mathewhe/aqua_rat huggingface dataset:
Question: How many integers between 1 and 10^19 are such that the sum of their digits is 2?
(A) 190
(B) 210
(C) 211
(D) 230
(E) 231
Rationale: The integers with a sum of 2 are:
2, 20, 200,...,2*10^18 and there are 19 integers in this list.
Also, these integers have a sum of 2:
11
101, 110
1001, 1010, 1100
etc...
The number of integers in this list is 1 + 2 + ... + 18
Thus, the total number of integers is 1 + 2 + ... + 18 + 19 = 20*19/2 = 190
The answer is A.
Answer: (A) 190
Question: From the third term,each term in the sequence a(1),a(2),a(3),a(4),a(5),a(6) is the sum of the preceding two terms that is a(n)=a(n-1)+a(n-2) for n=3,4,5,6.if a(5)=36 what is the sum of all the six terms?
(A) 142
(B) 143
(C) 144
(D) 145
(E) 146
Rationale: If x is the first term and y is second terem, then
terms are
x
y
x+y
x+2y...... equal to 36
2x+3y
3x+5y
sum of 6 terms = 8x+12 y = 4*(2x+3y)= 4*36=144
ANSWER:C
Answer: (C) 144
Question: If Henry were to add 4 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?
(A) 32
(B) 40
(C) 64
(D) 80
(E) 96
Rationale: 7/8x-3/4x=4galls
1/8*x=4gallons
x=32 gallons
Answer A
Answer: (A) 32
Question: 70% of all students in a class commute by public transportation. If 10% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists?
I.	10%
II.	25%
III.	80%
(A) I ONLY
(B) II ONLY
(C) III ONLY
(D) I AND II
(E) II AND III
Rationale: 70% Students use public transportation. This means 30% students do not use public transportation. 10% students aspire to be scientists means even if all these students use public transportation, minimum 30% - 10% = 20% students do not use public transportation and do not aspire to be scientists.This means correct answer is between 20% and 30%
Answer : B.
Answer: (B) II ONLY
Question: If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a club, or a red jack, or a red queen?
(A) 19/26
(B) 15/52
(C) 17/52
(D) 8/13
(E) 5/13
Rationale: There are 13 clubs and 2 red jacks and 2 red queens.
P(club or red jack or red queen) = 17/52
The answer is C.
Answer: (C) 17/52
Question: The average height of 20 students in a class was calculated as 175 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 131 cm. What was the actual average height of the students in the class?
(A) 174 cm
(B) 173 cm
(C) 172 cm
(D) 171 cm
(E) 170 cm
Rationale: The total height was 20 cm too much.
The average height should be reduced by 20 cm/20 = 1 cm
The answer is A.
Answer: (A) 174 cm
Question: A camera lens filter kit containing 5 filters sells for $72.50. If the filters are purchased individually, 2 of them are priced at $12.45 each, 2 at $14.05 each, 1 at $11.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?
(A) 10.03%
(B) 11.03%
(C) 12.03%
(D) 13.03%
(E) 11%
Rationale: Cost of kit = $72.50
If filters are purchased individually - $12.45*2 + $14.05*2 + $11.50 = $64.50
Amount saved = $72.50 - $64.50 = $8
Required %age = ($8/$72.50)*100 = 11.03%
So, the correct answer is B.
Answer: (B) 11.03%
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. what is the age of the youngest child ?
(A) 22
(B) 18
(C) 10
(D) 99
(E) 38
Rationale: Let x = the youngest child. Each of the other four children will then be x+3, x+6, x+9, x+12.
We know that the sum of their ages is 50 .
so, x+(x+3)+(x+6)+(x+9)+(x+12) = 50
therefore The youngest child is 4 years old
Answer: C
Answer: (C) 10
Question: David has $2,400 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have?
(A) $200
(B) $400
(C) $600
(D) $800
(E) $1,200
Rationale: Suppose total money spent = x
Not spend (Money he still has)= x-800
x+x-800 = 2400
x= 1600
Money not spend= 1600-800= 800
Answer : D
Answer: (D) $800
Question: An agent, gets a commission of 5% on the sales of cloth. If on a certain day, he gets Rs. 12.50 as commission, the cloth sold through him on that day is worth
(A) 333
(B) 500
(C) 887
(D) 250
(E) 132
Rationale: Explanation:
Let the total sale be Rs. x.
Then, 5%. of x = 12.50 <=> (5/100 * x) = 125/10 <=> x = 250.
