mathewhe/aqua_rat huggingface dataset:
Question: A carpenter can produce 10 chair in 5 days ,b can produce 10 chair in 5 days and c can produce 20% faster than a and b. Approximately how many days would it take to produce a 100 chairs with all three carpenter working simultaneously?
(A) 16
(B) 17
(C) 15
(D) 10
(E) 20
Rationale: since c is 20% faster , thus it will create 12 chair in 5 days.
in 5 days total number of hubcaps made by all three will be :
10+10+12=32
in 10 days:
32+32=64
in 15 days:
64+32=96
now only 4 more chairs are required , which will take 2 days
thus in all 17 days.
Ans:B
Answer: (B) 17
Question: A train running at the speed of 58 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 145 m
(B) 786 m
(C) 566 m
(D) 546 m
(E) 445 m
Rationale: Speed = 58 * 5/18 = 145/9 m/sec
Length of the train = speed * time = 145/9 * 9
= 145 m
Answer: A
Answer: (A) 145 m
Question: How many different values of positive integer x, for which |x+5|<x, are there?
(A) 0
(B) 2
(C) 3
(D) 8
(E) 16
Rationale: Answer E
I opted to put the random value option.
i used 0 , 5 , -5 and the the extreme of 40 and -40..
i was able to solve it in 1:09
E
Answer: (E) 16
Question: A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Rs. 240. What is original price per kg of sugar.
(A) Rs. 10 per Kg
(B) Rs. 8 per Kg
(C) Rs. 6 per Kg
(D) Rs. 5 per Kg
(E) Rs. 7 per Kg
Rationale: It is based on inverse proportion or product constancy concept. Reduction in price 20% amount of sugar will increase 25%.
It means,
25% = 6 Kg. So,
Initially, total Sugar = 6*4 = 24Kg. Thus,
Original price of the sugar was,
240/24 = Rs. 10 per kg.
Answer: A
Answer: (A) Rs. 10 per Kg
Question: The speed of a car is 10 m/s. What is the its speed in kmph.
(A) 25 kmph
(B) 30 kmph
(C) 50 kmph
(D) 36 kmph
(E) 37 kmph
Rationale: Explanation:
m/sec to km/hr conversion:
x m/sec = [x x (18/5)] km/hr
10 x (18/5) 36 kmph
Answer: Option D
Answer: (D) 36 kmph
Question: Simplify 1939392 * 625
(A) 1212120010
(B) 1212120000
(C) 1212120011
(D) 1212121010
(E) 1212101010
Rationale: Explanation:
Trick: when multiplying with
5n
5n
then put n zeros to the right of multiplicand and divide the number with
2n
2n
So using this we can solve this question in much less
time.
1939392×54=1939392000016=1212120000
Answer: Option B
Answer: (B) 1212120000
Question: A sum of money deposited at C.I. amounts to Rs.1890 in 2 years and to Rs.2350 in 3 years. Find the rate percent?
(A) 30%
(B) 24%
(C) 20%
(D) 19%
(E) 50%
Rationale: 1890 --- 460
100 --- ? => 24%
Answer: B
Answer: (B) 24%
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
(A) 13 1/7
(B) 13 1/3
(C) 13 1/09
(D) 13 1/4
(E) 13 1/1
Rationale: 5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer: B
Answer: (B) 13 1/3
Question: A fair coin is tossed repeatedly. If head appears on first 5 tosses what is the probability that tail appears on 6th toss ?
(A) 1/6
(B) 1/5
(C) 1/3
(D) 1/2
(E) 1/6
Rationale: Explanation :
Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on 6th toss is still 1/2.
Answer : D
Answer: (D) 1/2
Question: Of the female students at Barkely University, 1/6 are on the honor roll. Of the male students, 2/5 are on the honor roll. If 3/5 of the students are female, what fraction of all the students are on the honor roll?
(A) 5/9
(B) 3/15
(C) 26/100
(D) 43/60
(E) 53/90
Rationale: let the total students be 100
given 3/5 of the students are females = 60
then males = 2/5 = 40
1/6 of the females are on honor roll = 10
males on the honor roll = 2/5= 16
total students on honor roll = 10+16 =26
fraction = 26/100
C
Answer: (C) 26/100
Question: A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
(A) 4436 toys
(B) 5487 toys
(C) 6113 toys
(D) 2354 toys
(E) 1375 toys
Rationale: To find the number of toys produced every day, we divide the total number of toys produced in one week (of 4 days) by 4.
