mathewhe/aqua_rat huggingface dataset:
Question: A person buys an article at Rs.460. At what price should he sell the article so as to make a profit of 18%?
(A) 542
(B) 882
(C) 772
(D) 662
(E) 521
Rationale: Cost price = Rs.460
profit = 18% of 460 = Rs.82
Selling price = Cost price + Profit
= 460 + 82 = 542
Answer: A
Answer: (A) 542
Question: The number of boxes in a warehouse can be divided evenly into 12 equal shipments by boat or 32 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?
(A)  27
(B)  33
(C)  96
(D)  81
(E)  162
Rationale: Answer is the LCM of 12 and 32
= 96
Answer C
Answer: (C)  96
Question: If P(A) = 3/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.
(A) 6/25
(B) 3/25
(C) 8/25
(D) 2/13
(E) 3/17
Rationale: P (A n B) = P(A) . P(B)
P (A n B) = 3/5 . 2/5
P (A n B) = 6/25.
A
Answer: (A) 6/25
Question: Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $580 (before payroll deductions)?
(A) 400
(B) 500
(C) 600
(D) 700
(E) 800
Rationale: total pay = 40*$12.50 + $0.16*x = 580
x = 80 / 0.16 = 500
The answer is B.
Answer: (B) 500
Question: By the how much is two-fifth of 200 greater than three -fifths of 125?
(A) 15
(B) 3
(C) 5
(D) 30
(E) None of these
Rationale: Reqd no. = 2⁄5 × 200 - 3⁄5 × 125
= 80 - 75 = 5
Answer C
Answer: (C) 5
Question: The respective heights and volumes of a hemisphere and a right circular cylinder are equal, then the ratio of their radii is :
(A) 1.225
(B) 2.225
(C) 3.225
(D) 1.825
(E) 0.225
Rationale: Height of hemisphere = radius of hemisphere = Height of right circular cylinder = h
and
radius of right circular cylinder = r , then
(2/3)* pi*h^3 = pi*(r^2)*h
h/r = Root (3/2) = root 1.5 = 1.225
ANSWER:A
Answer: (A) 1.225
Question: Find the odd man out. 187, 264, 386, 473, 682, 781
(A) 386
(B) 187
(C) 781
(D) 682
(E) 564
Rationale: Explanation :
In all numbers except 386, the middle digit is the sum of other two digits. Answer : Option A
Answer: (A) 386
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 16. What is the middle number?
(A) 27
(B) 29
(C) 36
(D) 34
(E) 35
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 16 = 90
So, the middle number is (126 - 90 ) = 36
C
Answer: (C) 36
Question: The salary of Mr. X is 30% more than that of Mr. Y . Find what percent of Mr. Y’s salary is less than Mr. X’s?
(A) 23 1/8%
(B) 23 8/3%
(C) 23 1/3%
(D) 28 1/3%
(E) 13 1/3%
Rationale: y=100	x=130
130---------30
100---------? => 23 1/3%
Answer:C
Answer: (C) 23 1/3%
Question: On a wedding catering service, An experienced chef can prepare a service for a wedding in 12 hours while an novice chef would finish the preparations in 24 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 10
Rationale: Experienced chefs work = 1 wedding/12 hours
Novice chefs work = 1 wedding/24 hours
Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equalx
1hr and 36mins = 8/5 an hour
x/12 + x/24 = 1 wedding / (8/5)
x/12 + x/24 = 5/8
x=5
So there are 5 novice chefs and 5 experienced chefs. In total there are 10. The answer is E.
Answer: (E) 10
Question: If 11 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
(B) 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
(C) 11 × 10
(D) 55
(E) 45
Rationale: Total number of handshakes = C112=11∗10/2=55
Answer: D
Answer: (D) 55
Question: A reduction of 22% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) s.2.82
(B) s.2.4
(C) s.2.5
(D) s.2.2
(E) s.2.1
Rationale: 100*(22/100) = 22 --- 10
? --- 1 => Rs.2.2
100 --- 78
? --- 2.2 => Rs.2.82
Answer:A
Answer: (A) s.2.82
Question: Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 13.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 7 hours?
(A)  42
(B)  56
(C)  70
(D)  91
(E)  140
Rationale: We are told that:generallya cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 13.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 13 mph then the maximum distance, in miles, that the cyclist could travel in 7 hours would be 7*13=91 miles.
