mathewhe/aqua_rat huggingface dataset:
Question: Two trains start from A & B and travel towards each other at
speed of 70kmph and 80kmph resp. At the time of the meeting the
second train has traveled 200km more than the first.the distance
between them.
(A) 2500 km
(B) 3000 km
(C) 3500 km
(D) 4000 km
(E) 4500 km
Rationale: Let the distance traveled by the first train be x km
then distance covered by the second train is x + 200km
x/70 = x+200 / 80
x= 1400
so the distance between A & B is x + x + 200 = 3000 km
Answer is B.
Answer: (B) 3000 km
Question: In a particular city there are 100 homes numbered from 1,2,3,..,100. The city was build by a builder from Chennai. There was 4 to 5 shops in the town which was build by a builder from Mumbai. The 2nd builder can build in 1½ times as compared to time by 1st builder. The 2nd builder builds in 15 days, then how many 2's are used by the builder from Chennai in
numbering the 100 homes?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: in the last line it should be given
the builder from Chennai in numbering the 100 homes?
then ans is 20
ANSWER:D
Answer: (D) 20
Question: A container has 40L milk. 4L milk is taken out and replaced with water, the process done three times. What is the amount of milk now left?
(A) 29.16L
(B) 29.19L
(C) 29.12L
(D) 29.11L
(E) 29.14L
Rationale: Explanation:
In regard to the problem let after n times liquid in the container is x and liquid removed is y
=>Liquid in container= x
=>Liquid removed= y
After one trial, quantity of pure liquid= x- (1-y/x)
After n trials quantity of pure liquid = x - (1 -y/x)n
Therefore, Putting the values ( x = 40L y = 4L N=3) and solving
=> 40- (1-4/40)3
= 29.16L
ANSWER:A
Answer: (A) 29.16L
Question: An outlet pipe can empty 3/4 of a cistern in 12 minutes. In 4 minutes, what part of the cistern will be emptied?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: 4/12 * 3/4 = 1/4
The answer is C.
Answer: (C) 1/4
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
(A) 14020
(B) 11289
(C) 68928
(D) 14000
(E) 16881
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000
= 14000
Answer: D
Answer: (D) 14000
Question: Which voltage source converts chemical energy to electrical energy?
(A) 23
(B) 39
(C) 27
(D) 98
(E) 72
Rationale: Answer: Option B
Answer: (B) 39
Question: A and B can do a work in 8days, B and C can do it in 12days; A,B and C together can finish it in 6days. A and C together will do it in?
(A) 8days
(B) 10days
(C) 12days
(D) 7days
(E) 5days
Rationale: A+B+C 1day work = 1/6
A+B 1day work = 1/8
B+C 1day work = 1/12
A+C 1day work = 2*1/6 - 1/8+1/12 = 1/3 - 5/24 = 3/24 = 1/8
A and C together will do the work in 8 days.
Answer is A
Answer: (A) 8days
Question: What percent is 2 minutes 24 seconds of an hour?
(A) 6%
(B) 8%
(C) 4%
(D) 2%
(E) 9%
Rationale: 2mt 24s =144s
(144*100)/(60*60)=4%
ANSWER:C
Answer: (C) 4%
Question: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
(A) 65
(B) 80
(C) 85
(D) 82
(E) 89
Rationale: Speed = (240/24)m/sec = 10 m/sec.
Therefore, Required time = (240 + 650)/10 sec
= 89 sec.
Answer is E.
Answer: (E) 89
Question: The total of the ages of Mahesh, Suresh, Ramesh is 93 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?
(A) 32years
(B) 38years
(C) 42years
(D) 35years
(E) 30years
Rationale: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x
2x+10 + 3x+10 +4x+10 = 93
x = 7
Ramesh present age = 4*7+10 = 38 years
Answer is B
Answer: (B) 38years
Question: The cost price of a radio is Rs.1390 and it was sold for Rs.890, find the loss %?
