mathewhe/aqua_rat huggingface dataset:
Question: A, B and C can do a work in 7 , 14 and 21 days respectively. They completed the work and got $242. What is the share of C?
(A) $25
(B) $48
(C) $44
(D) $49
(E) $40
Rationale: C
$44
The ratio of their working rates = 1/7 : 1/14 : 1/21 = 6 : 3 : 2.
Since, they work together, the share of C
= 2/11 * 242 = $44
Answer: (C) $44
Question: How many cubes of 2cm edge can be cut out of a cube of 24cm edge
(A) 1136
(B) 1728
(C) 1216
(D) 1484
(E) None of these
Rationale: Explanation:
number of cubes=(24 x 24 x 24) / (2 x 2 x 2) = 1728
Answer: B
Answer: (B) 1728
Question: Working together at their respective constant rates, Machine A and Machine B can produce 1,800 units in 8 hours. Working alone, Machine B would complete that same output in 50% more time. If Machine A were to work on its own for an 8-hour shift, what percent of the 1,800 unit total would it produce?
(A) 25
(B) 33
(C) 30
(D) 67
(E) 75
Rationale: 1/A+1/B= 1/T
1/A +1/12= 1/8 (50% more of 8 is 12)
1/A= 1/24
Machine A can produce 1800 units in 24 hrs, so it can produce 1800*8/24= 600 units is 8 hrs.
600 is 30% of 1800.
C is the answer
Answer: (C) 30
Question: Set A: {1, 3, 4, 6, 9, 12, 15}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 2?
(A) 3/14
(B) 2/7
(C) 9/14
(D) 5/7
(E) 1/35
Rationale: using probability you can solve: 3/7*2/6*1/5=1/35.
Ans E
Answer: (E) 1/35
Question: A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by f meteres, What is the area of the rug in square meters?
(A) mn - p(m+n)
(B) mn – 2p(m+n)
(C) mn – p^2
(D) (m - p)(n - p)
(E) (m - 2p)(f - 2p)
Rationale: The answer must be E.
Plug in M 100
N 50
f 10.
Answer: (E) (m - 2p)(f - 2p)
Question: A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 10%. Their gross income from sales for one month decreases by what percent?
(A) 1%
(B) 3%
(C) 5%
(D) 7%
(E) 9%
Rationale: Let P be the original price and let x be the number of items sold originally.
The original income is P*x.
After the changes, the income is 0.9P*1.1x = 0.99*(P*x), a decrease of 1%.
The answer is A.
Answer: (A) 1%
Question: If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 2:5
(B) 2:3
(C) 2:8
(D) 2:1
(E) 2:2
Rationale: 5M + 2B = 4(1M + 1B)
5M + 2B = 4M + 4B
1M = 2B
The required ratio of work done by a man and a boy = 2:1
Answer:D
Answer: (D) 2:1
Question: A train 100 meters long completely crosses a 300 meters long bridge in 30 seconds. What is the speed of the train is?
(A) 32 kmph
(B) 48 kmph
(C) 34 kmph
(D) 43 kmph
(E) 40 kmph
Rationale: S = (100 + 300)/30
= 400/30 * 18/5
= 48
Answer:B
Answer: (B) 48 kmph
Question: In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
(A) 200
(B) 210
(C) 220
(D) 250
(E) 360
Rationale: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360
E
Answer: (E) 360
Question: The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly three elements each?
(A) 24
(B) 42
(C) 54
(D) 72
(E) 84
Rationale: nC2 = 36
=> n*(n-1)/2 = 36
=> n = 9
nC3 = 9C3 = 84
So, Answer is E.
Answer: (E) 84
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
(A) 96
(B) 720
(C) 120
(D) 6
(E) 64
Rationale: Consonants = L D N G (4)
Vowels = E A I (3)
No of ways the all vowels can be together is arranged by , -
we can arrange EAI together , this can be done by 3! = 6 ways
Now arrange consonants LNDG
LNDG can arrange in 5! = 120 ways
Required no of ways = 120 * 6
= 720
Ans- B
Answer: (B) 720
Question: Find the number of ways in which four men, two women and a child can sit at a table if the child is seated between two women.