Answer: D.
Answer: (D)  91
Question: On a certain transatlantic crossing, 30 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets?
(A) 33.3%
(B) 40%
(C) 50%
(D) 60%
(E) 75%
Rationale: 0.30P = RT + C
0.6(RT) = no C
=> 0.40(RT) had C
0.30P = 0.40(RT)
RT/P = 3/4=75%
Answer -E
Answer: (E) 75%
Question: There are 400 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
(A) 800
(B) 900
(C) 1000
(D) 1100
(E) None of these
Rationale: as per question stem 2/5M (Portion of Men employees who are managers) + 400 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+400= 2/5T, or 2/5(T-M)=400, from here we get that T-M=1000, that would be total number of female employees and the answer (C)
Answer: (C) 1000
Question: If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?
(A) 4
(B) 7
(C) 8
(D) 13
(E) 26
Rationale: Assume the sides to be x and y.
Perimeter = 2x + 2y = 42
Hence x + y = 21 - (i)
Area = xy = 104 - (ii)
Since these are the sides of a billboard, we are dealing with positive numbers only and the options tell us that they are integers.
104 can be written as a product of two numbers as 104*1 or 52*2 or 26*4 or 13*8
Of these, only 13*8 satisfies the equation (i)
Hence the lengths are 13 and 8
Length of shorter side = 8
ANSWER:C
Answer: (C) 8
Question: Two trains travelling in the same direction at 50 and 40 kmph completely pass off another in 1 1/2 minute. If the length of the first train is 125 m, what is the length of the second train?
(A) 300 m
(B) 287 m
(C) 125 m
(D) 250m
(E) 167 m
Rationale: RS = 50 â€“ 40 = 10 * 5/18 =25/9 mps
T = 90 sec
D = 25/9 *90 = 250 m
125
--------
125 m
Answer: C
Answer: (C) 125 m
Question: The function f is defined by subtracting 25 from the square of a number and the function s is defined as the square root of one-half of a number. If s(f(x))=10, then which of the following is a possible value of x?
(A) -15
(B) -5
(C) 0
(D) 5
(E) 25
Rationale: f(x) = x^2-25
s(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
s(f(x)) = 10
s(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A.
Answer: (A) -15
Question: A train 150 m long is running with a apecd of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going?
(A) 6 sec.
(B) 7 sec.
(C) 9 sec.
(D) 11 sec.
(E) None
Rationale: Solution
Speed of the train relative to man	=( 68 - 8 )
= 60 Kmph
= 60 x 5 / 18
=50/3 m/sec.
Time taken by it to cover 150 m at (50 /3)m/sec	= (112 - 50)kmph
= (150 x 3/50)sec
= 9 sec.
Answer C
Answer: (C) 9 sec.
Question: If 30% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
(A) 110
(B) 616
(C) 550
(D) 430
(E) 880
Rationale: Students enrolled in biology are 30% and therefore not enrolled are 70%. so of 880 is 880*.7 = 616
Answer is B 616
Answer: (B) 616
Question: A rectangular tiled patio is composed of 96 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 96 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
(A) 5
(B) 6
(C) 8
(D) 13
(E) 28
Rationale: Suppose there are c columns and there are r rows
Original Situation
So, Number of tiles = c*r = 96
Also. Reach column has r tiles and each row has c tiles
New Situation
Number of tiles in each column is r-2 and number of tiles in each row is c+4
So, number of rows = r-2 and number of columns is c+4
So, Number of tiles = (r-2)*(c+4) = 96
Comparing both of them we get
c*r = (r-2)*(c+4)
=> 4r -2c = 8
c = 2r - 4
Putting it in c*r=96
(2r-4)*r = 96
2r^2 - 4r - 96=0
r cannot be negative so r = 8
and c = 12
So, Answer will be C
Answer: (C) 8
Question: If M is the least common multiple of 90,196, and 300, which of the following is NOT a factor of M?
(A) 600
(B) 700
(C) 900
(D) 2,100
(E) 4,900
Rationale: first calculate the LCM of the given numbers
90 = 2*3*3*5
196=2*2*7*7
300=2*2*3*5*5
LCM = 2*2*3*3*5*5*7*7 this is the number M.
now check each number whether a factor of M.
