mathewhe/aqua_rat huggingface dataset:
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/7 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
(A) 0
(B) 1/14
(C) 2/15
(D) 1/10
(E) 2/10
Rationale: Suppose the water in each jug is L liters
CX x (1/7) = L
CX = 7L liters
CX is capacity of X
CY x (2/3) = L
CY = 3L/2 liters
CY is capacity of Y
Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X
Jug X's remaining water = L - L/2 = L/2
Fraction of X which contains water = water / CX
= (L/2)/ 7L
= 1/14
Answer will be B
Answer: (B) 1/14
Question: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 88 Θ 33 ) Θ 17 ) - ( 90 Θ (33 Θ 17)) ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: (( 88 Θ 33 ) Θ 17 )
The remainder of 88 divided by 33 is 22;
The remainder of 22 divided by 17 is 5;
( 98 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
The remainder of 98 divided by 16 is 2.
5 - 2 = 3.
Answer: D.
Answer: (D) 3
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 16% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 14000
(B) 27767
(C) 16688
(D) 26678
(E) 19987
Rationale: Let the CP be Rs. x.
Had he offered 16% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 16/100(18000) = Rs. 15120
=> 1.08x = 15120
=> x = 14000
\Answer: A
Answer: (A) 14000
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1:96
(B) 1:94
(C) 1:98
(D) 1:93
(E) 1:91
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1:96.
Answer: A
Answer: (A) 1:96
Question: If x=-4, which of the following is(are) true? I. x^2=-|x| II x/-4 = 1 III |x|=x
(A) I only
(B) III only
(C) II only
(D) I,II only
(E) II,III only
Rationale: -4/-4 =1
Answer : C
Answer: (C) II only
Question: A company that ships boxes to a total of 13 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)
(A) 6
(B) 5
(C) 8
(D) 9
(E) 10
Rationale: Back-solving is the best way to solve this problem.
You basically need 13 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - B
Answer: (B) 5
Question: A man can row 9km/hrin still water. it takes him twice as long to row upas to row down the river find the rate of the stream Rate of the current ?
(A) 2km/hr
(B) 63.8km/hr
(C) 8.9km/hr
(D) 9.6km/hr
(E) 7.9km/hr
Rationale: Lets man's rate in upstream =xkm/hr.
man's rate down stream =2xkm/hr. man's rate in still water =1/2(x+2x)km/hr ==>3x/2=6==>x=4 The rate upstream=4km/hr . The rate down stream=8km/hr. Rate of the current=1/2(8-4)km/hr=2km/hr
Answer is (A)
Answer: (A) 2km/hr
Question: There are 30 balls which are red, blue or green. If 11 balls are green and the sum of red balls and green balls is less than 25, at most how many red balls are there?
(A) 14
(B) 13
(C) 16
(D) 17
(E) 8
Rationale: r+g+b=30
g=11
r + g < 25
=> r + 11 < 25
=> r < 14
=> at most 13 red balls
ANSWER:B
Answer: (B) 13
Question: X starts a business with Rs.45000. Y joins in the business after 8 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 9:2
(C) 1:3
(D) 3:1
(E) 1:1
Rationale: Explanation:
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000Ã—12:30000Ã—4
=45Ã—12:30Ã—4
=3Ã—12:2Ã—4
=9:2
Answer: Option B
Answer: (B) 9:2
Question: Clarissa is driving home from work, 110 miles away. After driving 5 miles, she gets a flat tire. The replacement tire can't handle speeds above 35 miles per hour. How long will she have to drive, in hours, on the replacement before she arrives home?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: She has to travel 110 - 5 = 105 miles at 35 miles per hour
105 / 35 = 3 hours.
Correct answer C
Answer: (C) 3
Question: Gold is 19 times as heavy as water and copper is 9 times heavy. In what ratio must these metals be mixed so that the mixture may be 15 times as heavy as water?
(A) 2 : 3
(B) 3 : 2
(C) 1 : 3
(D) 2 : 1
(E) None of these
Rationale: ? Required ratio = 6?4 = 3 : 2
Answer B
Answer: (B) 3 : 2
Question: Convert the 13/36 m/s into kilometers per hour?
(A) 1.5
(B) 1.9
(C) 1.3
(D) 1.6
(E) 1.1
Rationale: 13/36 m/s = 13/36 * 18/5 = 13/10
= 1.3 kmph.