(A) 12
(B) 24
(C) 36
(D) 48
(E) 60
Rationale: The number of arrangements of n distinct objects in a row is given by n!n!.
The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.
We have M, M, M, M, W, W, C --> glue two women and the child so that they become one unit and the child is between women: {WCW}. Now, these 5 units: {M}, {M}, {M}, {M}, {WCW} can be arranged around the table in (5-1)!=4! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 4!*2=48.
Answer: 48. ANSWER:D
Answer: (D) 48
Question: P and Q started a business investing Rs. 54,000 and Rs. 18,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 3:1
(B) 4:3
(C) 5:4
(D) 6:5
(E) 17:4
Rationale: P:Q = 54000 : 18000
= 3:1.
Answer:A
Answer: (A) 3:1
Question: The sum of the two numbers is 13 and their product is 35. What is the sum of the reciprocals of these numbers?
(A) 12/35
(B) 13/35
(C) 35/8
(D) 7/32
(E) None of these
Rationale: Let the numbers be a and b. Then, a+b=13 and ab =35.
a+b/ab=13/35; (1/b+1/a)=13/35
Sum of reciprocals of given numbers=13/35.
Correct Option: B
Answer: (B) 13/35
Question: Three numbers are in the ratio 3 : 4 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 42. Find the third number?
(A) A)54
(B) B)75
(C) C)24
(D) D)46
(E) E)63
Rationale: Let the numbers be 3x, 4x, 8x.
Largest number = 8x.
Smallest number = 3x.
Third number = 4x.
8x + 3x = 4x + 42
7x = 42 =>x=6
4x=24 =>third number is 24.
Answer:C
Answer: (C) C)24
Question: Tough and Tricky questions: Distance/Rate.
On a reconnaissance mission, a state-of-the-art nuclear powered submarine traveled 500 miles to reposition itself in the proximity of an aircraft carrier. This journey would have taken 2.5 hour less if the submarine had traveled 10 miles per hour faster. What was the average speed, in miles per hour, for the actual journey?
(A) 40
(B) 30
(C) 60
(D) 80
(E) 100
Rationale: Say, if speed is 40, 500/40 = 12.5 hrs and 500/50 = 10 hrs (a reduction of 12.5 hr -> Correct answer)
Answer (A)
Answer: (A) 40
Question: When n is divided by 48, the remainder is 6. What is the remainder when 4n is divided by 8?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Let n=6 (leaves a remainder of 6 when divided by 48)
4n = 4(6) =24, which leaves a remainder of 0 when divided by 8.
Answer A
Answer: (A) 0
Question: Each side of a certain parallelogram has length 6. If the area of the parallelogram is 24. Which of the following is the measure of one of its angles?
(A) 30
(B) 42
(C) 60
(D) 90
(E) 120
Rationale: Ans is 30deg
area of a parallelogram = b*h
b*h=24
h=24/6=4
sin theta =opp/hyp= 4/6 = 2/3
theta = sin inv of 2/3=42 deg
B
Answer: (B) 42
Question: In a Quiz the points in each round for the first,second,third and fourth position were 100,50,20,10 . No other points were given. Rachel participated in several rounds in the competition and the product of her score was 10000. In How many rounds did she participate?
(A) 2
(B) Cannot be determined
(C) 4
(D) 6
(E) 10
Rationale: Correct answer is B because we are given that there won't be any points awarded for rounds other than 1st four position.
Thus, it may happen that she played 150 rounds out of only 8 rounds were there in which she was awarded some points.
Answer: (B) Cannot be determined
Question: How many integers less than 100 have exactly 4 odd factors but no even factors?