Answer: D
Answer: (D) 250
Question: 1,-3,2,-4,3,-5.... upto 2000 terms. find the average
(A) 2
(B) 1
(C) 0
(D) 2
(E) -1
Rationale: here in the question the average is asked for up to 2000 terms.
so up to 2000 terms will be
{1,-3,2,-4,3,-5,.........,1000,-1002}
so if we add them like this
{(1-3)+(2-4)+(3-5)+.........+(1000-1002)}
this will a sum of
{-2-2-2-2-......-2} for thousand times
i.e. {1000*(-2)}
therefore the sum is -2000
the average will be -2000/2000 = -1
ANSWER:E
Answer: (E) -1
Question: How many multiples of 5 are there between 10 and 100, exclusive ?
(A) 18
(B) 17
(C) 16
(D) 15
(E) 14
Rationale: 5 * 2 = 10
5 * 20 = 100
Total multiples = (20-2) + 1 = 19
Exclude 10 and 100 = 19-2 = 17
Answer is B
Answer: (B) 17
Question: If a lies in the range (-2,1) then which of the following statements must be true?
(A) a^4 >a^3 > a^2 > a
(B) a > a^2 > a^3 > a^4
(C) a^4 > a^2 > a^3 >a
(D) a^2 > a^4 > a^3 >a
(E) a^2 > a^4 > a > a^3
Rationale: consider any number from the given range (-2-1)..let a=-1/2
then a^2= 1/4
a^3=-1/8
a^4=1/16
so we have a^2>a^4>a^3>a
Ans D
Answer: (D) a^2 > a^4 > a^3 >a
Question: Peter read E books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
(A) E > 35N
(B) E< N − 35
(C) E > N + 35
(D) E = N − 35
(E) E = N + 35
Rationale: Peter read E books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
A. E > 35N
B. E < N − 35
C. E > N + 35
D. E = N − 35
E. E = N + 35
Since Peter read more books than Nikki we have E>N. Moreover since Peter reads 35 more books than Nikki easily we can have E=N+35.
So the answer is (E).
Answer: (E) E = N + 35
Question: If y is divisible by the square of an even prime number and x is the actual square of an even prime number, then what is the units digit of x^y?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: even prime number is 2, and its square=4
thus y=4k ;k=1,2,3,,,,,
and x=4
x^y=4^4k; unit digit of 4 is 4 if its power is odd, else it is 6. now since 4k will always be even. therefore the unit digit of 4^4k will always be 6.;ANSWER:D
Answer: (D) 6
Question: A's speed is 20/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 80% of the length of the race?
(A) 44%
(B) 48%
(C) 52%
(D) 42%
(E) 87%
Rationale: First calculate the distance, B has covered with his speed in the time, in which A reached 20% of the race.
Then Add the remaining distance as head start for B to win the race.
Its best to apply Ratios concept here.
Since A's speed is 20/13 of B, therefore, B's speed is 13/20 of A
Distance covered by B = speed x time = (13/20) x (0.2) = 0.13%
(Which means B would have covered 0.13 of the race length during the time in which A has covered 0.2 of the race length.
Therefore to win, B needs a headstart of (1 - 0.13 = ) 0.87 of the race length.
So the answer is E
Answer: (E) 87%
Question: When positive integer n is divided by 5, the remainder is 2. When n is divided by 11, the remainder is 8. What is the smallest positive integer k such that k+n is a multiple of 55?
(A) 2
(B) 3
(C) 6
(D) 7
(E) 10
Rationale: n = 5p + 2 = 11q + 8
n+3 = 5p + 5 = 11q + 11
n+3 is a multiple of 5 and 11, so it is a multiple of 55.
The answer is B.
Answer: (B) 3
Question: In how many different ways can the letters of the word ‘PREPTY’ be arranged?
(A) 220
(B) 250
(C) 276
(D) 320
(E) 360
Rationale: Number of ways = 61/21 6X5X4X3X2X1 - 360
E
Answer: (E) 360
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1260 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs. 4500
(B) Rs. 4800
(C) Rs. 5250
(D) Rs. 6888
(E) None of these
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1260
45k = 1260 => k = 28
246k = 246(28) = Rs. 6888
Thus the total rent paid by all the four agencies is Rs. 6888.
ANSWER:D
Answer: (D) Rs. 6888
Question: From 6 positive numbers and 6 negative numbers, how many groups Z of 4 numbers, yielding a positive product, can be formed?