5500 /4 = 1375 toys
correct answer E
Answer: (E) 1375 toys
Question: A man buys milk at 6 per litre and adds one third of water to it and sells mixture at 7.20 per litre. The gain is
(A) 40%
(B) 80%
(C) 60%
(D) 25%
(E) None of these
Rationale: C.P. of one litre = 6
After adding water to it One has to pay 7.20 for 2⁄3 litre of milk.
So S.P. of 2⁄3 litre of milk = 7.20
⇒ S.P. of 1 litre of milk = 7.20×3/2=10.80
∵ S.P. > C.P.
Hence gain = 10.80−6/6×100=4.80/6×100
= 0.80 × 100 = 80%
Answer B
Answer: (B) 80%
Question: In a simultaneous throw of pair of dice. Find the probability of getting
the total more than 7
(A) 1/2
(B) 1/4
(C) 5/12
(D) 7/12
(E) 1/6
Rationale: Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12.
Answer C) 5/12.
Answer: (C) 5/12
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 13% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
(A) 8°
(B) 40°
(C) 18°
(D) 36°
(E) 52°
Rationale: Here all percentage when summed we need to get 100% . As per data 13+24+15+29+8 = 89%.
So remaining 11% is the balance for the astrophysics.
Since this is a circle all percentage must be equal to 360 degrees.
100% ---- 360 degrees
Then 11% will be 40 degrees..
IMO option B.
Answer: (B) 40°
Question: A train crosses a bridge of length 800 m in 45 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?
(A) 375 m
(B) 750 m
(C) 400 m
(D) 800 m
(E) 300 m
Rationale: Let Length of Train = L
Case-1: Distance = 800+L (While crossing the bridge)
Time = 45 Seconds
i.e. Speed = Distance / Time = (800+L)/45
Case-2: Distance = L (While passing the lamp post)
Time = 15 Seconds
i.e. Speed = Distance / Time = (L)/15
But Since speed has to be same in both cases so
(800+L)/45 = (L)/15
i.e. 800 + L = 3L
i.e. 2L = 800
i.e. L = 400
Answer: option C
Answer: (C) 400 m
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 7967 for a computer table, then what was the cost price of the computer table?
(A) 6425
(B) 6887
(C) 6728
(D) 6725
(E) 2871
Rationale: :
CP = SP * (100/(100 + profit%))
= 7967(100/124) = Rs. 6425.
Answer: A
Answer: (A) 6425
Question: A rectangle has width a and length b.If the width is decreased by 20% and the length is increased by 10%,then what is the area of the new rectangle in percentage compared to 'ab' ?
(A) 77%
(B) 88%
(C) 92%
(D) 75%
(E) 68%
Rationale: New area =(80/100*a*110/100*b)=(4/5*11/10*ab)=(22/25*ab).
Required percentage =(22/25*ab*1/ab*100)%=88%.
Answer is B
Answer: (B) 88%
Question: 1370 , 1320 , 1070 , X, -6430
(A) -180
(B) 6530
(C) 6630
(D) 6730
(E) 6830
Rationale: 1370-50*(5^0)=1320
1320-50*(5^1)=1070
1070-50*(5^2)=-180
-180-50*(5^3)=-6430
ANSWER:A.
Answer: (A) -180
Question: If a & b are the root of the equation 4x^2+3x+7=0, then 1/a+1/b=
(A) -3/7
(B) 3/7
(C) -3/5
(D) 3/5
(E) -3/4
Rationale: we know that a+b=-3/4 and ab=7/4
so 1/a+1/b=(a+b)/ab
=(-3/7)
ANSWER:A
Answer: (A) -3/7
Question: A, B and C started a business by investing certain amount in the ratio 3 : 4 : 5 for two years, in the second year they earn 10% more profit than earned in the first year. If total profit for two years is Rs.44100. then what is the share of A in the second year ?
(A) Rs.5775
(B) Rs.6050
(C) Rs.5500
(D) Rs.3200
(E) Rs.8800
Rationale: Let first year profit be 100.
Then second year profit = 100 + 100 × 10 / 100 = 110
First year + second year = 100 + 110 = 210 or 210%
Second year profit = 44100 / 210 × 110 = 23100
A share in second year = 23100 × 3 / 12 = 5775
Option A
Answer: (A) Rs.5775
Question: Train A leaves the station traveling at 30 miles per hour. Two hours later train В leaves the same station traveling in the same direction at 35 miles per hour. How many miles from the station was train A overtaken by train B?
(A) 420
(B) 450
(C) 480
(D) 510
(E) 540
Rationale: After two hours, Train A is ahead by 60 miles.
Train B can catch up at a rate of 5 miles per hour.
The time to catch up is 60/5 = 12 hours.