(A) 18%
(B) 12%
(C) 22%
(D) 35%
(E) 21%
Rationale: 1390 ---- 500
100 ---- ? => 35%
Answer:D
Answer: (D) 35%
Question: Jack and Jill went up and down a hill. They started from the bottom and Jack
met jill again 20 miles from the top while returning. Jack completed the race
1 min a head of jill. if the hill is 440 mts high and their speed while down
journey is 1.5 times the up journey. how long it took for the Jack to
complete the race ?
(A) 10.6 min
(B) 11.6 min
(C) 12.6 min
(D) 13.6 min
(E) 14.6 min
Rationale: Let speed and time of Jack be s1 & t1 & Jill having s2 & t2.
Time taken for Jack to travel 440 miles up and 20 miles down
= Time taken for Jill to travel 440-20=420 miles up
440/s1 + 20/1.5s1 = 420/s2
68/1.5s1= 420/s2
68s2= 63s1
s2 = 63s1/68 ---(1)
Now from the second given condition- Jack reaches 1 min before Jill. So
t2-t1=1
880/s2 - 880/s1 = 1
1/s2 - 1/s2 = 1/880
from equation (1) put value of s2
Solving and putting value of s1 in t1=d/s1 (d=880)
t1 = 12.6 min
ANSWER:C
Answer: (C) 12.6 min
Question: The S.I. on a certain sum of money for 5 years at 6% per annum is half the C.I. on Rs. 3000 for 2 years at 15% per annum. The sum placed on S.I. is?
(A) 1525.2
(B) 1256.3
(C) 1612.5
(D) 1548.5
(E) 1254.5
Rationale: C.I. = [3000 * (1 + 15/100)2 - 3000]= (3000 * 23/20 * 23/20 - 3000) = Rs. 967.5.Sum = (483.75 * 100)/(5 * 6)= Rs.1612.5Answer:C
Answer: (C) 1612.5
Question: If 18 is 15 percent of 20 percent of a certain number, what is the number?
(A) 9
(B) 36
(C) 40
(D) 600
(E) 400
Rationale: Let the certain number be x.
=> (15/100)*(20/100)*x = 18;
300x=18*10000;
3x = 1800;
x=1800/3
=> x=600;
Ans is (D).
Answer: (D) 600
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 67
(B) 68
(C) 26
(D) 11
(E) 21
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer:B
Answer: (B) 68
Question: Avg cost of 3 apples and 5 bananas isRs. 40.The avg cost of 5 apples and 8 bananas is Rs.65.Find the total cost of 15 apples and 15 bananas?
(A) 75
(B) 90
(C) 80
(D) 130
(E) 110
Rationale: Avg cost of 3 apples and 5 bananas is Rs. 40
(3 apple + 5 bananas) 8=40
therefore 1 apple cost is 40/8=5, so 3 apple cost is 3x5=15 and 5 bananas cost is 5x5=25
Again, avg cost of 5 apples and 8 bananas is Rs.65
(5 apple + 8 bananas) 13=65
therefore 1 apple cost is 65/13=5, so 5 apple cost is 5x5=25 and 8 bananas cost is 8x5=40
So 15 apple cost is (15/a)=75 and 15 bananas cost is (15x5)=75
ANSWER:A
Answer: (A) 75
Question: An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid only Rs. 3894. For how many days was he absent?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: HCF of 4956, 3894 = 354
(4956 - 3894)/354 = 3
ANSWER:A
Answer: (A) 3
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
(A) 37 ½ days
(B) 22 days
(C) 31 days
(D) 22 days
(E) 21 days
Rationale: Explanation :
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
Answer : A
Answer: (A) 37 ½ days
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 17.66%
(D) 17.98%
(E) 18%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: (B) 16.66%
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 6 years?
(A) 14300
(B) 29859
(C) 14500
(D) 14600
(E) 15400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100^6 = 29859
B)
Answer: (B) 29859
Question: A book is bought for Rs.675 and sold for Rs.900, find the profit percentage?
