E) 120%
Rationale: The radius of tank A is 12/(2*pi).
The capacity of tank A is 10*pi*144 / (4*pi^2) = 360 / (pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 12*pi*100 / (4*pi^2) = 300 / (pi)
Tank A / Tank B = 360/300 = 12/10 = 120%
The answer is E.
Answer: (E) 120%
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 140 sq.units
(B) 186 sq.units
(C) 176 sq.units
(D) 865 sq.units
(E) 143 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square
= √1225 = 35 units
The radius of the circle
= side of the square
= 35 units Length of the rectangle
= 2/5 * 35
= 14 units
Given that breadth
= 10 units
Area of the rectangle
= lb = 14 * 10
= 140 sq.units
Answer:A
Answer: (A) 140 sq.units
Question: Which of the following is a prime number ?
(A) 33
(B) 81
(C) 93
(D) 97
(E) 95
Rationale: Explanation:
Clearly, 97 is a prime number.
ANSWER IS D
Answer: (D) 97
Question: A man buys an article for $10. and sells it for $30. Find the gain percent?
(A) 25%
(B) 50%
(C) 20%
(D) 150%
(E) 300%
Rationale: C.P. = $10
S.P. = $30
Gain = $20
Gain% = 20/10 *100 = 300%
Answer is E
Answer: (E) 300%
Question: The average age of 19 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?
(A) 9
(B) 71
(C) 85
(D) 92
(E) 90
Rationale: Age of the 15th student = 19*15 - (14*5+16*9) = 285-214 = 71 years
Answer is B
Answer: (B) 71
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.
(A) 208 km
(B) 637 km
(C) 342 km
(D) 300 kilometre
(E) 543 km
Rationale: Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11
=> x/60 + x/50 = 11 => (5x + 6x)/300
= 11 => x = 300 km
Answer:D
Answer: (D) 300 kilometre
Question: What is the probability of getting a sum of 12 when rolling 3 dice simultaneously?
(A) 10/216
(B) 12/216
(C) 21/216
(D) 23/216
(E) 25/216
Rationale: Sum of 12 can be achieved in following ways
6,5,1---Total cases = 3! = 6
6,4,2---Total cases = 3!= 6
6,3,3---Total cases = 3!/2! = 3
5,5,2---Total cases = 3!/2! = 3
5,4,3---Total cases = 3! = 6
4,4,4---Total cases = 3!/3! = 1
Total cases = 25
Probability = 25 * (1/6 * 1/6 * 1/6) = 25/216
ANSWER:E
Answer: (E) 25/216
Question: A sum of Rs.7000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) A)282
(B) B)4550
(C) C)8383
(D) D)8383
(E) E)3284
Rationale: Let A be the amount received at the end of the three years.
A = 7000[1 + 10/100][1 + 20/100][1 + 25/100]
A = 7000 * 1.65
A = Rs.11550
So the interest = 11550 - 7000 = Rs.4550
Answer: B
Answer: (B) B)4550
Question: In how many ways can the letters of the word ASTERIX be arranged in a row so that the vowels appear in alphabetic order?
(A) 800
(B) 820
(C) 880
(D) 960
(E) 840 eight hundred forty
Rationale: three letters can be arranged in 3! ways.
only one combination AEI is required.
7 letters can be arranged in 7! ways.
thus 7!/ 3! * 1 = 840.
Answer: (E) 840 eight hundred forty
Question: There are 3 numbers A, B and C. If A:B = 3/5, B:C = 5/4, C:D = 4/8, then A:D will be?
(A) 1 : 2
(B) 3 : 5
(C) 5 : 7
(D) 6 : 11
(E) 3:8
Rationale: Sol. A : B = 3 : 5, B : C = 5 : 4, C : D = 4 : 8
∴A∶B∶C∶D= 3 : 5:4 : 8
Thus, A : D = 3 : 8
E
Answer: (E) 3:8
Question: If y exceeds x by 28%, then x is less than y by?