In 12 hours, train A travels another 30*12 = 360 miles for a total of 420 miles.
The answer is A.
Answer: (A) 420
Question: Mary deposited $7,000 to open a new savings account that earned 14 percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Mary account one year after the account was opened?
(A)  $7,201
(B)  $7,205
(C)  $7,300
(D)  $7,454
(E)  $7,294
Rationale: Approach #1:
14 percent annual interest compounded semi-annually --> 7% in 6 moths.
For the first 6 moths interest was 7% of $7,000, so $140;
For the next 6 moths interest was 7% of $7,000,plus 7% earned on previous interest of $140, so $140+$14=$154;
Total interest for one year was $140+$154=$294, hence balance after one year was $7,000+ $294=$7,294.
Answer: E.
Answer: (E)  $7,294
Question: Together, Andrea and Brian weigh p pounds; Brian weighs 18 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds?
(A)  p/2 - 10
(B)  3p/4 - 9
(C)  3p/2 - 9
(D)  5p/4 - 10
(E)  5p - 5
Rationale: Together, Andrea and Brian weigh p pounds --> A + B = p.
Brian weighs 10 pounds more than Andrea --> B = A + 18 --> A + (A + 18) = p --> A = (p - 18)/2 = p/2 - 9.
Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 9) + p/4 = 3p/4 -9.
Answer: B.
Answer: (B)  3p/4 - 9
Question: 12.1212+17.0005 - 9.1101 = ?
(A) 20.0116
(B) 20.0105
(C) 20.0115
(D) 20.1015
(E) None
Rationale: Solution
Given expression
=(12.1212+17.0005)-9.1101
= (29.1217 - 9.1101)
=20.0116.
Answer A
Answer: (A) 20.0116
Question: The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?
(A) 11
(B) 30
(C) 99
(D) 88
(E) 61
Rationale: one man can consume the same food in 30*40 = 1200 days.
10 more men join, the total number of men = 40
The number of days the food will last = 1200/40 = 30 days.
Answer: B
Answer: (B) 30
Question: For how many integers n is 2^y = y^2 ?
(A) None of these
(B) One
(C) Four
(D) Three
(E) More than four
Rationale: draw a graph with y^2 and 2^y, you'll see 3 intercepts between the 2 curves, but one is in the 2nd quadrant, so it can't be an integer (for integer values of x, 2^x can be an integer only for x>0). Thus 2 are valid, and the answer is A
Answer: (A) None of these
Question: A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?
(A) 15028
(B) 15029
(C) 15000
(D) 13029
(E) 15921
Rationale: Principal = (100 * 5400) / (12 * 3)
= Rs.15000
Answer: C
Answer: (C) 15000
Question: Excluding stoppages, the speed of a train is 48 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) 16
(B) 17
(C) 15
(D) 18
(E) 12
Rationale: T = 12/48 * 60
= 15
Answer: C
Answer: (C) 15
Question: The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
(A) 13
(B) 33
(C) 23
(D) 43
(E) 53
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
Number to be added = (60 - 37) = 23. Answer: Option 'C'
Answer: (C) 23
Question: A shopkeeper forced to sell at cost price, uses a 900 grams weight for a kilogram. What is his gain percent?
(A) 10%
(B) 9%
(C) 11.11%
(D) 12 %
(E) None of these
Rationale: Shopkeeper sells 900g instead of 1000g.
So, his gain = 1000 - 900 = 100g.
Thus, %Gain = (100 *100)/900 = 11.11%.
answer : OPTION C
Answer: (C) 11.11%
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 120 m
(B) 240 m
(C) 300 m
(D) 120 m
(E) None of these
Rationale: Speed = 54 x	5/18	m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.Let the length of the platform be x metres.
Then,	9x + 3000/36	= 15
x + 300 = 540
x = 240 m. Answer: Option B
Answer: (B) 240 m
Question: If A is a negative integer, which of the following must be a negative integer?
(A) A + 1
(B) A/2+3
(C) A^4
(D) A – y
(E) A^11
Rationale: We need to check each option here:
A. A + 1
This will depend on the value of A. Nothing can be said
B. A/2+3
This will depend on the value of A. Nothing can be said
C. A^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. A – y
This will depend on the value of A. Nothing can be said
E. A^11
This will always be negative. Even powers of negative numbers are positive and odd powers are negative
Correct Option: E
Answer: (E) A^11
Question: If a coin is tossed 4 times what is the probability that it will land either heads 4 times or tails 4 times?
(A) 1/4
(B) 1/8
(C) 1/16
(D) 1/2
(E) 1/32
Rationale: The probability of 4 heads is (1/2)^4 = 1/16
The probability of 4 tails is (1/2)^4 = 1/16
The probability of 4 heads or 4 tails is 1/16 + 1/16 = 1/8
The answer is B.
