mathewhe/aqua_rat huggingface dataset:
Question: Josh and Dan have a 12 apples each. Together they flip a coin 6 times. For every heads, Josh receives an apple from Dan, and for every tails Dan receives an apple from Josh. After the coin has been flipped 6 times, what is the probability that Josh has more than 12 apples but fewer than 18?
(A) 1/64
(B) 15/64
(C) 21/64
(D) 21/32
(E) 5/6
Rationale: minimum number of times to win is 4 to have more than 12 apples .
coz: if he wins 3 times => he gets 3 apples and give 3 apples ; no change
so he needs to win 4 times OR 5 times
Not 6 times because ,
if he wins 6 times => he gets 6 apples and he will have 18 apples
Now number of ways to win 4 times out of 6 times 6C4
Now number of ways to win 5 times out of 6 times 6C5
Total number of ways 2626 ways
Probability =(6C4) + (6C5)/2^6
=21/64
Answer :C
Answer: (C) 21/64
Question: If 4x+y+z=800, 2x-y-z=40,3x+y-z = 12 for integers of x,y and z, find z =?
(A) 250
(B) 464
(C) 525
(D) 256
(E) 324
Rationale: 4x+y+z = 800----------1)
2x-y-z = 40-------------2)
3x+y-z = 12 ------------3)
from 1) and 2)
6x = 840
x = 140 substitute in 1) and 3)
560+y+z = 800
y+z = 240-------4)
420+y-z = 12
y-z = -408-------5)
from 4) and 5)
2z = 648
z = 324
Answer is E
Answer: (E) 324
Question: Bruce and Bhishma are running on a circular track of length 600m. Speed of Bruce is 30 m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same direction. When will they meet again for the first time?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 80
Rationale: Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma, they will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.
Since , they make a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.
D
Answer: (D) 60
Question: 20 marbles were pulled out of a bag of only white marbles, painted black, and then put back in. Then, another 20 marbles were pulled out, of which 1 was black, afterwhich they were all returned to the bag. If the percentage of black marbles pulled out the second time represents their percentage in the bag, how many marbles in total does the bag currently hold?
(A) 40
(B) 200
(C) 380
(D) 400
(E) 3200
Rationale: We know that there are 20 black marbles in the bag and this number represent 1/20 th of the number of all marbles in the bag, thus there are total of 20*20=400 marbles.
Answer: D.
Answer: (D) 400
Question: In an engineering class that contained 100 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 24
Rationale: 1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—100=60
2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(100âˆ’60)=4/5âˆ—40=32
total students who answered at least one Q correct =60+32=92
so students who answered BOTH incorrectly = 100âˆ’92=8
ANSWER:C
Answer: (C) 8
Question: How many multiples of 5 are there between 0 and 358?
(A) 54
(B) 75
(C) 76
(D) 71
(E) 58
Rationale: 5 * 1 = 5
5 * 71 = 355
Total number of multiples = (71 + 1)
= 72
Answer D
Answer: (D) 71
Question: Sachin is older than Rahul by 7 years. If the ratio of their ages is 11:9, find the age of Sachin
(A) 24.5
(B) 24.8
(C) 38.5
(D) 24.88
(E) 24.19
Rationale: Explanation:
If Rahul age is x, then Sachin age is x + 7,
so,
9x + 63 = 11x
2x = 63
x = 31.5
So Sachin age is 31.5 + 7 = 38.5
Answer: C) 38.5
Answer: (C) 38.5
Question: A certain company has budgeted $1320 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $300, how much was the company under budget or over budget?
(A) $60 under budget
(B) $30 under budget
(C) $30 over budget
(D) $60 over budget
(E) $180 over budget
Rationale: The budget for 3 months is (3/12)*$1320 = $330
The company is $30 under budget.
The answer is B.
Answer: (B) $30 under budget
Question: If Rs.460 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) Rs.575
(B) Rs.595
(C) Rs.590
(D) Rs.580
(E) Rs.585
Rationale: 80 = (460*4*R)/100
R = 4.34%
I = (460*6*4.34)/100 = 120
460 + 120 = 580
ANSWER:D
Answer: (D) Rs.580
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12200 after a year?