(A) 720
(B) 625
(C) 30
(D) 960
(E) 255
Rationale: Potential combinations of 4 numbers that will yield positive product
++++ 4C6
---- 4C6
++-- 2C6*2C6
4C6 + 4C6 + 2C6*2C6
Z=15 +15 + 15*15 = 255=E
Answer: (E) 255
Question: If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: We want to minimize z−xz−x, so we need to maximize xx.
Say z=11=oddz=11=odd, then max value of yy will be 9 (as yy is also odd). Now, since y−5>xy−5>x --> 9−5>x9−5>x --> 4>x4>x, then max value of xx is 2 (as xx is even).
Hence, the least possible value of z−xz−x is 11-2=9.
Answer: D.
Answer: (D) 9
Question: A sum was put at SI at certain rate for 2 years.Had it been put at 3% higher rate, it would have fetched Rs.300 more.Find the Sum
(A) RS 4000
(B) RS 5000
(C) RS 6000
(D) RS 7000
(E) RS 8000
Rationale: let P be the sum.and X be the interest rate.
(2*(X+3)*P/100) - (2*X*P/100)=300
THEREFORE 6P/100=300
P=RS 5000
ANSWER:B
Answer: (B) RS 5000
Question: If S is the sum of reciprocals of a list of consecutive integers from 35 to 44, inclusive, S is approximately equal to
(A) 0.1
(B) 0.2
(C) 0.25
(D) 0.4
(E) 0.5
Rationale: We need to find the approximate value of 1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44. Now, the sum of these 10 terms will be very close to 10 times 1/40, which is 0.025*10=0.25.
Answer: C.
Answer: (C) 0.25
Question: The diameter of the driving wheel of a bus is 140 cm. How many revolution, per minute must the wheel make in order to keep a speed of 66 kmph ?
(A) 150
(B) 250
(C) 350
(D) 550
(E) 650
Rationale: Circumference = No.of revolutions * Distance covered
Distance to be covered in 1 min. = (66 X1000)/60 m = 1100 m.
Circumference of the wheel = 2 x (22/7) x 0.70 m = 4.4 m.
Number of revolutions per min. =(1100/4.4) = 250.
Answer: B
Answer: (B) 250
Question: A departmental store has 6 managers and 36 associates. The 6 managers have an average salary of $700. The 36 associates have an average salary of $1500. What is the average salary for the departmental store?
(A) $1400
(B) $1385.71
(C) $1500.25
(D) $1466.58
(E) $1650.56
Rationale: Number of managers is 6
Their average salary is $700
Number of associates is 36
Their average salary is $1500
Total salary of managers is 6*700=$4200
Total salary of associates is 36*1500=$54,000
Total salary for the departmental store is 54000+4200=58200
Average salary for the departmental store is 58200/6+36=1385.71
Answer is B
Answer: (B) $1385.71
Question: The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 16%?
(A) 31.25%
(B) 35.5%
(C) 37.5%
(D) 39.5%
(E) 30.5%
Rationale: Let marked price = $100.
Then, C.P. = $64, S.P. = $84
Gain % = 20/64 * 100 = 31.25%. A
Answer: (A) 31.25%
Question: A car averages 50 mph for the first 4 hours of a trip and averages 80 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: Let the time for which car averages 80 mph = t
65*(t+4)= 50*4 + 80 t
=>15 t= 60
=> t = 4
Total duration of the trip = 4+4=8
Answer A
Answer: (A) 8
Question: A, B and C invested Rs.600, Rs.800 and Rs.1200 respectively, in a partnership business. Find the share of B in profit of Rs.900 after a year?
(A) 276.92
(B) 267.92
(C) 266.27
(D) 900
(E) 237.8
Rationale: Explanation:
600:800:1200
3:4:6
4/13 * 900 = 276.92
Answer: A
Answer: (A) 276.92
Question: A shepherd has 1million sheep at the beginning of Year 2010. The numbers grow by xx during the yr. A famine hitshis village in the next year & many of his sheep die. The sheep population decreases by yy during 2001 and at the beginning of 2011 the shepherdfinds that he is left with 1 million sheep. Which of the following is correct?
(A) x=y
(B) x>y
(C) x<y
(D) x<=y
(E) x>=y
Rationale: Let us assume the value of xx to be 10%10%.
Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10%10% of 1 million = 1.1 million
In 2001, the numbers decrease by y%y% and at the end of the year the number sheep in the herd = 1 million.
i.e., 0.1 million sheep have died in 2001.
In terms of the percentage of the number of sheep alive at the beginning of 2001,
it will be (0.1/1.1)×100%=9.09%(0.1/1.1)×100%=9.09%.