Answer: (B) 1/8
Question: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 450?
(A) 5
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: 450 = 2*222 + 3*2
K weight of 600 = 2 +3 = 5
AnswerA
Answer: (A) 5
Question: 69 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?
(A) 10^7
(B) 10^8
(C) 10^9
(D) 10^10
(E) 10^11
Rationale: 69 laboratories raise the bacterium, the laboratory have 48 culture dishes on average, which has about 25,075 bacteria each. How many bacteria are there approximately?
A. 10^7
B. 10^8
C. 10^9
D. 10^10
E. 10^11
-> Due to approximately, 69=70, 48=50, 25,075=25,000 are derived, which makes (69)(48)(25,075)=(70)(50)(25,000)=10^7. The answer is A.
Answer: (A) 10^7
Question: A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.5, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?
(A) $3.00
(B) $20.75
(C) $22.50
(D) $41.50
(E) $45.00
Rationale: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .
A= 2O
S= 2G
A= 2S
A= 4G
A+O+S+G = 90
=>A + A/2 + A/2 +A/4 = 90
=> 9A/4 = 90
=> A = 40
O = 20
S = 20
G = 10
Cost of each candy = .5 $
Mininum amount of money required to guarantee that you would buy at least three of each type of candy
We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .
Total = 83 candies
Amount required = 83 * .5 = 41.50 $
Answer D
Answer: (D) $41.50
Question: If Aug 15th,2012 falls on Thursday then June 11th,2013 falls on which day ?
(A) Wednesday
(B) Monday
(C) SaturdaY
(D) Tuesday
(E) MONDAY
Rationale: Explanation:
First,we count the number of odd days for the left over days in the given period.
Here,given period is 15.8.2012 to 11.6.2013
Aug Sept Oct Nov Dec Jan Feb Mar Apr May Jun
16 30 31 30 31 31 28 31 30 31 11(left days)
2 + 2 + 3 + 2 + 3 + 3 + 0 + 3 + 2 + 3 + 4 (odd days) = 6 odd days
So,given day Thursday + 6 = Wednesday is the required result.
Answer: A) Wednesday
Answer: (A) Wednesday
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 17 days more?
(A) 89 men
(B) 120 men
(C) 90 men
(D) 60 men
(E) 134 men
Rationale: 760 ---- 22
760 ---- 20
x ----- 17
x*17 = 760*20
x = 894
760
-------
134
ANSWER:E
Answer: (E) 134 men
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 8 charts have been brought to the meeting, how many people are present?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 10
Total charts are 11 so A + 2B = 8
Add both: 3A + 3B = 18 so A + B = 6
Total number of people = 6
A
Answer: (A) 6
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 210 inclusive?
(A) 90
(B) 95
(C) 100
(D) 105
(E) 110
Rationale: The multiples of ten from 10 to 190 inclusive would be an evenly spaced set with 21 terms - 10, 20, 30,.......210
So average = (First term + Last Term)/2 = (10 + 210)/2 = 220/2 = 110
Hence, the correct answer is E.
Answer: (E) 110
Question: When x is divided by y, the quotient is z with remainder r. Which of the following is y in terms of r, x, and z? (Assume both y and z are nonzero.)
(A) x – r – z
(B) (x+r)/z
(C) x/z−r
(D) (x−r)/z
(E) xr – z
Rationale: When x is divided by y, the quotient is z with remainder r. Which of the following is y in terms of r, x, and z? (Assume both y and z are nonzero.)
A. x – r – z
B. (x+r)/z
C. x/z−r
D. (x−r)/z
E. xr – z
Given that when x is divided y, the quotient is z and remainder is r. This implies x-r is divisible by y and yz=(x-r) or y = (x-r)/z.
Answer D.
Answer: (D) (x−r)/z
Question: A bullet train leaves Kyoto for Tokyo traveling 240 miles per hour at 12 noon. Ten minutes later, a train leaves Tokyo for Kyoto traveling 160 miles per hour. If Tokyo and Kyoto are 320 miles apart, at what time will the trains pass each other?
(A) 12:40pm
(B) 12:49pm
(C) 12:52pm
(D) 1:00pm
(E) 1:05pm
Rationale: Train A: going from K to T
Train B: going from T to K
First I calculated how far Train A will have travelled by the time Train B starts at 12:10:
10 minutes at 240 mph
1/6*240=40miles
They have 320-40=280 miles to travel to meet each other.