(A) 3660
(B) 2881
(C) 2887
(D) 9977
(E) 2212
Rationale: 6300:4200:10500
3:2:5
3/10 * 12200 = 3660.Answer: A
Answer: (A) 3660
Question: When N is divided by T, the quotient is S and the remainder is Q. Which of the following expressions is equal to N?
(A) ST
(B) S + V
(C) ST + Q
(D) T(S+V)
(E) T(S – V)
Rationale: Using the rule dividend = Quotient * divisor + remainder =>ST + Q C is correct
Answer: (C) ST + Q
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
(A) 235
(B) 256
(C) 260
(D) 350
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: If n divided by 3 has a remainder of 2, what is the remainder when 2 times n is divided by 3?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 0
Rationale: As per question => N=3P+2 for some integer p
hence 2N => 6Q + 4 => remainder => 1 for some integer Q
hence A
Answer: (A) 1
Question: Population of a city in 2004 was 1000000. If in 2005 there is an increment of 25% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
(A) 967532
(B) 977522
(C) 984424
(D) 997454
(E) 1178125
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 25/100)(1 - 35/100)(1 + 45/100)
= 1178125
E
Answer: (E) 1178125
Question: If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?
A. 38
B. 46
C. 72
D. 86
E. 102
(A) 38
(B) 46
(C) 72
(D) 86
(E) 102
Rationale: Without limitations, 5 children can be seated in 5!=120 ways. Find the number of ways to seat the 5 children so that the siblings DO sit together. The siblings can be regarded as one unit so there are 4! combinations. But within this unit the siblings can sit in two different ways. So the number of ways to seat the 5 children so that the siblings DO sit together is 4!∗2=48. Thus, the number of combinations in which the siblings DO NOT sit together is 120 - 48 = 72.
Answer: C
Answer: (C) 72
Question: In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent S of his family’s total income?
(A)  15%
(B)  17%
(C)  24%
(D)  30%
(E)  33%
Rationale: Lets suppose the Total Family income in Feb = 100x
Wilson's earning in Feb = 40% of 100x = 40x
Earnings of remaining family in Feb = 100x - 40x = 60x
Wilson's earning in March = 75% of Wilson's Feb earnings = 75% of 40x = 30x
Earnings of remaining family in March = Earnings of remaining family in Feb = 60x
Thus Wilson's earning as % of Total family income in March S= 30x/ (30+60)x = 30x/90x = 33.33%
Thus Answer is E
Answer: (E)  33%
Question: If the seller selling his goods with the profit of 200 and profit percentage of the good is 50%, then what is the Cost price of that goods.
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: Explanation:
Profit = 200
Profit% = 50% = (Profit/C.P)*100
C.P = (200*100) / 50 = 400. Answer: C
Answer: (C) 400
Question: A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?
(A) 59
(B) 33
(C) 52
(D) 68
(E) 80
Rationale: A
59
The first 56 balls could be of all colours except red. This would leave 8 balls, all of which are red. so any three chosen would be red.
Answer: (A) 59
Question: In a school of 300 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) 54
(B) 63
(C) 70
(D) 42
(E) 31
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
300 * 18/100 = 54
ANSWER:A
Answer: (A) 54
Question: What percent of 50 is 80?
(A) 133 1⁄3
(B) 75
(C) 160
(D) 33 1⁄3
(E) 25
Rationale: To find out the % of 80 in 50
Do 80/50 = 160%
Answer C)
Answer: (C) 160
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 1/459
(C) 1/458
(D) 1/451
(E) 1/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455
Answer:A
Answer: (A) 1/455
Question: A, B, C hired a car for Rs. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were?
(A) 127
(B) 160
(C) 287
(D) 237
(E) 111
Rationale: A : B : C = 7 : 8 : 11.
Hire charges paid by B = Rs. (520 * 8/26) = Rs. 160.
Answer: B
Answer: (B) 160
Question: A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train, which of the following information is necessary:
(A) Only the length of the train
(B) Only the length of the engine
(C) Either the length of the train or the length of the engine.
(D) Both the length of the train and the length of the engine.