(A) 11
(B) 13
(C) 15
(D) 17
(E) 19
Rationale: Two cases are possible:
x1y1=xy=odd<100x1y1=xy=odd<100, where xx and yy are odd prime numbers, then # of factors will be (1+1)(1+1)=4(1+1)(1+1)=4;
If x=3, then y can be: 5, 7, 11, 13, 17, 19, 23, 29, 31 - 9 numbers.
If x=5, then y can be: 7, 11, 13, 17, 19 - 5 numbers.
If x=7, then y can be: 11, 13 - 2 numbers.
OR:
x3=odd<100x3=odd<100, where xx is odd prime number, then # of factors will be (3+1)=4(3+1)=4.
x can be only 3 - 1 number.
Total 9+5+2+1=179+5+2+1=17 .
Answer: D.
Answer: (D) 17
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 50 men left the fort. The number of days for which the remaining food will last, is:
(A) 29 1/5
(B) 37 1/4
(C) 42
(D) 5 1/4
(E) 48
Rationale: After 10 days : 150 men had food for 35 days.
Suppose 100 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 100 : 150 :: 35 : x <=> 100 x x = 150 x 35
=> x =150 x 35/100
=> x = 5 1/4.
Correct answer is D
Answer: (D) 5 1/4
Question: If q = 20! + 17, then q is divisible by which of the following?
I. 15
II. 17
III. 19
(A)  None
(B)  I only
(C)  II only
(D)  I and II
(E)  II and II
Rationale: Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.
So q!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer.
Answer: (C)  II only
Question: The average marks scored by Ganesh in English, Science, Mathematics and History is less than 15 from that scored by him in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography scored by him?
(A) 40
(B) 50
(C) 60
(D) Data inadequate
(E) None of these
Rationale: E+H+G+M/4−E+S+M+H/4=15
⇒ G - S = 60
Answer C
Answer: (C) 60
Question: When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 4. If 1 < m < 200, what is the greatest possible value of m?
(A) 47
(B) 65
(C) 103
(D) 117
(E) 173
Rationale: Looking at the choices, options BD can be eliminated as they are divisible by 13
Starting from the highest number 164;
173 = 171 + 2 (171 divisible by 9)
173 = 169 + 4 (169 divisible by 13)
it fits the result
Answer = E
Answer: (E) 173
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum m of all the even integers between 99 and 301?
(A) 10,100
(B) 20,200
(C) 22,650
(D) 40,200
(E) 45,150
Rationale: I would solve it in a different way.
First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101
Average = (301+99)/2 = 400/2 = 200
Sum m= Average*total count = 200*101 = 20,200
Answer is B
Answer: (B) 20,200
Question: A computer can perform x calculations in s seconds. How many minutes will it take the computer to perform k calculations?
(A) 60ks/x
(B) ks/x
(C) ks/60x
(D) 60x/ks
(E) k/60xs
Rationale: As 'thick' as this question might look, it's actually a fairly straight-forward Rate question and can be solved by TESTing VALUES.
We're told that a computer can perform X calculations in S seconds.
Let's TEST....
x = 2
S = 3
2 calculations every 3 seconds =
40 calculations every 1 minute
We're asked how many MINUTES it will take to perform K calculations.
Since we already know that the computer can perform 40 calculations in 1 minute, let's TEST...
K = 80
So we're looking for an answer that = 2 when C = 2, S = 3 and K = 80
Answer A: 60KS/x = 60(80)(3)/2 = 7200 This is NOT a match
Answer B: KS/x = (80)(3)/2 = 120 This is NOT a match
Answer C: KS/60x = (80)(3)/(60)(2) = 2 This IS a match
Answer D: 60x/KS = 60(2)/(80)(3) = 1/2 This is NOT a match
Answer E: K/60xS = 80/(60)(2)(3) = a fraction. This is NOT a match
C
Answer: (C) ks/60x
Question: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 348, the cost of the article is
(A) 289
(B) 231
(C) 200
(D) 40
(E) 111
Rationale: Explanation:
Let C.P. be Rs. x.
