mathewhe/aqua_rat huggingface dataset:
Question: The Racing magic takes 90 seconds to circle the racing track once. The Charging bull makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Time taken by Racing magic to make one circle = 90 seconds
Time taken byCharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds
LCM of 90 and 90 seconds = 90 seconds
Time taken for them to meet at the starting point for the second time =2*90 sec=180 seconds = 3 mins
Answer A
Answer: (A) 3
Question: How many strings of 6 letters can be made using only the letters A, B, and C, or only the letters D, E, and F ?
(A) 2×3^6
(B) 3×2^6
(C) 3×3^6
(D) 2×2^6
(E) 6^6
Rationale: 3^6 + 3^6 = 2*3^6
ANS : A
Answer: (A) 2×3^6
Question: 10 men and 15 women together can complete a work in 7 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
(A) 127 days
(B) 667 days
(C) 177 days
(D) 187 days
(E) 350 days
Rationale: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/7
15 women's 1 day work = (1/7 - 10/100) = 3/70
1 woman's 1 day work = 1/350
1 woman alone can complete the work in 350 days.
Answer:E
Answer: (E) 350 days
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 76% of the required amount. What is the net difference in the expenditure on that product?
(A) 12.5%
(B) 13%
(C) 5%
(D) 17%
(E) 19%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.76 x 1.25 = 0.95
Decrease in price = (0.05/1) × 100 = 5%
C)
Answer: (C) 5%
Question: The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on $4000 for 2 years at 10% per annum. The sum placed on simple interest is ?
(A) $1250
(B) $1300
(C) $1750
(D) $2015
(E) $1452
Rationale: C.I. = 4000* (1 + 10/100)^2 - 4000 = 4000* 11/10 * 11/10 -4000 = $840
Sum = 420*100/3*8 = $1750
Answer is C
Answer: (C) $1750
Question: In year Y imported machine tools accounted for 50 percent of total machine-tools sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 10x
(B) 12x
(C) 15x
(D) 17x
(E) 20x
Rationale: Sales of imported tools = 50% of the total sales = 0.50*{total} = {total}/2;
Sales of Japanese tools = 40% of the sales of imported tools = 0.40*{total}/4 = 4/10*{total}/4 = total}/10.
Since the sales of of Japanese tools was x, then {total}/10 = x --> {total} = 10x
Answer: A
Answer: (A) 10x
Question: one prototyping machine can make 10 copies every 4 seconds. At this rate, How many copies
can the machine make in 6 min.?
(A) 900
(B) 600
(C) 360
(D) 240
(E) 150
Rationale: 10 copies--4 sec
10/4 copies--1 sec
(10/4)*6*60---1*6*60 sec
900 copies--6 min
ANSWER:A
Answer: (A) 900
Question: How many integers N are prime numbers in the range 200 < N < 220?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: To test a number N on whether it is a prime number , take square root(N) .
Consider as it is if it is a natural number. Otherwise, increase the sq. root to the next natural no.
Then divide given no. by all prime numbers BELOW the sq. root obtained.
If the no. is divisible by any of the prime numbers, then it is not a prime number; else it is.
Square root of 200 or 220 is less than 15
So, lets check if any number between 200 and 220 is not divisible by prime numbers 2,3,5,7,11(<15). That's it.
Out: 201, 202, 203, 204, 205, 206, 207, 208, 209, 210,
212, 213, 214, 215, 216, 217, 218, 219
Only 211 is a prime number in the given range
Correct Option : A
Answer: (A) 1
Question: In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 15P pots?
(A) 4/M
(B) 4M
(C) 900M
(D) M/900
(E) M/4
Rationale: The time it takes to wash 15P pots is 15M minutes which is 15M / 60 = M/4 hours.
The answer is E.
Answer: (E) M/4
Question: What is the diffference between the place value and face value of 2 in the numeral 6328?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: place value of 2 = 2 * 10 = 20
face value of 2 = 2
20 - 2 = 18
E
Answer: (E) 18
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
(A) 8 PM
(B) 4 PM
(C) 7 PM
(D) 5 PM
(E) 2 PM
Rationale: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer: D
Answer: (D) 5 PM
Question: 20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 9:10 in the morning?
(A) 32.
(B) 36.