(A) 30 %
(B) 33%
(C) 33 1/3%
(D) 40%
(E) 45%
Rationale: 675--->225
100--> 33 1/3%
ANSWER C
Answer: (C) 33 1/3%
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 25
(C) 27
(D) 29
(E) 30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 80
(B) 90
(C) 95
(D) 98
(E) 100
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
B
Answer: (B) 90
Question: Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/3 of capacity in 6 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
(A) 3.25
(B) 3.6
(C) 4.2
(D) 4.4
(E) 6
Rationale: Time taken by First tank Fill 1/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = 18 hours
Time taken by Second tank Fill 2/3 the tank = 6 hours
i.e. Time taken by First tank to Fill 1 complete the tank = (3/2)*6 = 9 hours
in 1 Hour, Both tanks together Fill the tank = (1/18)+(1/9) = 1/6 tank
i.e. Time taken by Both tank to Fill 1 complete the tank = 6 hours
Answer: option E
Answer: (E) 6
Question: (X+1 )is an even number and Y is a positive odd number. Which of the following expressions cannot be even?
(A) (X+1)Y
(B) Y
(C) (X+1)^Y
(D) (Y+1)^3
(E) (Y+1)^2
Rationale: Y WILL BE ODD
B
Answer: (B) Y
Question: If x^2 + 1/x^2 = √12, what is the value of x^4 + 1/x^4 ?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = √12 andSQUAREboth sides:
(x² + 1/x²)²= 12
So, (x² + 1/x²)(x² + 1/x²) = 12
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 12
Simplify: x⁴ + 1/x⁴ = 10
Answer: A
Answer: (A) 10
Question: Find the L.C.M of 16, 25, 24 and 10.
(A) 1000
(B) 1400
(C) 1320
(D) 1200
(E) 1650
Rationale: Explanation:
4 x 5 x 2 x 3 x 5 X 2= 1200
Answer: Option D
Answer: (D) 1200
Question: The smallest value of n, for which n+3 is not a prime number, is
(A) 1
(B) 2
(C) 6
(D) 8
(E) 3
Rationale: (1 + 3) = 3.
(2 + 3) = 5.
(3 +3) = 6.
( 4+ 3) = 7.
which is not prime , n=3.
ANSWER:E
Answer: (E) 3
Question: If the number92737*2 is completely divisible by 8, then the smallest whole number in place of * will be?
(A) 2
(B) 1
(C) 3
(D) 4
(E) None of these
Rationale: The number 7x2 must be divisible by 8.
x=1 as 712 is divisible by 8.
Correct Option : B
Answer: (B) 1
Question: Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 15 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip?
(A) 35
(B) 42.5
(C) 44
(D) 50
(E) 52.5
Rationale: Total Time taken by jerry = (8/40)*60 Minutes + 15 Minutes + (20/60)*60 Minutes = 47 Minutes
Average Speed = Total Distance / Total Time = (8+20) miles / (47/60)Hours = 28*60 / 47 = 35 Miles per hour
Answer: option A
Answer: (A) 35
Question: X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ3, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I)	7
II)	8
III)	9
(A) I only
(B) II only
(C) III only
(D) I , II and III
(E) I and II only
Rationale: it can be a combination of 9,4 or 8,5 or 7,6
I choose D as an answer.
Answer: (D) I , II and III
Question: List R contains five numbers that have an average value of 40. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: The middle number is 40.
Let the smallest number be x. Then the largest number is 2x+20.
To make x as small as possible, let's make the remaining numbers as large as possible.
So the second largest = the largest = 2x+20.
The second smallest should be equal to the median.
The numbers are x, 40, 40, 2x+20, 2x+20.
x + 40 + 40 + 2x + 20 + 2x + 20 = 5*40 = 200
5x = 80
x = 16
The answer is B.
Answer: (B) 16
Question: The length of a room is 6 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
(A) 25650
(B) 25750
(C) 26550
(D) 26750
(E) 25725
Rationale: Area = 6 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 6 × 4.75 × 900
= 6 × 4275 = Rs. 25650
Answer is A.