Answer A is 600.
Answer: (A) 600
Question: A sum of Rs.66000 is divided into three parts such that the simple interests accrued on them for six, two and eleven years respectively may be equal. Find the amount deposited for 11 years.
(A) 6500
(B) 2000
(C) 4500
(D) 3000
(E) 6000
Rationale: Let the amounts be x, y, z in ascending order of value. As the interest rate and interest accrued are same for 2 years 6 years and 11 years i.e. 2x = 6y = 11z = k.
L.C.M. of 2,6,11 = 66 So x:y:z: = 33000 : 11000 :6000
The amount deposited for 11 years = 6000
ANSWER:E
Answer: (E) 6000
Question: A watch was sold at a loss of 10%. If the watch was sold for $12 more, there would have been a gain of 6%. What is the cost price?
(A) $55
(B) $65
(C) $75
(D) $85
(E) $95
Rationale: 0.9x + 12 = 1.06x
0.16x = 12
x = 75
The answer is C.
Answer: (C) $75
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/7%
(B) 16 2/6%
(C) 16 2/3%
(D) 16 9/3%
(E) 16 1/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: (C) 16 2/3%
Question: If (x+2) is the HCF of x2 + ax + b and x2 + cx + d , then which one of the following is correct ?
(A) a + c = b + d
(B) 2a + b = 2c + d
(C) b + 2c = 2a + d
(D) b - 2c = 2a - d
(E) None
Rationale: Answer
If (x+2) is the HCF of x2 + ax + b and x2 + cx + d.
Then, (-2)2 -2a +b = (-2)2 -2c + d
b + 2c = 2a + d
Correct Option: C
Answer: (C) b + 2c = 2a + d
Question: Which of the following is equal to the value of 2^4 + 2^4 + 3^4 + 3^4 + 3^4 ?
(A) 2^5 + 3^10
(B) 2^5 + 3^9
(C) 2^5 + 3^8
(D) 2^5 + 3^5
(E) 2^5 + 3^7
Rationale: 2^4 + 2^4 + 3^4 + 3^4 + 3^4
= 2 (2^4) + 3 (3^4)
= 2^1 (2^4) + 3^1 (3^4)
= 2^(1+4) + 3^(1+4)
= 2^5 + 3^5
Ans: D
Answer: (D) 2^5 + 3^5
Question: 9. On level farmland, two runners leave at the same time from the intersection of two country roads. One runner jogs due north at a constant rate of 6 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour faster than the first runner's rate. How far apart, to the nearest mile, will they be after 1/2 hour ?
(A)  6
(B)  7
(C)  5
(D)  12
(E)  14
Rationale: If runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle.
Side 1 = 6 m/h --> 3 m in 1/2 hr
Side 2 = 8 m/h --> 4 m in 1/2 hr
to complete this right angle triangle
d^2 = 4^2 + 3^2
d^2 = 25
= 5
Answer option C
Answer: (C)  5
Question: In store A there are 10 pairs of pants for every 30 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?
(A) 3:16.
(B) 2:3.
(C) 4:9
(D) 3:4.
(E) 2:5.
Rationale: 1st statement : ratio of pants
Store A : Store B
10x : 30x
X:3X
Price :
4y:3y
Total revenue
4xy : 9xy
4:9
Answer : C
Answer: (C) 4:9
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
(A) 14 years
(B) 18 years
(C) 20 years
(D) 22 years
(E) 24 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22. Answer: Option D
Answer: (D) 22 years
Question: In feb Mrs Bil's earnings were 70 percent of the Bil family's total income. In June Mrs Bil earned 10 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Bil's earnings were approximately what percent of the Bil family's total income ?
(A) 72
(B) 34
(C) 78
(D) 37
(E) 27
Rationale: Lets say the Family Income is 100
In May, Bil earned 70Family income is 30
In june, Bil earned 10% more than May, so it is (70+10*70/100 = 77)
Family Income is same 30
In June Bil's Income percent is 77*100/107 ~ 72
Ans is A
Answer: (A) 72
Question: Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability M that the new color will be one of theJaunecolors?
(A) 5/42
(B) 37/42
(C) 1/21
(D) 4/9
(E) 5/9
Rationale: I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune MM = (40 + 34)/84 = 37/42.B
Answer: (B) 37/42
Question: Tough and Tricky questions: Word Problems.