(A) 16 2/8%
(B) 16 8/3%
(C) 21 7/8%
(D) 76 2/3%
(E) 17 2/3%
Rationale: X=100	y=128
128------28
100-------? => 21 7/8%
Answer:C
Answer: (C) 21 7/8%
Question: If 14 men do a work in 80 days, in how many days will 20 men do it?
(A) 18 days
(B) 38 days
(C) 42 days
(D) 48 days
(E) 56 days
Rationale: 14 * 80 = 20 * x
x = 56 days
ANSWER:E
Answer: (E) 56 days
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.1446 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
(A) 32200
(B) 41897
(C) 58799
(D) 60000
(E) 62782
Rationale: P(11/10)^4 - P(6/5)^2 = 1446
P = 60000
Answer: D
Answer: (D) 60000
Question: A soccer team played 160 games and won 65 percent of them. How many games did it win?
(A) 84
(B) 94
(C) 104
(D) 114
(E) 124
Rationale: 65% of 160 =x
0.65*160 = x
104=x
answer :C
Answer: (C) 104
Question: If the numerator of a fraction be increased by 15% and its denominator be diminished by 8%, the value of the fraction is 15/16. Find the original fraction ?
(A) 1/2
(B) 3/5
(C) 5/7
(D) 9/11
(E) 3/4
Rationale: Let the original fraction be x/y
Then, 115% of x/92% of y = 15/16
115x/92y = 15/16
x/y = 3/4
Answer is E
Answer: (E) 3/4
Question: A driver goes on a trip of 50 kilometers, the first 25 kilometers at 66 kilometers per hour and the remaining distance at 33 kilometers per hour. What is the average speed of the entire trip in kilometers per hour?
(A) 38
(B) 40
(C) 44
(D) 45
(E) 48
Rationale: The time for the first part of the trip was 25/66 hours.
The time for the second part of the trip was 25/33 hours.
The total time fro the trip was 25/66 + 25/33 = 75/66 = 25/22 hours.
The average speed for the trip was 50 / (25/22) = 44 kph
The answer is C.
Answer: (C) 44
Question: The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 10, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers?
(A) 16
(B) 18
(C) 13
(D) 20
(E) 22
Rationale: We need to find the median which is the third value when the numbers are in increasing order. Since k<m<r<s<t, the median would be r.
The average of the positive integers is 10 which means that in effect, all numbers are equal to 10. If the largest number is 20, it is 10 more than 20. We need r to be maximum so k and m should be as small as possible to get the average of 10. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average. 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s. Since s must be greater than r, r can be 10+3 = 13 and s can be 10+4 = 14.
So r is 13.
Answer (C)
Answer: (C) 13
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number R?
(A) a. 2^96 + 1
(B) b. 2^16 - 1
(C) c. 2^16 + 1
(D) d. 7 * 2^33
(E) e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of R=(a+b) is a factor of (a³ + b³)
Henca A
Answer: (A) a. 2^96 + 1
Question: If the product of 10 integers is negative, at most how many of the integers can be negative?
(A) 2
(B) 3
(C) 4
(D) 9
(E) 6
Rationale: The product of 10 integers is negative
Thus an odd number of integers need to be negative to have a negative product
We are asked at most how many are required.
So, the highest odd integer before 6,i.e. 9
Correct Option : D
Answer: (D) 9
Question: A cistern can be filled in 9 hours but due to a leak at its bottom it takes 10 hours. If the cistern is full, then the time that the leak will take to make it empty will be ?
(A) 20 hours
(B) 19 hours
(C) 90 hours
(D) 80 hours
(E) None of these
Rationale: Explanation:
Part filled without leak in 1 hour = 1/9
Part filled with leak in 1 hour = 1/10
Work done by leak in 1 hour
=1/9−1/10=1/90
We used subtraction as it is getting empty.