(E) none of these
Rationale: Explanation:
Since the sum of the length of the train and the length of the engine is needed, so both the lengths must be known.
Correct Option : D
Answer: (D) Both the length of the train and the length of the engine.
Question: what is the compound interest on rs:50,000 for 4 months at the rate of 5% per annum
(A) 1058.24
(B) 2006.24
(C) 838.55
(D) 848.55
(E) 858.55
Rationale: it is monthly compound
rate=5/12% per month
50000*(1+5/1200)^4-50000=838.55
ANSWER:C
Answer: (C) 838.55
Question: Diana picked a number of pears, each of which she sold, canned, or poached. If she canned 60 percent more than she poached, and she poached 50 percent less than she sold. If there were a total of 115 pears, then how many pears did she sell?
(A) 41
(B) 44
(C) 47
(D) 50
(E) 53
Rationale: Let x be the amount of pears that she sold.
Then she poached 0.5x.
Then she canned 1.6*0.5x=0.8x.
The total amount of pears is x+0.5x+0.8x=2.3x
The fraction of pears that she sold is 1/2.3=10/23.
The number of pears she sold is (10/23)*115=50.
The answer is D.
Answer: (D) 50
Question: Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 7x-15=10+2x
7x-2x=25
x=5
ANSWER:C
Answer: (C) 5
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
(A) 10
(B) 99
(C) 77
(D) 55
(E) 21
Rationale: 1/6 – 1/15 = 1/10
=> 10
Answer: A
Answer: (A) 10
Question: x =3 4 5
y= 27 36 9 then what is the relation between x and y
(A) 1*X)^2
(B) 1*X)^3
(C) 1*X)^4
(D) 1*X)^5
(E) 1*X)^6
Rationale: Y=(1*X)^2
9=(1*3)^2
9=9
ANSWER:A
Answer: (A) 1*X)^2
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
(A) 8789
(B) 7500
(C) 8392
(D) 8390
(E) 2804
Rationale: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs. 7500
Answer:B
Answer: (B) 7500
Question: 50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what D percent of the apartments with windows have hardwood floors?
(A) 10
(B) 16 2/3
(C) 40
(D) 50
(E) 83 1/3
Rationale: yup you need to construct a matrix
X********| Windows'|No Windows'''| total
hardFl****'|50*****''|10*********'|60
Not hardFl*|10******|30*********'|40
Total*****|60******'|40*********'|100
so D percent of the apartments with windows have hardwood floors = 50/60 *100
= 83 1/3
so E is the answer.[/u]
Answer: (E) 83 1/3
Question: John's lottery get prize on any given day is 1/2. What is the probability that it get prize on 4 out of 7 consecutive days?
(A) 4/7
(B) 3/7
(C) 31/128
(D) 4/28
(E) 35/128
Rationale: using Binomial. theorem
nCr (p)^r (q)^n-r
7C4 (1/2)^4 (1/2)^r
which is 35/128
Answer is E
Answer: (E) 35/128
Question: How many prime numbers between 100 to 150?
(A) 10
(B) 11
(C) 15
(D) 14
(E) 13
Rationale: primes are of the form 6n+1 or 6n-1
Put n=25 ==> 151
for n=26 ==> 157
for n=27 , ==>163
for n=28 , ==> 167
for n =29 ==> 173
for n =30 ==> 179 and 181
for n =31 ==> no prime no.
for n= 32 ==> 191
for n =33 ==> 199
therefore total number of prime numbers = 11
Ans - B
Answer: (B) 11
Question: The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 20 percent of b, what is the value of m/x?
(A) 2/5
(B) 3/4
(C) 4/5
(D) 5/4
(E) 3/2
Rationale: x equals a increased by 25 percent of a => x = a + 25%a = 1.25a
m equals b decreased by 20 percent of b => m = b - 20%b = 0.8b
m/x = 0.8b/1.25a
Putting the value of b/a = 5/4 we get m/x = 4/5
ANSWER:C
Answer: (C) 4/5
Question: 2 is what percent of 50
(A) 2%
(B) 4%
(C) 6%
(D) 8%
(E) None of these
Rationale: Explanation:
2/50 * 100 = 1/25 * 100 = 4 %
Option B
Answer: (B) 4%
Question: If Y = 2Z+1 where Y is an Integer then which of the following is true?