If Bill's salary increased by 16 percent, he would earn $812 per month. If instead, his salary were to increase by only 10 percent, how much money T would he earn per month?
(A) $700
(B) $754
(C) $770
(D) $782
(E) $893
Rationale: OFFICIAL SOLUTION:
(C) If Bill’s salary increased by 16% he would earn $812. Algebraically, this can be written as:
$812 = 1.16S, where S is his current salary.
Then S = $812/1.16 = $700.
Now that we know his current salary is $700, we can calculate what his salary would be if it were increased by 10%. We know that 10% of $700 is $70, so his salary would be:
T=$700 + $70 = $770.
The correct answer is choice (C).
Answer: (C) $770
Question: The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 28 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?
(A)  27
(B)  33
(C)  84
(D)  81
(E)  162
Rationale: Answer is the LCM of 6 and 28
= 84
Answer C
Answer: (C)  84
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
(A) 8/15
(B) 2/5
(C) 3/5
(D) 11/15
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 7/15
ANSWER:E
Answer: (E) 7/15
Question: When a positive integer A is divided by 7 and 3, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 7 and 3, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)?
(A) 10
(B) 14
(C) 21
(D) 28
(E) 36
Rationale: A = 7k+1 = 3j+2
B = 7m+1 = 3n+2
A-B = 7(k-m) = 3(j-n)
A-B is a multiple of both 7 and 3, so it is a multiple of 21.
The answer is C.
Answer: (C) 21
Question: A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
(A) 36 kmph
(B) 16 kmph
(C) 26 kmph
(D) 46 kmph
(E) 50 kmph
Rationale: . Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph
ANSWER A
Answer: (A) 36 kmph
Question: Of all the homes on Gotham Street, 2/3 are termite-ridden, and 2/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
(A) a) 2/15
(B) b) 3/15
(C) c) 4/5
(D) d) 2/5
(E) e)1/5
Rationale: let total homes be 15
termite ridden= 2/3(15)= 10
termite ridden and collapsing = 2/5(10)=4
thus homes that are termite ridden, but not collapsing = 10-4=6
thus required ratio = 6/15=2/5
Answer D
Answer: (D) d) 2/5
Question: How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDQTERRANEAN such that the first letter is E and the last letter is R?
(A) 34
(B) 45
(C) 46
(D) 49
(E) 56
Rationale: Therefore, we have to find two more letters from the remaining 11 letters.
Of the 11 letters, there are 2 Ns, 2Es and 2As and one each of the remaining 5 letters.
The second and third positions can either have two different letters or can have both as same letters.
Case 1: When the two letters are different
One has to choose two different letters from the 8 available different choices.
This can be done in 8 * 7 = 56 ways.
E
Answer: (E) 56
Question: A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 160 square feet and its length is 6 feet longer than its width. If the uniform width between the rug and room is 6 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
(A) 32
(B) 456
(C) 40
(D) 46
(E) 104
Rationale: Rug's area = 160
which is (x) x (6+x) = 160
so x= 10
rug maintains a uniform distance of 6 feet
so room has dimension 10+12 and 16+12 i.e. 22 and 28
area of room 22x28 = 616
area covered is 160
so uncovered area is 616-160=456 (ANSWER B)
Answer: (B) 456
Question: If the total income of a state increases by 50% and the population of the state increases by 20%, What is the percent change in per capita income for the state?
(A) A net increase of 40%
(B) A net increase of 30%
(C) A net increase of 25%
(D) A net increase of 20%
(E) A net decrease of 20%
Rationale: We're told that the total income of a state increases by 50% and the total population increases by 20%
To start:
Total Income = $100
Total Population = 100 people
$100/100 = $1 per person
After the increase:
New Total Income = $150
New Total Population = $120
$150/120 = $5/4 per person
The question asks for the percent increase in per capita income, which means that we need to use the Percentage Change Formula:
Percent Change = (New - Old)/Old
New = 5/4
Old = 1
(5/4 - 1)/1 = (1/4)/1 = 1/4 = 25% increase
C
Answer: (C) A net increase of 25%
Question: In a box of 10 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
(A) 6/11
(B) 7/15
(C) 8/17
(D) 9/22
(E) 10/23
Rationale: P(neither pen is defective) = 7/10*6/9 = 7/15
The answer is B.