(C) 42.
(D) 46.
(E) 50.
Rationale: @ 6:30 - 2
@ 7 - 4+7 =11
@ 7:30 - 2
@ 8 - 12
@ 8:30 - 2
@ 9 - 13
totals to 42=C
Answer: (C) 42.
Question: The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 80 percent of the pollutant?
(A) $500,000
(B) $100,000
(C) $50,000
(D) $10,000
(E) $5,000
Rationale: Cost to remove 90% - Cost to remove 80% = 100,000*90/(100 - 90) - 100,000*80/(100 - 80) = 9*100,000 - 4*100,000 = 5*100,000 =500,000
Answer: A
Answer: (A) $500,000
Question: If y ≠ 3 and 3x/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 III
Rationale: There are other possibilities here: 3 might be a factor of y, and might therefore cancel in the fraction, leaving us with a prime that comes from the factors of x. For example, if x = 10, and y = 6, then 3x/y = 5. So we can see that none of I, II, or III need to be true
ANSWER:A
Answer: (A) None
Question: A and B together can complete work in 10 days. A alone starts working and leaves it after working for 6 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
(A) 4
(B) 8
(C) 5
(D) 6
(E) 30
Rationale: Explanation:
(A+B) one day work =1/10
now A does half of the work in 6 days so A can complete the whole work in 12 days
A’s one day work =1/12
B’s one day work=1/10 - 1/12= 2/120= 1/60
B alone can complete the work in 60 days so half of the work in 30 days
Answer: Option E
Answer: (E) 30
Question: Find the odd man out
2, 5, 10, 17, 26, 37, 50, 64
(A) 50
(B) 26
(C) 64
(D) 27
(E) 17
Rationale: Difference is series of ODD numbers
2+3 = 5
5+5 =10
10+7=17
17+9=26
26+11=37
37+13=50
50+15=65
ANSWER:C
Answer: (C) 64
Question: The speeds of three motor bikes are in the ratio 12 : 4 : 2. The ratio between the time taken by them to travel the same distance is :
(A) 1 : 3 : 4
(B) 1 : 3 : 6
(C) 1 : 2 : 6
(D) 1 : 3 : 5
(E) 1 : 4 : 6
Rationale: Ratio of time taken :
1/12 :1/4 : 1/2 = 1 : 3 : 6
ANSWER:B
Answer: (B) 1 : 3 : 6
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 40. He was allowed to drop his lowest score. After doing so, his average test score improved to 45. What is the lowest test score that was dropped?
(A) 20
(B) 25
(C) 55
(D) 65
(E) 80
Rationale: The arithmetic mean of 4 equally weighted tests was 40. So what we can assume is that we have 4 test scores, each 40.
He dropped his lowest score and the avg went to 45. This means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 40.
So the lowest score = 40 - 15 = 25
Answer (B)
Answer: (B) 25
Question: If x+|x|+y=4 and x+|y|-y=6 what is x+y=?
(A) 11
(B) -1
(C) 3
(D) 5
(E) 13
Rationale: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.
If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).
Answer: C.
Adding both eqn we get 2x +IxI+IyI = 13
Now considering X <0 and y>0
2x-x +y = 13
we get x+y =11
Hence answer should be A
Answer: (A) 11
Question: Bob is about to hang his 8 shirts in the wardrobe. He has four different styles of shirt, two identical ones of each particular style. How many different arrangements are possible if no two identical shirts are next to one another?