From the above illustration it is clear that x>y
B
Answer: (B) x>y
Question: Pipes A and B can fill a cistern in 10 and 90 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
(A) 13
(B) 12
(C) 16
(D) 18
(E) 19
Rationale: :
1/10 + 1/90 = 1/9
9 * 2 = 18.Answer:D
Answer: (D) 18
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 50% goods during theft. His loss percent is:
(A) 72%
(B) 45%
(C) 32%
(D) 12%
(E) 22%
Rationale: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 50.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 50 = Rs. 55
Hence, loss % = 45/100 * 100 = 45%
Answer:B
Answer: (B) 45%
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 64 km/hr.
(B) 96 km/hr.
(C) 78 km/hr.
(D) 42 km/hr.
(E) 36 km/hr.
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =36 km/hr.
ANSWER:E
Answer: (E) 36 km/hr.
Question: In the first 10 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 4.25
(B) 5
(C) 6
(D) 7
(E) 7.5
Rationale: Required run rate = 282 - (4.2 x 10) =	240
240/40= 6
C)
Answer: (C) 6
Question: 3 balls inside a bag having nos on it written 1 , 2, 3 on it. a ball is taken and then put inside it. Find probability that all 3 nos r the same when it is taken 3 times
(A) 1/27
(B) 1/3
(C) 1/4
(D) 1/2
(E) 1/5
Rationale: by law of probability = 1/3 * 1/3 * 1/3 = 1/27
ANSWER:A
Answer: (A) 1/27
Question: Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 5:1
(B) 6:3
(C) 5:3
(D) 9:3
(E) 9:1
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 5000
Amount lent at 10% = 1000
Required ratio = 5000 : 1000 = 5 : 1
Answer:A
Answer: (A) 5:1
Question: Five female friendsfive male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with menwomen alternating. How many possible arrangements may she chose?
(A) 40320
(B) 28800
(C) 1152
(D) 576
(E) 70
Rationale: now any of the alternate 5 places can be filled by 5 male or female in 5!
similarily,
other 5 alternate places can be filled in 5!
hence required probability= 2*5!*5!=28,800
hence B
Answer: (B) 28800
Question: A train 200m long takes 6 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
(A) 85kmph
(B) 115kmph
(C) 105kmph
(D) 95kmph
(E) 125kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
200/[(x+5)*5/18] = 6
30(x+5) = 3600
x = 115kmph
Answer is B
Answer: (B) 115kmph
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 120 pastries ?
(A) 2 hours.
(B) 1 hours.
(C) 5 hours.
(D) 4 hours.
(E) 3 hours.
Rationale: A
2 hours.
In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 120 pastries would take 120 ÷ 60 = 2 hours.
Answer: (A) 2 hours.
Question: A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day?
(A) 11pm
(B) 01pm
(C) 08pm
(D) 09pm
(E) 12pm
Rationale: Time from 5 am. on a day to 10 pm. on 4th day = 89 hours.
Now 23 hrs 44 min. of this clock = 24 hours of correct clock.
356/15 hrs of this clock = 24 hours of correct clock
89 hrs of this clock = (24 x 31556 x 89) hrs of correct clock.
= 90 hrs of correct clock.
So, the correct time is 11 p.m.
Answer: A
Answer: (A) 11pm
Question: A and B invested money together in a business and share of capital of A is 1/4th that of B. If they incurr a loss of Rs.500 then loss for B is
(A) 400
(B) 300
(C) 200
(D) 100
(E) 80
Rationale: Let the investment of B be x
investment of A = 1/4 of B = (1/4)x
ratios of investment of A and B = 1/4 x : x
= x : 4x
Loss for B =[ 4 / (1+4) ] * 500
= (4/5) * 500
= 400 rs/-
ANSWER:A
Answer: (A) 400
Question: The ratio of three numbers is 1:3:4 and the sum of their squares is 2600. The sum of the numbers is?
(A) A)10
(B) B)12
(C) C)15
(D) D)14
(E) E)9
Rationale: Let the numbers be x,3x,4x
then, x^2+9x^2+16x^2 = 2600
26x^2 = 2600
x^2 = 100
x=10
Answer is A
Answer: (A) A)10
Question: The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed five times, what is the probability that the coin turns up tails on at least one of the tosses?
(A) 7/8
(B) 15/16
(C) 31/32
(D) 21/32
(E) 31/64
Rationale: P(5 heads)= 1/2*1/2*1/2*1/2*1/2=1/32.