Answer: (A) 25650
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average of the team?
(A) 23 years
(B) 67 years
(C) 15 years
(D) 88 years
(E) 66 years
Rationale: Let the average of the whole team be x years.
11x - (26 + 29) = 9(x - 1)
= 11x - 9x = 46
= 2x = 46 => x = 23
So, average age of the team is 23 years.
Answer:A
Answer: (A) 23 years
Question: The volume of water in a certain tank is x percent greater than it was one week ago. If r percent of the current volume of water in the tank is removed, the resulting volume will be 90 percent of the volume it was one week ago. What is the value of r in terms of x?
(A) x+10
(B) 10x+1
(C) 100(x+10)
(D) 100( x+10/x+100)
(E) 100 ( 10x+1/10x+10)
Rationale: Given that, the water was increased by x percent -> then reduced by r percent -> to 90 percent of what it was one week ago.
Consider, the 100 units of water was increased by 20% to 120 units -> then reduced by 25% of 120 (i.e. by 30 units) -> to 90 units.
i.e. Pick numbers as x = 20% and r = 25%
Substitute x=20 and identify the answer that gives r=25
A) x+10 --20+1=30
b) 10x+1 --200+1=201
c) 100(x+10) --100(20+10)=3000
d) 100( x+10/x+100) --100(20+10/20+100) = 100(30/120)=25
e) 100 ( 10x+1/10x+10) -- 100(200+1/200+10)= 100(201/210)
Hence choice(D) is the answer.
Answer: (D) 100( x+10/x+100)
Question: Indu gave Bindu Rs.500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 0.2
(B) 1.2
(C) 3
(D) 4
(E) 0.8
Rationale: 500 = D(100/4)2
D = 0.8
Answer: E
Answer: (E) 0.8
Question: A chair is bought for Rs.800/- and sold at a loss of 10% find its selling price
(A) Rs.500/-
(B) Rs.510/-
(C) Rs.515/-
(D) Rs.720/-
(E) Rs.540/-
Rationale: Loss = 800*10/100 = 80
S.P = C.P - Loss
= 800- 80
=Rs.720/-
Answer :D
Answer: (D) Rs.720/-
Question: What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
(A) 2592
(B) 2348
(C) 2377
(D) 2999
(E) 2772
Rationale: Explanation:
The usual way to find the compound interest is given by the formula A = .p(1+r/100)^n
In this formula,
A is the amount at the end of the period of investment
P is the principal that is invested
r is the rate of interest in % p.a
And n is the number of years for which the principal has been invested.
In this case, it would turn out to be A =1500(1+20/100)^3
= 2592.
Answer: A) Rs.2592
Answer: (A) 2592
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 2% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:3
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (4 - 2)/(10 - 4) = 2/6 = 1/3
So they should be mixed in the ratio 1:3
Answer - E
Answer: (E) 1:3
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+n is a multiple of 36?
(A) 3
(B) 4
(C) 12
(D) 32
(E) 5
Rationale: n = 5p + 1 = 6,11,16,21,26,31
n = 7q + 3 = 3,10,17,24,31
=>n = 36m + 31
To get this, we need to take LCM of co-efficients of p and q and first common number in series.
So we need to add 5 more to make it
36m + 36
Answer - E
Answer: (E) 5
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $150, how much more remains to be paid?
(A) $880
(B) $990
(C) $1,350
(D) $1,100
(E) $1,210
Rationale: 10/100P = 150 >> p= 150*100/10 = 1500
1500 - 150 = 1350
ANSWER:C
Answer: (C) $1,350
Question: By selling 66 metres of cloth a person gains the cost price of 22 metres. Find the gain percent.
(A) 22%
(B) 22 1⁄2%
(C) 33%
(D) 33 1⁄3%
(E) None of these
Rationale: Let C.P. of one metre of cloth = 1
then C.P. of 66 metres of cloth = 66
Gain = C.P. of 22 metres = 22
% gain = 22⁄66 × 100 = 331⁄3%
Shortcut method :
If on selling ‘x’ articles, a man gains equal to the C.P. of ‘y’ articles, then % gain = y⁄x × 100
∴ % gain = = 22⁄66 × 100 = 331⁄3%
Answer D
Answer: (D) 33 1⁄3%
Question: 6 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 5 professor, how many ways can this committee be formed?