Answer: (B) 7/15
Question: If a young child was 15 months old one year ago, how old was the child, in months, x months ago?
(A) x − 27
(B) x − 12
(C) 15 − x
(D) 24 − x
(E) 27 − x
Rationale: The child's age today is 15 months + 12 months = 27 months
x months ago, the child's age was (27 - x) months old.
The answer is E.
Answer: (E) 27 − x
Question: How many positive factors do 180 and 90 have in common?
(A) 6
(B) 12
(C) 16
(D) 18
(E) 24
Rationale: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 180 and 90 is 90
Number of factors of 90 = 12
Answer :B
Answer: (B) 12
Question: A car is purchased on hire-purchase. The cash price is $22 000 and the terms are a deposit of 10% of the price, then the balance to be paid off over 60 equal monthly installments. Interest is charged at 12% p.a. What is the monthly installment?
(A) $503
(B) $504
(C) $515
(D) $528
(E) $537
Rationale: Explanation:
Cash price = $22 000
Deposit = 10% Ã— $22 000 = $2200
Loan amount = $22000 âˆ’ $2200
Number of payments = 60
= $19800
I=p*r*t/100
I=11880
Total amount = 19800 + 11880 = $31680
Regular payment = total amount /number of payments = 528
Answer: D
Answer: (D) $528
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 15 miles per hour." What was their average speed in the whole journey?
(A) 10 miles/hour
(B) 12 miles/hour
(C) 11 miles/hour
(D) 13 miles/hour
(E) 14 miles/hour
Rationale: 2xy/x+y=2*150/25=12 miles/hour
ANSWER:B
Answer: (B) 12 miles/hour
Question: Yesterday it took Robert 4 hours to drive from City A to City B. Today it took Robert 2.5 hours to drive back from City В to City A along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 70 miles per hour. What is the distance between city A and city B?
(A)  90
(B)  120
(C)  150
(D)  210
(E)  300
Rationale: 2d/70 = 6 ( because time = 4 + 2.5 - 0.5 hrs)
=> d = 210
Answer - D
Answer: (D)  210
Question: A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3
Rationale: This is a weighted average question. Average of -11% and +7% is +1%.
Using w1/w2 = (A2 - Avg)/(Avg - A1),
we get w1/w2 = (7 - 1)/(1- (-11)) = 6/12
Revenue from Car:Revenue from Trucks = 1:2
ANSWER:A
Answer: (A) 1:2
Question: A sum amounts to Rs.5292 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
(A) s.4000
(B) s.5000
(C) s.4500
(D) s.4800
(E) s.5800
Rationale: CI=5292,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
5292=P[21/20]^2
5292[20/21]^2
4800
ANSWER:D
Answer: (D) s.4800
Question: In a certain country 1/5 of 8 = 4. Assuming the same proportion, what would be the value of 1/4of 16 ?
(A) 13
(B) 12
(C) 10
(D) 16
(E) 14
Rationale: C
10
Answer: (C) 10
Question: How many litres of pure acid are there in 8 litres of a 20% solution?
(A) 1.4
(B) 1.5
(C) 1.6
(D) 2.4
(E) None
Rationale: Solution
Quantity of pure acid	= 20% of 8 litres
= (20/100×8)litres
= 1.6 litres.
Answer C
Answer: (C) 1.6
Question: There are 5 boxes numbered from 1 to 5. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
(A) 15
(B) 17
(C) 19
(D) 21
(E) 23
Rationale: 1 green ball: 5 ways
2 green balls: 4 ways
3 green balls: 3 ways
4 green balls: 2 ways
5 green balls: 1 way
The total number of ways is 5*6/2=15
The answer is A.
Answer: (A) 15
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 5, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)(2x-5) = 0?
(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=5,x=-10andx=5/2=2.5. So, three solutions present in our set of 12 distinct numbers, therefore P=3/12=1/4.
Answer: C.
Answer: (C) 1/4
Question: Anitha runs her own baking company.This morning,Anitha worker baked 810 plum pies.They also baked some more after lunch. In total,they baked 888 plum pies. How many plum pies did Anitha workers bake after lunch?
(A) 28
(B) 56
(C) 78
(D) 13
(E) 34
Rationale: 888-810=78. Answer is C.
Answer: (C) 78