Then, 5% of x = 350 - 348 = 2
x/20 = 2 => x = 40
Answer: D
Answer: (D) 40
Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 17 1/7 days
(B) 5 days
(C) 6 days
(D) 9 days
(E) 10 days
Rationale: Explanation:
1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
Answer: A
Answer: (A) 17 1/7 days
Question: Solve below question 2x - 1 = 17
(A) -8
(B) -9
(C) -5
(D) -4
(E) 9
Rationale: 1. Add 1 to both sides: 2x - 1 + 1 = 17 + 1 2. Simplify both sides: 2x = 18 3. Divide both sides by 2: 4. Simplify both sides: x = 9 E
Answer: (E) 9
Question: Car Dealership X, the total profit from sales increased by 15 percent over the previous years, while the number of cars sold decreased by 15 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.
(A) 18%
(B) 20%
(C) 22%
(D) 35.29%
(E) 55%
Rationale: Let Profit be x and cars sold be y
Originally Profit/Car = x/y
Now it is 1.15x / 0.85 y = 115/85 (x/y)
Increase in profit per car = ((30/85) (x/y)) / (x/y) * 100 = 35.29%
Answer = D
Answer: (D) 35.29%
Question: Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 5 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?
(A) 5
(B) 6
(C) 15
(D) 20
(E) 25
Rationale: Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12
Collective work Time = 12/7 = 1.7 Hrs
Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 5 breaks
=.3/5=.06 hrs = 6 m
so Answer is B) 10 mins
Answer: (B) 6
Question: In a G6 summit held at london. A french, a german, an italian, a british, a spanish, a polish diplomat represent their respective countries. (i) Polish sits immediately next to british (ii) German sits immediately next to italian, British or both (iii) French does not sit immediately next to italian (iv) If spanish sits immediately next to polish, spanish does not sit immediately next to Italian Which of the following does not violate the stated conditions?
(A) DKSOO
(B) UDFHD
(C) DKJHIU
(D) FSPBGI
(E) OIHDSD
Rationale: FSPBGI
Answer:D
Answer: (D) FSPBGI
Question: A is thrice as good as B. A is able to finish a job in 60 days less than B.Theycan finish the work in how many days if they work together.
(A) 21 days
(B) 21 ½ days
(C) 22 days
(D) 22 ½ days
(E) 23 ½ days
Rationale: If A completes a work in 1 day, B completes the same work in 3 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> Amount of work B can do in 1 day= 1/90
Amount of work A can do in 1 day = 3 × (1/90) = 1/30
Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45
=> A and B together can do the work in 45/2 days = 22 ½ days
D
Answer: (D) 22 ½ days
Question: If
1 = 6 ,
2 = 12 ,
3 = 18,
4 = 24,
5 = 30,
Then 6 = ?
(A) 5
(B) 3
(C) 1
(D) 7
(E) 9
Rationale: Solution:
1
As stated
1=6 => 6=1
Answer C
Answer: (C) 1
Question: On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every six minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 150%
Rationale: Dolphin once in 3 min;
Beluga once in 6 min;
So, dolphin comes up 2 times frequently than beluga, which is 150% (6-3)/2*100.
Answer: E.
Answer: (E) 150%
Question: There are 8 cars parked in the lot 5 red and 3 blue, James threw two stone at the cars and three of the cars were hit, what is the probability that a stone did not hit any red car provided each stone hit one different car?.
(A) 2/3
(B) 2/5
(C) 5/28
(D) 3/5
(E) 3/28
Rationale: Since there were 5 red cars, the subset from which the 2 car hit should be chosen are the 3 blue cars from the universe of 8,
The first car can be one of the 3 from the 8 with probability 3/8.
The second car can be one of the 2 from the 7 remaining with probability 2/7.