(A) 764
(B) 864
(C) 964
(D) 1064
(E) None of these
Rationale: Explanation :
Total number of 8-perms of 8 shirts, recognising identical pairs, is:=8!2!4=2520In order to find the number of perms with no adjacency we subtract from this the number of perms with 4 pairs adjacent, 3 pairs adjacent, 2 pairs adjacent and 1 pair adjacent.The following four intermediate results aid explanation of the final calculation :Let the shirts be called A, A, B, B, C, C, D, D and let {A,.....} be the set of 8-perms that have only the styles named in the argument list adjacent to each other. So, for instance, {B,D} is the set of perms that contain BB and DD but not AA and CC. Let s{A,....} be the number of perms in {A,...}(i) s{A,B,C,D} = 24. This is because we can imagine each pair as one object and simply permute the four twin objects amongst themselves in 4! ways to give {A,B,C,D}.(ii) s{A,B,C} = 36. To see this we first permute the 5 objects AA, BB, CC, D, D. This can be done in5!2!=60 ways but includes {A,B,C,D}. Hence s{A,B,C} =5!2!−24(iii) s{A,B}=84. As before, we first permute the 6 objects AA, BB, C, C, D, D. This can be done in 6!/(2!)^2 ways but includes {A,B,C}, {A,B,D} and {A,B,C,D}.Hence s{A,B} =6!2!2–2×36−24(iv) s{A}=246. This time we start by permuting the 7 objects AA, B, B, C, C, D, D in7!2!3ways and then removing from it the subsets {A,B}, {A,C}, {A,D}, {A,B,C}, {A,B,D}, {A,C,D} and {A,B,C,D}. Hence s{A}=7!2!3−3×36−3×84–24Assembling the total number of perms with some adjacency:There are 4C4 subsets of type (i) ie {A,B,C,D}Total number of 8-perms of this type is 24.There are 4C3 subsets of type (ii) ie {A,B,C} {A,B,D} {A,C,D} {B,C,D}Total number of 8-perms of this type is 4×36=144There are 4C2 subsets of type (iii) ie {A,B} {A,C} {A,D} {B,C} {B,D} {C,D}Total number of 8-perms of this type is 6×84=504Finally there are 4C1 subsets of type (iv) ie {A} {B} {C} {D}Total number of 8-perms of this type=4×246=984Therefore, number of perms with some adjacency is 24+144+504+984=1656Number of perms with no adjacency is 2520−1656= 864
Answer : B
Answer: (B) 864
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 128.9 m
(B) 127.5 m
(C) 812.9 m
(D) 127.7 m
(E) 712.7 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs
= (900 * 700)/800
= 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5)
= 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 * 212.5)/1000 = 127.5 m.
Answer: B
Answer: (B) 127.5 m
Question: If the area of a circle decreases by 25%, then the radius of a circle decreases by
(A) 13%
(B) 18%
(C) 36%
(D) 64%
(E) None of these
Rationale: If area of a circle decreased by x % then the radius of a circle decreases by
(100−10√100−x)%=(100−10√100−25)%
= (100−10√75)%
= 100 - 87 = 13%
Answer A
Answer: (A) 13%
Question: A and B complete a work in 50 days. A alone can do it in 40 days. If both together can do the work in how many days?
(A) 1.075 days
(B) 0.185 days
(C) 0.065 days
(D) 0.045 days
(E) 0.0775 days
Rationale: 1/50 + 1/40 = 0.045 days
ANSWER:D
Answer: (D) 0.045 days
Question: Three dice are thrown together, Find the probability of getting a total of atmost 6?
(A) 1/3
(B) 1/8
(C) 3/13
(D) 2/25
(E) 5/54
Rationale: Three different dice are thrown at the same time.
Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.
Number of events of getting a total of atmost 6 = 20
i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1), (1, 2, 2), (1, 1, 4), (1, 4, 1), (4, 1, 1), (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1) and (2, 2, 2).
Therefore, probability of getting a total of atmost 6
P(E) = Number of favorable outcomes/Total number of possible outcome
= 20/216
= 5/54
Answer: (E) 5/54
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 287
(B) 350
(C) 828
(D) 277
(E) 122
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: B
Answer: (B) 350
Question: Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5 ?
(A) 3: 4
(B) 4 : 3
(C) 9 : 7
(D) 7 : 9
(E) 8 : 1
Rationale: Explanation:
Let Cost Price(CP) of 1 litre spirit be Rs.1
Quantity of spirit in 1 litre mixture from vessel A =5/7
Cost Price(CP) of 1 litre mixture from vessel A = Rs. =5/7
Quantity of spirit in 1 litre mixture from vessel B =7/13
Cost Price(CP) of 1 litre mixture from vessel B =Rs. =7/13
Quantity of spirit to be obtained in 1 litre mixture from vessel C =8/13
Cost Price(CP) of 1 litre mixture from vessel C(Mean Price) = Rs. =8/13
=> Mixture from Vessel A : Mixture from Vessel B
=1/13:9/91 =7:9
Answer IS D
Answer: (D) 7 : 9
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 4,500, how much money did investors B and C earn in total?