Answer: C
Answer: (C) 1.3
Question: A can do a piece of work in 40 days; B can do the same in 40 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
(A) 20 days
(B) 65 days
(C) 86 days
(D) 45 days
(E) 17 days
Rationale: 10/40 + 10/40 + 10/x = 1
x = 20 days
Answer:A
Answer: (A) 20 days
Question: A train 200 m long passed a pole in 18 sec. How long will it take to pass a platform 600 m long?
(A) 12 sec
(B) 73 sec
(C) 74 sec
(D) 21 sec
(E) 46 sec
Rationale: Speed = 200/18
= 11 m/sec.
Required time = (200 + 600)/11
= 72.7 sec.
Answer: B
Answer: (B) 73 sec
Question: Find the cost price of an item if by selling at Rs.720, a profit of 13% is made?
(A) Rs.616
(B) Rs.726
(C) Rs.326
(D) Rs.926
(E) Rs.626
Rationale: SP = 720
CP = (SP)*[100/(100+P)]
= 720 * [100/(100+13)]
= Rs.626
Answer: E
Answer: (E) Rs.626
Question: Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there?
(A) 15
(B) 20
(C) 25
(D) 35
(E) 30
Rationale: x : the total number of toys
x/10 : the number of toys for first child
x/10 + 12 : the number of toys for second child
x/10 + 1 : the number of toys for the third child
2(x/10 + 1) : the number of toys for the fourth child
x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x
x = 30 toys.
Answer is E.
Answer: (E) 30
Question: What is the difference between local value & face value of 5 in the numeral 65793?
(A) 4455
(B) 4955
(C) 4995
(D) 4890
(E) 10000
Rationale: (Local value of 5) - (Face value of 5)
= (5000 - 5) = 4995
C
Answer: (C) 4995
Question: Mangala completes a piece of work in 15 days, Raju completes the same work in 45 days. If both of them work together, then the number of days required to complete the work is?
(A) 8 days
(B) 10 days
(C) 11 days
(D) 12 days
(E) 14 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 15 × 45 /60 = 11 days
C)
Answer: (C) 11 days
Question: If a function f is defined by f(x)= (1-x)/x for all non zero numbers x. If f(a) = 1 and f(a/b) = 3 then b= ?
(A) 3
(B) 1/3
(C) 2
(D) 1/2
(E) -2
Rationale: Given that f(x)= (1-x)/x and f(a) = 1, then f(a) =(1-a)/a=1 ===> a=1/2, then backsolve using the answer choices:
f(a/b) = f(1/2b) = 3
A) 3 ===> f(1/2*3) = f(1/6) = 5
B) 1/3 ===> f((1/2)/(1/3)) = f(3/2) = (-1/2)/(3/2) = -1/3
C) 2 ===> f(1/2*2) = f(1/4) =3 WINS
D) 1/2 ===> f((1/2)/(1/2)) = f(1) = 0
E) -2 ===> f((1/2)/-2) = f(-1/4) = (5/4)/(-1/4) = -5
Answer: C
Answer: (C) 2
Question: A thief is noticed by a policeman from a distance of 290 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 100
(B) 190
(C) 2987
(D) 278
(E) 271
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 290 - 100 = 190 m.
Answer: B
Answer: (B) 190
Question: Compound interest of Rs.3000 at 10% per annum for 1 l/2years will be (interest compounded half yearly).
(A) Rs.473
(B) Rs.374
(C) Rs.495
(D) Rs.347
(E) None of the above
Rationale: 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)
So compound interest=3000[1+(5/100)]^3 - 3000=3000[(21/20)^3 -1]
=3000(9261-8000)/8000
=3*1261/8
=472.8 ~ 473
ANSWER:A
Answer: (A) Rs.473
Question: The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph
(B) 67 kmph
(C) 22 kmph
(D) 88 kmph
(E) 15 kmph
Rationale: Speed of the boat in still water
= (50+80)/2
= 65 kmph. Speed of the stream
= (80-50)/2
= 15 kmph.
Answer:E
Answer: (E) 15 kmph
Question: The compound interest earned on a sum for the second and the third years are $1200 and $1272 respectively. What is the rate of interest?
(A) 4%
(B) 6%
(C) 8%
(D) 10%
(E) 12%
Rationale: 1272 - 1200 = 72 is the rate of interest on $1200 for one year.
The rate of interest = (100 * 72) / (1200) = 6%
The answer is B.
Answer: (B) 6%
Question: My flight takes of at 2am from a place at 18N 10E and landed 10 Hrs later at a place with coordinates 36N70W. What is the local time when my plane landed?
(A) 6: 40 AM
(B) 1: 90 AM
(C) 5: 50 AM
(D) 2: 40 AM
(E) 6: 20 AM
Rationale: Remember, while moving from east to west countries lag in time. Remember when Test cricket starts in England? 3. 30 in afternoon. Right? ie., We are in after noon means they are in morning.