(A) 36
(B) 60
(C) 72
(D) 80
(E) 4
Rationale: you count up combinations twice.
6*9*8... and let me name 6 with students A,B,C,..,G
after choosing a professor, when you choose Student A and B, you can choose A first, then B. Or B first, then A. Both combination are same.
I don't think that's the only mistake.
4 is a factor of = 2^2*1^2
18 is a factor of = 2^1*3^2.
These are very different numbers and you cannot divide 18 with something to get to 4. ans E
Answer: (E) 4
Question: If A^2 + B^2 = 15 and AB = 10, what is the value of the expression (A - B)^2 + (A + B)^2
(A) 10
(B) 20
(C) 60
(D) 30
(E) 70
Rationale: (a-b)^2 = a^2 + b^2 - 2ab = 15-20= -5
(a+b)^2 = a^2 + b^2 + 2ab = 15+20=35
so (a+b)^2 + (a-b)^2 = 35 - 5 = 30
D
Answer: (D) 30
Question: What is the greatest positive integer x such that 3^x is a factor of 9^7?
(A) 5
(B) 14
(C) 10
(D) 20
(E) 30
Rationale: What is the greatest positive integer x such that 3^x is a factor of 9^7?
9^7 = (3^2)^7 = 3^14
B. 14
Answer: (B) 14
Question: There are 190 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?
(A) 72
(B) 85
(C) 94
(D) 105
(E) 108
Rationale: You had the answer almost right. The x = 82 refers to ONLY set A.
However what's being asked is how many members are part of set A. This will include:
1. Only Set A
2. Set A and Set B
So the answer is Set A = 82 + Set AB = 82+23 = 105
D
Answer: (D) 105
Question: One fast typist type some matter in 4hrs and another slow typist type the same matter in 7hrs. If both do combine in how much time they will take to finish.
(A) 1 hr 10 mins
(B) 1 hr 30 mins
(C) 2 hr 32 mins
(D) 3 hr 15 mins
(E) 4 hr 20 mins
Rationale: Fast's 1 hr work = 1/4
slow's 1 hr work = 1/7
1/4 + 1/7 = 11/28
they ll finish in 28/11hrs= 2 6/11 ==> 2 hr 32 mins
ANSWER:C
Answer: (C) 2 hr 32 mins
Question: If 2x + y = 7 and x + 2y = 5, then 2xy/3 =?
(A)  1
(B)  2
(C)  17/5
(D)  18/5
(E)  4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
(2*3*1)/3
= 6/3
=2
B
Answer: (B)  2
Question: On a summer camp, 20% of the campers paid $120 each, 35% paid $80 each and the rest paid $65 each. What percentage of the total amount paid came from the campers who paid $80?
(A) 18%
(B) 21%
(C) 26%
(D) 33.3%
(E) 35.89%
Rationale: let the total no of campers be 100
total amount = (20*120)+(35*80)+(40*65) = 2400+2800+2600= $7800
required percentage = (28/78)*100 =33.89%
E
Answer: (E) 35.89%
Question: What are the last two digits of 33*76*47*22*58*91?
(A) 16
(B) 20
(C) 18
(D) 22
(E) 24
Rationale: 33*76*47*22*58*91=
We have to focus on the last two digits only, so 33*76=08*47=76*22=72
72*58=76 therefore 76*91=16
Hence Answer is A
Answer: (A) 16
Question: The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
(A) 1008
(B) 1015
(C) 1022
(D) 1032
(E) None of these
Rationale: Explanation:
Required Number = (L.C.M of 12, 16, 18,21,28)+7
= 1008 + 7
= 1015. Answer: B
Answer: (B) 1015
Question: A man has some hens and cows. If the number of heads be 50 and the number of feet equals 160, then the number of hens will be:
(A) 22
(B) 23
(C) 24
(D) 20
(E) 28
Rationale: Explanation:
Let the number of hens be x and the number of cows be y.