(A) $4,000
(B) $4,900
(C) $5,600
(D) $9,500
(E) $13,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 34500
5x = 4500=>x=900
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x = 15*900 = 13,500
Answer E
Answer: (E) $13,500
Question: The salary of A, B, C, D, E is Rs. 8000, Rs. 5000, Rs. 15000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
(A) Rs. 7000
(B) Rs. 8000
(C) Rs. 8800
(D) Rs. 9000
(E) None
Rationale: Answer
Average salary
= 8000 + 5000 + 15000 + 7000 + 9000 / 5
= Rs. 8800
Correct Option: C
Answer: (C) Rs. 8800
Question: x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 9 will be equal to:
(A) 3
(B) 6
(C) 1/9
(D) 1/3
(E) 9
Rationale: Explanation :
Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.
.'. x = 9/y^2
=> x =9 /9^2 = 1/9
Answer : C
Answer: (C) 1/9
Question: What amount does Kiran get if he invests Rs. 16000 at 15% p.a. simple interest for four years?
(A) Rs. 25800
(B) Rs. 15600
(C) Rs. 21600
(D) Rs. 24800
(E) Rs. 25600
Rationale: Simple interest = (16000 * 4 * 15)/100 = Rs. 9600
Amount = P + I = 16000 + 9600 = Rs. 25600
ANSWER:E
Answer: (E) Rs. 25600
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
(A) 3.5
(B) 4.5
(C) 5.6
(D) 6.5
(E) None of these
Rationale: Explanation :
C.P. of 1 dozen of toys = Rs. 375
So, C.P. of 1 toy = Rs. 375/12 = Rs. 125/4
S.P. of 1 toy = Rs. 33
Profit = Rs. 33 - (125/4) = Rs. 7/4
% Profit = 7/4∗4/125∗100%= 5.6%
Answer : C
Answer: (C) 5.6
Question: At 30 minutes past 8 o'clock, what is the angle between the two hands?
(A) 15
(B) 30
(C) 45
(D) 60
(E) 75
Rationale: The hour hand moves 360 degrees in 12 hours.
The hour hand moves 30 degrees in 1 hour and 15 degrees in 30 minutes.
The minute hand moves 360 degrees in 60 minutes and 180 degrees in 30 minutes.
At 30 minutes past 8, the hour hand has moved 255 degrees.
At 30 minutes past 8, the hour hand has moved 180 degrees.
The angle between the two hands is 75 degrees.
The answer is E.
Answer: (E) 75
Question: I. m-14, m, m, m, m+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c
The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?
(A) I, II, III
(B) I, III, II
(C) II, III, I
(D) III, I, II
(E) III, II, I
Rationale: S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of m or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end.
A.
Answer: (A) I, II, III
Question: A certain office supply store stocks 2 sizes of self-stick notepads, each in 5 colors. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 6
(B) 8
(C) 16
(D) 20
(E) 30
Rationale: Notepads of the same color = 5 (we have 5 colors). As we have two sizes then total for the same color=5*2=10
Notepads of the different colors = 5C3=10 (we should choose 3 different colors out of 5). As we have two sizes then total for the different color=10*2=20
Total=10+20=30
Answer: E.
Answer: (E) 30
Question: City X has a population 8 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
(A) 1:8
(B) 1:4
(C) 2:1
(D) 4:1
(E) 16:1
Rationale: x= 8y, y= 2*z
X : Y , Y : Z
8 : 1 , 2 : 1
16 : 2 , 2 : 1
So, X : Z = 16 : 1
(E)
Answer: (E) 16:1
Question: Diana is painting statues. She has 7/8 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint?
(A) 10
(B) 20
(C) 28
(D) 14
(E) 19
Rationale: number of statues=all the paint÷amount used per statue
=7/8 ÷ 1/16
=7/8*16/1
=112/8
=14.
Answer is D.
Answer: (D) 14
Question: If the area of a circle is 49pi square feet, find its circumference.