So total time to empty the cistern is 90 hours
Option C
Answer: (C) 90 hours
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12 m
(B) 111.19 m
(C) 111.82 m
(D) 113.12 m
(E) 211.12 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Answer: (A) 111.12 m
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 95 m is?
(A) 286 m
(B) 899 m
(C) 200 m
(D) 205 m
(E) 187 m
Rationale: 2(l + 95) = 600 => l
= 205 m
Answer: D
Answer: (D) 205 m
Question: Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,800 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees?
(A) 38,000
(B) 40,000
(C) 42,500
(D) 45,800
(E) 48,500
Rationale: Median is just the value in the middle when you arrange all values in the ascending order
In this question, the 7th value would be the median (Since there are 13 employees)
38, 40, 40, 40, 42.5, 42.5,45.8
So, answer is D.
Answer: (D) 45,800
Question: FOG + FOG + FOG + FOG = 1464.
If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: given,FOG + FOG + FOG + FOG = 1464
4(FOG)=1464
=>FOG=366
Face value of F is:3
Face value of O is:6
Face value of G is:6
so F+O+G=3+6+6=15
ANSWER:E
Answer: (E) 15
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 3 inches wide on each side, the total area would have been (M + 64) square inches. What is the perimeter of the photograph, in inches?
(A) 16
(B) 24
(C) 32
(D) 40
(E) 48
Rationale: Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+6)(y+6)=M and so (2) xy + 6x + 6y + 36 = M+64
Let's subtract equation (1) from equation (2).
4x + 4y + 32 = 64
2x + 2y = 16, which is the perimeter of the photograph.
The answer is A.
Answer: (A) 16
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 65 sec
(B) 30 sec
(C) 87 sec
(D) 88 sec
(E) 55 sec
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer: B
Answer: (B) 30 sec
Question: Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations X of project assignments are possible?
(A) 252
(B) 1,680
(C) 2,340
(D) 362,880
(E) 592,704
Rationale: The ways to select three employees out of 9 for first project = 9C3
The ways to select three employees out of Remaining 6 for Second project = 6C3
Third Project already has the group of three to be assigned to it so need to select that
So total ways to assign 3 employees to each of 3 projects X= 9C3 * 6C3 * 1 = 1,680
Answer: Option B
Answer: (B) 1,680
Question: How many coins of 0.5 dollars each and 0.7 dollars each together make exactly 4.6 dollars?
(A)   1,6
(B)   2,7
(C)   3,5
(D)   4,3
(E)   5,3
Rationale: Straightaway use answer options ( Ignoring the decimal point ) -
(A)  1,6
1*5 + 6*7 => 47 ( Incorrect )
(B)  2,7
2*5 + 7*7 => 59 ( Incorrect )
(C)  3,5
3*5 + 5*7 => 50 ( Incorrect )
(D)  4,3
4*5 + 3*7 => 41 ( Incorrect )
(E)  5,3
5*5 + 3*7 => 46 ( Correct )
Hence answer will be (E)
Answer: (E)   5,3
Question: An investment of d dollars at k percent simple annual interest yields $500 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,000 over a 4 year period?
(A) 2d
(B) (3d)/4
(C) (4d)/3
(D) (3d)/2
(E) (8d)/3
Rationale: 500 dollars in 2 years means 250 dollars in 1 year.
To get 2000 dollars' it will take 8 years.
To get 2000 in 4 years, we need 8/4 =2 times money. Answer is A
Answer: (A) 2d
Question: The price of a jacket is reduced by 35%. During a special sale the price of the jacket is reduced another 10%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
(A) 70.9
(B) 75
(C) 48
(D) 65
(E) 67.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 35% , therefore bringing down the price to $65.
3) Again it is further discounted by 10%, therefore bringing down the price to $58.5
4) Now 58.5 has to be added byX %in order to equal the original price.
58.5 + ( X% ) 58.5 = 100.
Solving this eq for X, we get X = 70.9
Ans is A.
Answer: (A) 70.9