(A) Y is always Odd
(B) Y is always Even
(C) Y is even if Z is a non integer and a multiple of 0.5
(D) Y= 1
(E) Y is a non multiple of 2
Rationale: C
Answer: (C) Y is even if Z is a non integer and a multiple of 0.5
Question: If 2^z is a factor of 27!, which of the following could be the value of z?
I. 22
II. 23
III. 24
(A) I ​ only
(B) II only
(C) I​ and II
(D) I, II, and III
(E) None
Rationale: 27! contains all numbers from 1 to 27. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 13
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 23
The answer is C.
Answer: (C) I​ and II
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
(A) 640
(B) 500
(C) 3000
(D) 1000
(E) 2000
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 â€“ 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
ANSWER A
Answer: (A) 640
Question: A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 200km less in time. Find his speed?
(A) 20km/hr
(B) 30km/hr
(C) 40km/hr
(D) 50km/hr
(E) 60km/hr
Rationale: Let the speed be x km/hr
50x-50* 9/10 *x = 200
50x - 45x = 200
5x = 200
x = 40km/hr
Answer is C
Answer: (C) 40km/hr
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
(A) 153
(B) 150
(C) 143
(D) 141
(E) 89
Rationale: Let x be the original 2-digit number.
If each digit is halved, then the sum of G and H is 3x/2.
Note the sum must be a multiple of 3 and less than 150.
Of these five choices, only 141 satisfies these two conditions.
The answer is D.
Answer: (D) 141
Question: In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
(A) 30,000
(B) 35,000
(C) 37,000
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let the number of applicants be x.Number of eligible candidates	= 95% of x.
Eligible candidates of each other categories	= 15% of (95% of x).
=(15/100×95/100×x)
= 57/400×x.
Therefore, 57/400×x	= 4275
‹=› x =(4275×400 / 57)
‹=› 30000
Answer A
Answer: (A) 30,000
Question: The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum
(A) Rs.17037
(B) Rs.17000
(C) Rs.17276
(D) Rs.170287
(E) Rs.171881
Rationale: Explanation:
The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000
Answer:B
Answer: (B) Rs.17000
Question: A sum of money at simple interest amounts to Rs. 820 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) 647
(B) 718
(C) 654
(D) 847
(E) 976
Rationale: S.I. for 1 year = Rs. (854 - 820) = Rs. 34.
S.I. for 3 years = Rs.(34 x 3) = Rs. 102.
Principal = Rs. (820 - 102) = Rs. 718.
Answer:B
Answer: (B) 718
Question: If the sum of two positive integers is 26 and the difference of their squares is 52, what is the product of the two integers?
(A) 108
(B) 119
(C) 128
(D) 135
(E) 168
Rationale: Let the 2 positive numbers x and y
x+ y = 26 -- 1
x^2 - y^2 = 52
=> (x+y)(x-y)=52 -- 2
Using equation 1 in 2 , we get
=> x-y = 2 -- 3
Solving equation 1 and 3 , we get
x= 14
y= 12
Product = 14*12 = 168
Answer E
Answer: (E) 168
Question: On day one, a store sold 86 cups. On each of the next d days, the company sold 50 cups. If the average daily sales of cups over this time period (including day one) is 53 cups, what is the value of d?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: 86 + 50d = 53(d+1).
3d = 33.
d = 11.
The answer is C.
Answer: (C) 11
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
16 minutes more to walk to work than to ride his bicycle, then x equals
(A) 4
(B) 7
(C) 10
(D) 15
(E) 24
Rationale: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 16 mins or 16*60 secs in 16*60/40 =24 km
ANSWER:E
Answer: (E) 24
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is
(A) 12
(B) 13
(C) 15
(D) 17
(E) 18
Rationale: Explanation:
Let the three integers be x, x+2 and x+4.
Then, 3x = 2(x+4)+3,
x= 11
Therefore, third integer x+4 = 15
Answer: Option C
Answer: (C) 15
Question: A bag contains 23 purple jellybeans, 12 green jellybeans, and 15 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be purple?