(A) 14 pi feet
(B) 43 pi feet
(C) 42 pi feet
(D) 18 pi feet
(E) 64 pi feet
Rationale: The area is given by pi * r * r. Hence
pi * r *r = 491 pi
r *r = 49 ; hence r = 7 feet
The circumference is given by
2 *pi *r = 2 * pi * 7 = 14 pi feet
correct answer A
Answer: (A) 14 pi feet
Question: If m = ||n – 3| – 2|, for how many values of n is m = 5?
(A) 5
(B) 4
(C) 2
(D) 3
(E) 1
Rationale: m = ||n – 3| – 2| can be 4 only and only when n-3= +/-7. so there are 2 values of n
Answer : C
Answer: (C) 2
Question: The product of all the prime numbers less than 14 is closest to which of the following powers of 10 ?
(A)  10^4
(B)  10^8
(C)  10^7
(D)  10^6
(E)  10^5
Rationale: P = 2*3*5*7*11*13
= 21 * 11 * 13*10
~ 10^ 4
Answer : A
Answer: (A)  10^4
Question: In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 85% of the total?
(A) 515.
(B) 545.
(C) 606.
(D) 644.
(E) 666.
Rationale: Answer is C :606
Solution : Total number of students studying both are 423 + 226 - 134 = 515 (Subtracting the 134 since they were included in the both the other numbers already).
So 85% of total is 515, so 100% is approx. 606.
Answer: (C) 606.
Question: A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is?
(A) A
(B) B
(C) C
(D) D
(E) ALL
Rationale: Answer: Option C
Let b = 100
a = 50
c * (150/100) = 50
3c = 100
c = 33.3 then 'c' cheapest
Answer: (C) C
Question: How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 8?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: The numbers should be of the form 8c+3.
The minimum is 3 when c=0.
The maximum is 43 when c=5.
There are six such numbers.
The answer is B.
Answer: (B) 6
Question: In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turnon to be white, if all possible hypothesis concerning thecolor of theballs that initiallyin the bag were equally possible ?
(A) 2/3
(B) 5/8
(C) 3/5
(D) 3/8
(E) 4/9
Rationale: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
Answer: (B) 5/8
Question: The sale price Mobiles listed for Rs.8000 after successive discount is 20% and 10% is?
(A) 5670
(B) 5560
(C) 5770
(D) 5660
(E) 5760
Rationale: 8000*(80/100)*(90/100)
= 5760
Answer: E
Answer: (E) 5760
Question: The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
(A) 18
(B) 19
(C) 21
(D) 22
(E) 27
Rationale: 5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27
E
Answer: (E) 27
Question: For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 6 of whom are females, by how much does the index for the females exceed the index for the males in the group?
(A)  0.4
(B)  0.0625
(C)  0.2
(D)  0.25
(E)  0.6
Rationale: Index for females = (20-6)/20 = 7/10 = 0.7
Index for males = (20-14/20 = 3/10 = 0.3
Index for females exceeds males by 0.7 - 0.3 = 0.4
Answer: A
Answer: (A)  0.4
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 12 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 120%
(D) 96%
(E) 138%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,12 = 12/100
x= 80*12/100
x= 9.6
9.6/10 = 0.96 = 96%, Answer D
Answer: (D) 96%
Question: What must be added to each term of the ratio 4 : 15, so that it may become equal to 3 : 4?
(A) 18
(B) 29
(C) 39
(D) 49
(E) 59
Rationale: Let x be added to each term of the ratio 4:15.
New ratio becomes (4+x)/(15+x), which is given to be equal to 3:4.
This means,
(4+x)/(15+x)=3/4
Solving we get, x = 29.
Ans B
Answer: (B) 29
Question: The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 80 percent of the pollutant from the pond than it would cost to remove 80 percent of the pollutant?
(A)  0
(B)  $100,000
(C)  $50,000
(D)  $10,000
(E)  $5,000
Rationale: To remove 80% of pollutant
C= 100,000(80)/(100-80) = 400,000
To remove 80% of pollutant
C' = 100,000(80)/(100-80) = 400,000
Difference = C - C'=0
Answer - A
Answer: (A)  0
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 10 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
(A) 3 1/5min
(B) 3 2/5min
(C) 3 3/5min
(D) 3 3/4min
(E) 3 min
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(1/10+1/6)=(8/30) = (4/15)
So both punctures will make the type flat in
(15/4)mins=3 3/4mins
Option D
Answer: (D) 3 3/4min