If the coordinates change from 10 E to 70W, the plane has moved a total of 80 degrees. We know that with each degree time increases by 4 minutes while going from east to west. (How? 24 x 60 min / 360 degrees, So 1 degree = 4 min)
So total time change = 4 x 80 = 320 min = 5 hrs + 20 minutes.
After 10 hours local time is (2 am + 10 - 5.20 hrs) = 6.40 AM.
Answer:A
Answer: (A) 6: 40 AM
Question: If n is the smallest integer such that 144 times n is the square of an integer, what is the value of n?
(A)  2
(B)  3
(C)  6
(D)  12
(E)  24
Rationale: 144 can written as = 2 * 2 * 2 * 2 * 3 * 3 --> 2^4 * 3^2 ---(1)
so for 144 * n to be a square of an integer, the integer should have even powers to the prime numbers it composed of.
here 2 already has even power -> So n has to be 3 to make the power of 2 in (1) even
Option A is correct
Answer: (A)  2
Question: In a certain store, the profit is 300% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 65%
(B) 66.7%
(C) 68.75%
(D) 70%
(E) 71.2%
Rationale: Let C.P.= Rs. 100. Then, Profit = Rs. 300, S.P. = Rs. 400.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 400.
Profit = Rs. (400 - 125) = Rs. 275.
Required % =(275/400)x100 %
= 68.75%
ANSWER :C
Answer: (C) 68.75%
Question: If ‘MADRAS’ is coded as ‘DADIAA’, then ‘HARYANA’ is coded as
(A) HRAAYNA
(B) HAIGAEA
(C) GARYNDA
(D) GARYNDB
(E) None
Rationale: M=13,1+3=4=D
A=1=A
SIMILARLY,
H=8=H
A=1=A
R=18=1+8=9=I
SO ANS IS
HAIGAEA
ANSWER:B
Answer: (B) HAIGAEA
Question: Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.
(A) 5.9
(B) 7.8
(C) 5.5
(D) 8.1
(E) 6.3
Rationale: A
If we place a decimal between the numbers it will become 5.9 which is what we needed.
Answer: (A) 5.9
Question: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If q of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
(A)  y/R
(B)  y/(R-x)
(C)  xy/(R-x)
(D)  qy/(R(R-q))
(E)  y/(R(R-x))
Rationale: y/(R-q)- y/R
if we simplify this we get choice D, which is the correct answer.
Answer: (D)  qy/(R(R-q))
Question: Raj writes a number. He sees that the number of two digits exceeds four times the sum of its digit by 3. If the number is increased by 18, the result is the same as the number formed by reversing the digit. Find the number
(A) 3
(B) 5
(C) 6
(D) 7
(E) 87
Rationale: Ans: A
Going by the options, 35 = 8(4) + 3.
Answer:A
Answer: (A) 3
Question: If A : B = 4 : 7 and B : C = 5 : 9 then A : B : C is :
(A) 20 : 35 : 63
(B) 35 : 36 : 63
(C) 30 : 35 : 65
(D) 25 :34: 68
(E) None of these
Rationale: A : B = 4 : 7
B : C = 5 :9 = 5*7/5 : 9 *7/5 = 7 : 63/5
A : B : C = 4 : 7 : 63/5 = 20 : 35 : 63
ANSWER:A
Answer: (A) 20 : 35 : 63
Question: Raman's salary was decreased by 50% and subsequently increased by 50%. How much percent does he loss.
(A) 75
(B) 65
(C) 45
(D) 25
(E) 85
Rationale: Explanation:
Let the origianl salary = Rs. 100
It will be 150% of (50% of 100)
= (150/100) * (50/100) * 100 = 75
So New salary is 75, It means his loss is 25%
Option D
Answer: (D) 25
Question: Two pipes A and B can separately fill a tank in 10 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 6min
(B) 9min
(C) 7min
(D) 8min
(E) 10min
Rationale: 4/10 + x/15 = 1
x = 9
ANSWER:B
Answer: (B) 9min
Question: one-fourth of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 40 workers in the Palabras bookstore, how many of them have read both books?
(A) 3
(B) 2
(C) 9
(D) 8
(E) 7
Rationale: There are total 40 workers.
one-fourth of the workers in Palabras bookstore have read the latest book by J. Saramago,
So 10 have read Saramago.
5/8 of the workers have read the latest book by H. Kureishi.
So (5/8) * 40 = 25 have read Kureishi
The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book
If B workers have read both books, 20 - B have read Saramago but not Kureishi.