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) 46%
Rationale: p = 23 , g=12 , y=15
total = 50
p(purple)=(23/50)*100 = 46% . Ans = E
Answer: (E) 46%
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.25
(B) 7.25
(C) 7.75
(D) 7.35
(E) 8.25
Rationale: Runs scored in the first 10 overs = 10 × 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 40
Run rate needed = 25040=6.25
ANSWER:A
Answer: (A) 6.25
Question: 85 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?
(A) 80 litres
(B) 90 litres
(C) 120 litres
(D) 170 litres
(E) None of these
Rationale: Explanatory Answer
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*85= 113.33 litres.
However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.
i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.
Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*113.33 = 170 litres.
Answer D
Answer: (D) 170 litres
Question: How many ways can 5 friends be arranged around a circular dinner table?
(A) A)24
(B) B)48
(C) C)96
(D) D)120
(E) E)720
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)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
n!n=(n−1)!n!n=(n−1)!.
So, the answer is (5 - 1)! = 4! = 24.
Answer: A.
Answer: (A) A)24
Question: (A% of 3B + B% of A) is equal to ?
(A) A% of B
(B) B% of A
(C) 4% of AB
(D) AB% of 3
(E) None
Rationale: Answer
A% of 3B + B% of A =3AB/100 + AB/100
= 4AB/100 = 4% of AB
Correct Option: C
Answer: (C) 4% of AB
Question: A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate?
(A) 20 years
(B) 28 years
(C) 24 years
(D) 27 years
(E) 57 years
Rationale: 100 ---- 100 --- 10
100 --- 10
--------------------
300 ---- 20 years
Answer:A
Answer: (A) 20 years
Question: In a group of cows and chickens, the number of legs was 12 more than twice the number of heads. The number of cows was:
(A) 6
(B) 7
(C) 10
(D) 12
(E) 14
Rationale: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 12 more than twice the number of heads.
Therefore, 2 × (x + y) + 14 = 4x + 2y.
or, 2x + 2y + 12 = 4x + 2y.
or, 2x + 12 = 4x [subtracting 2y from both sides].
or, 12 = 4x – 2x [subtracting 2x from both sides].
or, 12 = 2x.
or, x = 6 [dividing by 2 on both sides].
Therefore, the number of cows = 6.
Correct Answer:A)6
Answer: (A) 6
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 3 buckles is how many times that of 5 buckles and 6 buttons?
(A) 7/15.
(B) 4/9.
(C) 6/11.
(D) 5/9.
(E) 8/15.
Rationale: 2buttons + 2buckles = 1/3(11buckles + 3buttons)
6buttons + 6buckles = 11buckles + 3buttons
3buttons = 5buckles
Weight of 3buttons and 3buckles = 5buckles + 3buckles = 8buckles
Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles
(3buttons and 2buckles) = x * (6buttons and 5buckles)
8 = x*15
x = 8/15
Answer: E
Answer: (E) 8/15.
Question: Express a speed of 180 kmph in meters per second?
(A) 10 mps
(B) 05 mps
(C) 50 mps
(D) 12 mps
(E) 11 mps
Rationale: C
50 mps
180 * 5/18 = 50 mps
Answer: (C) 50 mps
Question: Hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench. If the total weight of 3 hammers and 4 wrenches is one-third that of 10 hammers and 5 wrenches, then the total weight of one wrench is how many times that of one hammer?
(A) 1/2
(B) 2/3
(C) 1
(D) 3/2
(E) 1/7
Rationale: x be the weight of a hammer and y be the weight of a wrench.
(3x+4y)=1/3*(10x+5y)
3(3x+4y)=(10x+5y)
9x+12y=10x+5y
7y=x
y=x/7
Ans - E
Answer: (E) 1/7
Question: In a bowl, the no. of marbles gets doubled after every minute. if the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled?
(A) 1 hr 48 mins
(B) 1 hr 39 mins
(C) 1 hr 49 mins
(D) 1hr 59 mis
(E) 1 hr 58 mins
Rationale: Correct Answer : D
If you go backward , if the no. of marbles gets doubled after every minute and after two hours. it is filled completely. one minute ago it would be half.
Answer: (D) 1hr 59 mis