The total probability will be 3/8 × 2/7. On cancellation, this comes to 3/28
Thus, the answer is E - 3/28
Answer: (E) 3/28
Question: The cost price of a radio is Rs.1590 and it was sold for Rs.1450, find the loss %?
(A) 8%
(B) 12%
(C) 10%
(D) 14%
(E) 21
Rationale: 1590 ---- 140
100 ---- ? => 8%
Answer:A
Answer: (A) 8%
Question: A sum of money at simple interest amounts to Rs. 824 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) 500
(B) 698
(C) 780
(D) 910
(E) 725
Rationale: Sol.
S.I. for 1 year = Rs. (854 - 824) = Rs. 30.
S.I. for 3 years = Rs. (30 * 3) = Rs. 90.
âˆ´ Principal = Rs. (815 - 90) = Rs. 725
Answer E
Answer: (E) 725
Question: A driver covers a certain distance by car driving at 60 km/hr and returns back to the starting point riding on a scooter at 15 km/hr. What was the average speed for the whole journey?
(A) 20 km/h
(B) 22 km/h
(C) 24 km/h
(D) 26 km/h
(E) 28 km/h
Rationale: time 1 = d / 60
time 2 = d / 15
total time = d/60 + d/15 = 5d/60 = d/12
average speed = total distance / total time = 2d / (d/12) = 24 km/h
The answer is C.
Answer: (C) 24 km/h
Question: In a class of 250 students, on JAN 2 15% of the girls and 10% of the boys are absent. If on 100% attendance there are 10 boys. Find the percentage present?
(A) 81.2%
(B) 82.2%
(C) 84.2%
(D) 85.2%
(E) 86.2%
Rationale: The reason is explained below:
on 100% attendance,toital no of boys=10
that means there are 240 girls and 10 boys in a class
if 10% boys are absent, then it means that 1 boy is absent
if 15% of girls are absent, then it means that (15/100)*240=36 girls are absent
therefore no of students present=250-(1+36)=250-37=213
% of no of students present=(213/250)*100=85.2%
ANSWER:D
Answer: (D) 85.2%
Question: Calculate 469158 x 9999 = ?
(A) 4586970843
(B) 4686970743
(C) 4691100843
(D) 4586870843
(E) 4691110842
Rationale: Answer
469158 x 9999 = 469157 x (10000-1)
= 4691580000 - 469158
= 4691110842.
Option: E
Answer: (E) 4691110842
Question: If two typists can type two pages in two minutes, how many typists will it take to type 25 pages in five minutes?
(A) 3
(B) 4
(C) 10
(D) 12
(E) 36
Rationale: In 2 minutes 2 typists type 2 pages which means that in 5 minutes they will type 5 pages but to type 25 pages (5 times) we need 5 times more typists i.e. 2 x 5 = 10 typists.
C
Answer: (C) 10
Question: A restaurant meal cost $32.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
(A)  $40 and $42
(B)  $39 and $41
(C)  $38 and $40
(D)  $36 and $38
(E)  $36 and $37
Rationale: The total amount for the meal was between 32.5*1.1=35.75 and 32.5*1.15=37.375. Only option which covers all possible values of the meal is D.
Answer: D.
Answer: (D)  $36 and $38
Question: Tap 'A' can fill the tank completely in 4 hrs while tap 'B' can empty it by 8 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the tapes, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onward, would the tank be full?
(A) 2
(B) 3
(C) 1/2
(D) 1/4
(E) 5
Rationale: Explanation :
Rate of filling tap A = 1/4 per hr
Rate of emptying of tap B = 1/8 per hr
When both the taps remain open, the effective rate of filling
= 1/4 - 1/8 = 1/8 of the tank
Hence in 4 hr, the tank must have been full to the
Extent of 4 x 1/8 = 1/2 Capacity
Remaining volume = 1/2 capacity
Now emptying tap is closed rate of filling would be 1/4 per hr
Time reqd. to fill = Empty volume/Filling rate
= (1/2)/(1/4) = 2 hrs
Answer : A
Answer: (A) 2
Question: A parking garage rents parking spaces for $10 per week or $40 per month. How much does a person save in a year by renting by the month rather than by the week?