So, (10 - B - 1) have read neither.
Total = n(A) + n(B) - Both + Neither
40 = 10 + 25 - B + (10 - B - 1)
B = 2
Answer (B)
Answer: (B) 2
Question: A group of men decided to do a work in 20 days, but 8 of them became absent. If the rest of the group did the work in 28 days, Find the original number of men?
(A) 60
(B) 28
(C) 40
(D) 50
(E) 25
Rationale: Original number of men = 8*28 / (28-20) = 28
Answer is B
Answer: (B) 28
Question: A group of boy scouts and girls scouts is going on a rafting trip. 70% of the scouts arrived with signed permission slips. If 60% of the scouts were boy scouts and 75% of the boy scouts arrived with signed permission slips, then what percentage of the girl scouts arrived with signed permission slips? Round to the nearest percent.
(A) 50%
(B) 60%
(C) 63%
(D) 66%
(E) 70%
Rationale: 60% were boy scouts so 40% (100-60=40) were girl scouts.
# of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed
(75% of 60% of the total going) + (?% of 40% of the total going) = 70% of the total going
We can let the "total going" = 1,000 arbitrarily since we only care about the percent (of girl scouts w/ permission signed)
.75*.60*1,000 + x*.40*1,000 = .70*1,000
450 + x*400 = 700
400x=250
x=250/400
x=.625
Converting this to a percent, we have 62.5%. Rounding, we have 63%.
C
Answer: (C) 63%
Question: If the operation @ is defined for all a and b by the equation a@b =(a-b)/5,then (3@-2)@6=?
(A) 0
(B) 1
(C) 2
(D) -2
(E) -1
Rationale: work within the parenthesis first so solve (3@-2) first
(3@-2)=(3-(-2))/5=(3+2)/5=1
now take 1 plug back into equation and solve the rest
(1@6)=(1-6)/5=-5/5=-1
so -1 is the answer....this question is merely testing order of operations
remember PEMDAS
Answer is option:E
Answer: (E) -1
Question: A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 5¢ envelopes. If the company requested 3 more 4¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?
(A) 3x+32
(B) 5x-1
(C) (7x+15)/2
(D) (9x-4)/2
(E) 6x+2
Rationale: We can take
X+1 = 9
X= 8
So 4c envelopes will be 6
and 5c envelopes will be 3
So total cost will be 39
Then that is our target
Plug x =8 in answer choices
Only B works
Correct Answer : B
Answer: (B) 5x-1
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 6%. What was its profit on the items sold in February?
(A) 27.5%
(B) 30%
(C) 35%
(D) 37.5%
(E) 41%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.94*150x = 141x
Hence total profit = 41%
Option E
Answer: (E) 41%
Question: Taps A and B can fill a bucket in 15 minutes and 30 minutes respectively. If both are opened and A is closed after 4 minutes, how much further time would it take for B to fill the bucket?
(A) 19 mins.
(B) 15 mins.
(C) 18 mins.
(D) 16 mins.
(E) 17 mins.
Rationale: Explanation:
Part filled in 3 minutes =
4∗(1/15+1/30)=4∗1/10=2/5
Remaining part =1−2/5=3/5
=>1/30:3/5=1:X
=>X=18
=>X=18 mins.
So it will take further 18 mins to fill the bucket.
Option C
Answer: (C) 18 mins.
Question: If y>x>0, which of the following must be true:
I. y^2>x^2
II. y^3 > x^3
III. |y|>x
(A) I only
(B) II only
(C) I, II and III
(D) II and III
(E) III only
Rationale: Assuming x and y to be integers
X=3,Y=2
X^2=3^2=9
Y^2=2^2=4
So I is true
Now lets look at option III because if option 3 is true E is the answer or else A
As per question X>Y>0 Hence |X| >Y
So OA=C
Answer: (C) I, II and III
Question: Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 1.5 times the amount of the second solution?
(A) 61
(B) 65
(C) 68
(D) 70
(E) 72
Rationale: SOL:
Lets assume that 15L of sol1 was mixed with 10L of sol2.
Alcohol in Sol1: 15*3/4 = 11.25L
Alcohol in Sol2: 10*2/5 = 4L
Total Alcohol in the mixed solution of 25L = 11.25 + 4 = 15.25L
Alcohol concentration in the new sol: (15.25/25)*100 = 61%
ANSWER:A
Answer: (A) 61
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 655200000 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
(A) 1300000000
(B) 12500
(C) 14000
(D) 12000
(E) None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 655200000.