I found the combined rate of the two trains
Rate(A) + Rate(B) = 400mph
Divide Distance/Rate to find total time each will travel:
280/400>>> 42 Minutes to meet
12:10+42 minutes = 12:52 or Answer C
Answer: (C) 12:52pm
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 62 percent of those who attended the meeting were stockholders and 46 percent were employees, what percent were stockholders who were not employees?
(A)  34%
(B)  38%
(C)  54%
(D)  53%
(E)  62%
Rationale: Let M represent the number of meeting attendees. Then, since 62% of M or 0.62M
were stockholders and 46% of M or 0.47M were employees, it follows that 0.62M +
0.46M = 1.08M were either stockholders, employees, or both. Since 1.08M exceeds
M, the excess 1.08M − M = 0.08M must be the number of attendees who were both
stockholders and employees, leaving the rest 0.62M − 0.08M = 0.54M, or 54%, of
the meeting attendees to be stockholders but not employees.
The correct answer is C.
Answer: (C)  54%
Question: A portion of the 90% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced?
(A) 5/7
(B) 6/7
(C) 9/5
(D) 13/9
(E) 13/6
Rationale: This is a weighted average question. Say x% of the solution was replaced --> equate the amount of chemicals: 0.90(1-x)+0.2*x=0.4 --> x=5/7.
Answer: A.
Answer: (A) 5/7
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 70 metres?
(A) 22 seconds
(B) 65 seconds
(C) 78 seconds
(D) 12 seconds
(E) 14 seconds
Rationale: Speed of the boat downstream
= 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 70/5 = 14 seconds.
Answer:E
Answer: (E) 14 seconds
Question: There are 8 people and 5 chairs. In how many different ways people can occupy the chairs?
(A) 1640
(B) 1650
(C) 1660
(D) 1670
(E) 1680
Rationale: number of ways = 8*7*6*5 = 1680
Answer is E
Answer: (E) 1680
Question: Two Trains starting at same time from two stations 320km apart and going in opposite directions cross each other at a distance of 140km from first stations. What is the ratio of their speeds
(A) 6:7
(B) 4:7
(C) 7:9
(D) 7:11
(E) 7:12
Rationale: Explanation:
As the two trains are starting at same time
Total distance is 320km
Crossed each other 140km from first stations
Therefore first train speed = 140kmph
And other one is 320-140 = 180kmph
Ratio of the two train speeds 140:180 = 7:9
Answer: Option C
Answer: (C) 7:9
Question: Which of the following is closer to (9!+8!)-(9!-8!)?
(A) 80460
(B) 80640
(C) 80540
(D) 80440
(E) 80740
Rationale: 9!+8!)-(9!-8!)=362880+40320-362880+40320
= 80640
Answer: B
Answer: (B) 80640
Question: A certain boxer has agreed to pay his opponent a fee of 3% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $26,250 after weighing in seven pounds over the specified limit, what was the boxer's purse?
(A) $65,625
(B) $105,000
(C) $125,000
(D) $183,750
(E) $1,050,000
Rationale: .03*7 = .21
26250/.21 = $125,000
Answer: C
Answer: (C) $125,000
Question: A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points L that an individual player might have scored?
(A) 7
(B) 13
(C) 16
(D) 21
(E) 23
Rationale: General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.
Minimum number of points for a player is 7, so the minimum number of points of 11 players is 7*11=77.
Therefore, the maximum number of points L for 12th player is 100-77=23.
Answer: E.
Answer: (E) 23
Question: What number is that, to which if 1, 5, and 13, be severally added, the first sum shall be to the second, as the second to the third?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Solution
Let x= the number required.
By the conditions, x+1:x+5 = a+5:x+13
Subtracting terms, (Art. 385,2.) x+1:4 = x+5:8
Therefore 8x+8 = 4x+20. And x = 3.
Answer C
Answer: (C) 3
Question: A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.8.40 less, he would have gained 30%. Find the cost of the article.
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Let C.P=100
Gain=25%
S.P=125
Supposed C.P=80
Gain=30%
S.P=(130*80)/100=104
Diff=(125-104)=21
Diff 21 when C.P=100
then Diff 8.40 when C.P=(100*8.40)/21=40
ANSWER:B
Answer: (B) 40
Question: Find the least number which when divided by 12,24,36,42 leaves remainder 9,21,33,39 respectively.
(A) 499
(B) 501
(C) 452
(D) 365
(E) 325
Rationale: The difference of 12-9 = 3 , 24-21 = 3 , 36-33= 3 , 42-39 = 3
LCM of 12,24,36,42 = 504
Required number = 504 - 3 = 501
Answer is B
Answer: (B) 501