(A)  $40
(B)  $160
(C)  $220
(D)  $240
(E)  $260
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 40 = 480$
520 - 480 = 40
Ans A
Answer: (A)  $40
Question: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
(A) 68
(B) 67
(C) 25
(D) 27
(E) 60
Rationale: The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
Answer: E
Answer: (E) 60
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 36.Find the number of notes of Rs.50 denomination.
(A) 15
(B) 21
(C) 17
(D) 19
(E) 21
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 36 - X
Now,
50*X + 500 * (36 - X) = 10350
50X + 18000 - 500X = 10350
- 450X = - 7650
X = 17.
No. of 50 rupees note = 17.
Answer: Option C
Answer: (C) 17
Question: A bowl of fruit contains 10 apples and 23 oranges. How many oranges must be removed so that 50% of the pieces of fruit in the bowl will be apples?
(A)  3
(B)  13
(C)  14
(D)  17
(E)  20
Rationale: Number of apples = 10
number of oranges = 23
let number of oranges that must be removed so that 50% of pieces of fruit in bowl will be apples = x
Total number of fruits after x oranges are removed = 10+(23-x) = 33-x
10/(33-x) = 5/10
=>20 = 33-x
=>x= 13
Answer B
Answer: (B)  13
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along theoundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 143600 m
(B) 145600 m
(C) 153600 m
(D) 154354 m
(E) 156778 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600 m
Question: 20 litres of mixture contains 20% alcohol and the rest water. If 3litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
(A) 16.67%
(B) 23%
(C) 18.3%
(D) 19.75%
(E) 17.4%
Rationale: Alcohol in the 20litres of mix. = 20% of 20litres = (20*20/100) = 4litres
water in it = 20-3 = 17litres
new quantity of mix. = 20+3 = 23 litres
Quantity of alcohol in it = 4litres
Percentage of alcohol in new mix. = 4*100/23 = 17.4%
Answer is E
Answer: (E) 17.4%
Question: The average age of husband, wife and their child 3 years ago was 30 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
(A) 35 years
(B) 49 years
(C) 50 years
(D) 55 years
(E) None
Rationale: Solution
Sum of the present ages of husband, wife and child	= (30x3+3x3) years
= 99 years.
Sum of the present ages of wife and child	= (20x2+5x2) years
= 50 years.
âˆ´ Husband's present age	= (99 - 50) years
= 49 years.
Answer B
Answer: (B) 49 years
Question: Seven white balls and three black balls are randomly placed in a row. Find the probability that no two black balls are placed adjacently to each other.
(A) 7/15
(B) 2/15
(C) 3/7
(D) 2/7
(E) 1/7
Rationale: The total ways of placing seven white balls and three black balls in a row = 10! / 7! / 3! = 120.
The number of ways in which no two black balls are placed next to each other:
Assume that seven white balls are placed in a continuous line with gaps before and after each ball. There are totally 8 such gaps. Out of these 8 gaps, 3 gaps should be chosen in order to place the black balls. There are a total of 8C3 = 56 ways in which this can be done.
Hence, the required probability = 56/120 = 7/15.
ANSWER:A
Answer: (A) 7/15
Question: A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.
(A) 360, 160, 200
(B) 160, 360, 200
(C) 200, 360,160
(D) 200,160,300
(E) None of these
Rationale: Explanation:
let ratio be x.Hence no. of coins be 5x ,9x , 4x respectivelyNow given total amount = Rs.206=> (.50)(5x) + (.25)(9x) + (.10)(4x) = 206we get x = 40=> No. of 50p coins = 200
=> No. of 25p coins = 360
=> No. of 10p coins = 160 Answer: C
Answer: (C) 200, 360,160