(75/100 * 96/100 * 70/100 * x) = 655200000.
=> x = (655200000*100*100*100)/(75*96*70) = 1300000000
Answer : A
Answer: (A) 1300000000
Question: Laura took out a charge account at the General Store and agreed to pay 7% simple annual interest. If she charges $35 on her account in January, how much will she owe a year later, assuming she does not make any additional charges or payments?
(A) $2.10
(B) $37.10
(C) $37.45
(D) $38.10
(E) $38.80
Rationale: Principal that is amount taken by Laura at year beginning = 35$
Rate of interest = 7%
Interest = (7/100)*35 = 2.45$
Total amount that Laura owes a year later = 35+2.45 = 37.45 $
Answer C
Answer: (C) $37.45
Question: In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 3 people play both cricket and football. How many people play only cricket?
(A) 11
(B) 4
(C) 5
(D) 3
(E) 9
Rationale: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.
people play only cricket = 11-4-3 = 4
Answer is B
Answer: (B) 4
Question: If an item that originally sold for A dollars was marked up by x percent and then discounted by M percent, which of the following expressions represents the final price of the item?
(A) (10,000z + 100z(x – y) – xyz)/10,000
(B) (10,000z + 100z(y – x) – xyz)/10,000
(C) (100z(x – y) – xyz)/10000
(D) (A+ Ax/100) - M/100 ( A +Ax/100)
(E) 10000 /(x – y)
Rationale: value of item =A ..marked up by x% = Ax/100
total value = A +ax/100 .discounted by L% on Total M/100 * ( A+Ax/100)
Final price =(A+ Ax/100) - M/100 ( A +Ax/100)
D
Answer: (D) (A+ Ax/100) - M/100 ( A +Ax/100)
Question: The speed of train, 150m long, is 50km/hr. How much time will it take to pass a plateform 600m long?
(A) 46 seconds.
(B) 58 seconds.
(C) 54 seconds.
(D) 52 seconds.
(E) 45 seconds.
Rationale: Distance covered =150+600 =750m speed =50km/hr =50*5/18 m/s =125/9 m/s. Time taken =750/125*9 = 54 seconds. Answer : C
Answer: (C) 54 seconds.
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 238
(B) 150
(C) 988
(D) 177
(E) 171
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Answer: (B) 150
Question: Find the smallest four-digit number which is a multiple of 112
(A) 137
(B) 112
(C) 287
(D) 121
(E) 191
Rationale: Explanation:
The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104.
112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112.
Answer: B
Answer: (B) 112
Question: All the students of class are told to sit in circle shape. Here the boy at the 5 th position is exactly opposite to 20 th boy. Total number of boys in the class?
(A) 30
(B) 40
(C) 45
(D) 25
(E) 20
Rationale: As half the circle shape consist of 20-5=15 boys,
So total number of boys in full circle=2*15=30
ANSWER:A
Answer: (A) 30
Question: If m > 1 and n = 2^(m+1), then 4^m =
(A) 16n^2
(B) 4n^2
(C) n^2
(D) n^2/4
(E) n^2/16
Rationale: n = 2^(m+1) = 2^m*2
2^m = n/2
4^m = (2^m)^2 = (n/2)^2 = n^2/4
The answer is D.
Answer: (D) n^2/4
Question: What is the area of the hall?
I.	Material cost of flooring per square metre is Rs. 2.50
II.	Labour cost of flooring the hall is Rs. 3500
III.	Total cost of flooring the hall is Rs. 14,500.
(A) I and II only
(B) II and III only
(C) All I, II and III
(D) Any two of the three
(E) None of these
Rationale: EXPLANATION
I. Material cost = Rs. 2.50 per m2
II. Labour cost = Rs. 3500.
III. Total cost = Rs. 14,500.
Let the area be A sq. metres.
Material cost = Rs. (14500 – 3500) = Rs. 11,000.
5A/2 = 11000⇔A = (11000x2/5) = 4400 m2.
Answer C
Answer: (C) All I, II and III
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
(A) 11
(B) 25
(C) 77
(D) 99
(E) 21
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%.Answer:B
Answer: (B) 25
Question: A monkey start climbing up a tree 22 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
(A) 15 hrs
(B) 18 hrs
(C) 20 hrs
(D) 17 hrs
(E) 16 hrs
Rationale: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 19hrs it wil be 19ft.
Bt since the height of the tree is 22ft, so if the monkey hops up the tree in the next hr i.e 20th hr then it reaches at the top of the tree.
hence it takes 20 hrs for monkey to reach at the top
ANSWER:C
Answer: (C) 20 hrs