P(at least one tail)=1-1/32=31/32.
The answer is C.
Answer: (C) 31/32
Question: A composer’s guild is planning its spring concert, and seven pieces have been submitted for consideration. The director of the guild knows that they will only have time to present five of them. If the pieces can be played in any order, how many combinations of pieces are possible?
(A) 40
(B) 25
(C) 21
(D) 27
(E) 32
Rationale: Combination question..
7C5 = 21..
IMO option C is correct..
Answer: (C) 21
Question: Ramesh purchased a refrigerator for Rs. 15500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 34778
(B) 26888
(C) 2899
(D) 17600
(E) 21725
Rationale: Price at which the TV set is bought = Rs. 15,500
Discount offered = 20%
Marked Price = 15500 * 100/80 = Rs. 19375
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 19375 + 375 = Rs. 19750
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 19750* 110/100
= Rs. 21725
Answer: E
Answer: (E) 21725
Question: What is the value 201st term of a sequence if the first term of the sequence is 2 and each successive term is 3 more the term immediately preceding it?
(A)  602
(B)  800
(C)  802
(D)  804
(E)  806
Rationale: COMMON DIFFERENCE d = 3
first term = a
nth term = a+(n-1)d
201st term = 2+(200)3
= 602
hence A
Answer: (A)  602
Question: If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly once in 3 consecutive flips ?
(A) 0.125
(B) 0.25
(C) 0.75
(D) 0.375
(E) 0.666
Rationale: Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 * 2 = 8 ways
For 2 T and 1 H
Thus probability is
= P(HTT) + P(TTH) + P(THT)
= 1/8 + 1/8 + 1/8
= 3/8
= .375
Answer : D
Answer: (D) 0.375
Question: In a manufacturing plant, it takes 48 machines 4 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
(A) 3
(B) 6
(C) 8
(D) 9
(E) 12
Rationale: the choices give away the answer..
48 machines take 4 hours to fill 8 standard orders..
in next eq we are doubling the machines from 48 to 72, but the work is not doubling(only 1 1/2 times),
= 4*48/72*12/8
=4
Ans A
Answer: (A) 3
Question: In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
(A) 156 m
(B) 140 m
(C) 145 m
(D) 169 m
(E) 172 m
Rationale: C
145 m
By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 - 855 = 145 m.
Answer: (C) 145 m
Question: The Guests at a football banquet consumed a total of 319 pounds of food. if no individual guest consumed more than 2 pounds of food, What is the minimum number of guests that could have attended the banquet?
(A) 160
(B) 161
(C) 162
(D) 163
(E) 164
Rationale: To minimize one quantity maximize other.
159*2 (max possible amount of food a guest could consume) = 318 pounds, so there must be more than 159 guests, next integer is 160.
Answer: A.
Answer: (A) 160
Question: Instead of multiplying a number by 5, the number is divided by 10. What is the percentage of error obtained ?
(A) 96%
(B) 98%
(C) 95%
(D) 97%
(E) 96%
Rationale: let the number be x
the right number is 5x
the wrong number is x/10
error is(5x-x/10)=49x/10
percentage of error is((49x/10)/5x)*100=98%
ANSWER:B
Answer: (B) 98%
Question: The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 7500 sq. m, the cost of fencing the field @ 25 paise per metre is
(A) Rs. 55.50
(B) Rs. 67.50
(C) Rs. 86.50
(D) Rs. 87.50
(E) None of these
Rationale: Solution
Let length = (3x) metres and breadth = (4x) metres.
Then, 3x × 4x = 7500 ⇔ 12x2 = 7500 ⇔ x2 = 625 ⇔ x = 25.
So, length = 75 m and breadth = 100 m.
Perimeter = [2(75 + 100)] m = 350 m.
∴ Cost of fencing = Rs. (0.25 × 350) = Rs. 87.50. Answer D
Answer: (D) Rs. 87.50
Question: Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 3125 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.
(A) 1287
(B) 1285
(C) 1283
(D) 1280
(E) 1281
Rationale: Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate A, B, C,E The answer to be D
Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year.
If x = initial number of trees = 1280
Year 1 = 5/4x
Year 2 = (5/4)(5/4)x
Year 3 = (5/4)(5/4)(5/4)x
Year 4 = (5/4)(5/4)(5/4)(5/4)x
Only for Answer D: (5/4)(5/4)(5/4)(5/4)1280 = 3125
Hence, correct answer = D
Answer: (D) 1280