Then, x + y = 50 .... (i)
and 2x + 4y = 160 x + 2y = 80 .... (ii)
Solving (i) and (ii) we get: x = 20, y = 30
The required answer = 20.
Answer: D
Answer: (D) 20
Question: A and B play a game where each is asked to select a number from 1 to 16. If the two numbers match , both of them win a prize. Find the probability that they will not win a prize in a single trial.
(A) 15/16
(B) 1/16
(C) 7/8
(D) 9/8
(E) None of these
Rationale: Explanation :
A and B win a prize, only if both A and B select the number. So, if A chooses a number, B has to select the same number. Hence, it is problem on dependent event.
Let A select a number., then P(A) = 1/16 = probability of A.
Now, B selects the same number after A has already selected that number.
Then, P(B/A) = 1/1 = dependent probability of B given A has occurred.
P(AB) = Probability of winning a prize by both A and B is :-
=> P(A) x P(AB).
=> (1/16) x 1 = 1/16.
Hence, the probability of not winning a prize is :-
= 1 - (1/16).
= 15/16.
Answer : A
Answer: (A) 15/16
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 7 flight to return. In how many ways, can the boy perform his journey?
(A) 28
(B) 30
(C) 43
(D) 45
(E) 80
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 7 From, fundamental principle, total number of ways of performing the journey = 4 x 7 = 28 ways
Answer: (A) 28
Question: In an examination, a student scores 4 marks for every correct answer and loses I mark for every wrong answer. If he attempts in all 60 questions and secures 130 marks, the number of questions he attempts correctly, is:
(A) 35
(B) 38
(C) 40
(D) 42
(E) 52
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
= 4x – (60 – x) = 130
=> 5x = 190 => x = 38
Answer: B
Answer: (B) 38
Question: Find the value of x: x² - 4x + 4.
(A) 2
(B) 4
(C) -2
(D) -4
(E) 0
Rationale: That quadratic is factored as follows:x² - 4x +4 = (x-2)(x-2).Lesson 17.Now, it is easy to see that the second factor will be 0 when x = 2.The solution is:x	=	2 A
Answer: (A) 2
Question: A factory produces x widgets per day. The factory's fixed costs are $8000 per day. The price per widget is $80 and the variable costs are $20 per widget. How many widgets need to be produced for profits of $5000 a day?
(A) 42.33
(B) 90.33
(C) 168
(D) 216.67
(E) 400
Rationale: profits=5000=60x-8000 --> x=216.67
Answer D.
Answer: (D) 216.67
Question: A circle has 29 points arranged in a clock wise manner from o to 28. A bug moves clockwise manner from 0 to 28. A bug moves clockwise on the circle according to following rule. If it is at a point i on the circle, it moves clockwise in 1 sec by (1 + r) places, where r is the remainder (possibly 0) when i is divided by 11. If it starts in 23rd position, at what position will it be after 2012 sec.
(A) 2012
(B) 2997
(C) 2977
(D) 1979
(E) 7112
Rationale: Ans: After 1st second, it moves 1 + (23/11)r = 1 + 1 = 2, So 25th position
After 2nd second, it moves 1 + 25/11 = 1 + 3 = 4, So 29th position = 0
After 3rd second, it moves 1 + 0/11 = 1 + 0 = 1, So 1st position
After 4th second, it moves 1 + 1 = 3rd position
after 5th, 1 + 3/11 = 4 So 7th
After 6th, 1 + 7/11 = 8 so 15th
After 7th, 1 + 15/11 = 5 so 20th
After 8th, 1 + 20/11 = 10th, So 30th = 1st
So it is on 1st after every 3 + 5n seconds. So it is on 1st position after 2008 seconds (3 + 5 x 401) So on 20th after 2012 position.
Answer:E
Answer: (E) 7112