mathewhe/aqua_rat huggingface dataset:
Question: when a number is divided by 13,the remainder is 11.When the same number is divided by 17,the remainder is 9.What is the number ?
(A) 389
(B) 356
(C) 380
(D) 350
(E) 349
Rationale: x=13p+11 and x=17q+9
13q+11=17q+9
17q-13q=2
q=2+13q/17
The least value of p for which q=2+13q/17 is a whole number is p=26
x=(13*26*11)=(338+11)=349.
Answer is E
Answer: (E) 349
Question: If, for all integers n ≥ 1, xnxn is the probability of selecting at random an integer with an odd number of unique positive factors from among the positive integers less than or equal to n^2, then the sum of the first 5 values of xnxn is
(A) less than 1
(B) between 1 and 2
(C) between 2 and 3
(D) between 3 and 4
(E) greater than 4
Rationale: x1 : 1/1
x2 : 1,4 of 1,2,3,4 ----2/4
x3 : 1,4,9 of 1,2...9 ----3/9
x4 : 1,4,9,16----------4/16
x5 : 1,4,9,16,25--------5/25
Total 1+2/4+3/9+4/16+5/25 = 2.3
C is the right answer
Answer: (C) between 2 and 3
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 6 years ago?
(A) 152460
(B) 214560
(C) 131632
(D) 210000
(E) 200000
Rationale: population 2 years ago = 176400/(1 + 5/100)^6
Answer is C
Answer: (C) 131632
Question: At 6′o a clock ticks 6 times. The time between first and last ticks is 35 seconds. How long does it tick at 12′o clock
(A) 77
(B) 76
(C) 28
(D) 66
(E) 11
Rationale: Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 35/5 = 7 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 7 = 77 secs.
Answer: A
Answer: (A) 77
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 24 km
(B) 76 km
(C) 99 km
(D) 77 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer: E
Answer: (E) 20 km
Question: A can do a piece of work in 80 days. He works at it for 10 days & then B alone
finishes the remaining work in 42 days. In how much time will A and B, working
together, finish the work?
(A) 122days
(B) 41days
(C) 80days
(D) 42days
(E) 30days
Rationale: Work done by A in 10 days=10/80=1/8
Remaining work=(1-(1/8))=7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42*8/7)=48 days
Therefore, A's one day's work=1/80
B’s one day's work=1/48
(A+B)'s one day's work=1/80+1/48=8/240=1/30
Hence, both will finish the work in 30 days.
answer E 30days
Answer: (E) 30days
Question: A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 21 inches and the width of the wall is 28 inches, what is the length of the wall, in inches?
(A)  21.5
(B)  31.5
(C)  41.5
(D)  61.5
(E)  71.5
Rationale: Since the mirror is 42 inches in all sides, it must be a square. Area of a square is A=a^2; 21^2=441.Area of rectangle is double of that 2 *441=882.Now A=lw and we need find w so A/l=w ; 882/28= 31.5 Answer!
Answer is B
Answer: (B)  31.5
Question: At Veridux Corporation, there are 215 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there?
(A) 50
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Well, first letâ€™s take care of the â€œtotalsâ€. The numbers in the â€œtotalsâ€ row must add up. If 90 are females, the other 215 â€“ 90 = 125 must be males. Similarly, the numbers in the â€œtotalsâ€ column must add up. If 40 are managers, then the other 215 â€“ 40 = 175 must be associates.
Now, in the â€œassociateâ€ row, 135 + E = 175, which means E = 40â€” the other 40 associates must be female.
Now, to find B, which is what the question is asking, we need only look at the sum in the â€œfemaleâ€ column: B + 40 = 90, which means B = 50. There are fifteen female managers in this company. Thus, the answer = 50(A).
Answer: (A) 50
Question: The ratio of toddlers to infants at a day care center is 7 to 3. If twelve more infants join the day care to change the ratio to 7 to 5, how many toddlers are there at this day care center?
(A) 24
(B) 36
(C) 42
(D) 72
(E) 120
Rationale: 5x - 3x = 12
So, 2x = 6
hence no of toddlers is 6*7 =42
Answer will be (C) 42
Answer: (C) 42
Question: For integers U and V, when U is divided by V, the remainder is odd. Which of the following must be true?
(A) At least one of U and V is odd
(B) The sum U + V is odd
(C) U and V share no common factors other than 1
(D) UV is odd.
(E) U is odd
Rationale: At least one of U and V is odd
A
Answer: (A) At least one of U and V is odd
Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is?
(A) 4/5
(B) 4/7
(C) 5
(D) 5/7
(E) None
Rationale: Let the required fraction be x. Then 1 - x = 9
x 20
1 - x2 = 9
x 20
20 - 20x2 = 9x
20x2 + 9x - 20 = 0
20x2 + 25x - 16x - 20 = 0
5x(4x + 5) - 4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
x = 4/5
Option A
Answer: (A) 4/5
Question: In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets T can be created from this process?
(A)  35
(B)  105
(C)  210
(D)  420
(E)  630
Rationale: T=7C4 * 3C2 = 105 Answer B.
7C4 ways to choose 4 numbers for Box 1
3C2 ways to choose 2 numbers for Box2
1 way for Box 3 .
every combination will give a different product and can be arranged least to highest only in one way .B
Answer: (B)  105
Question: If the volume of a cube is x^3 cubic units, what is the number of square units in the surface area of the cube?
(A) x^2
(B) x^3
(C) x^6
(D) 6x^2
(E) 6x^3
Rationale: The question basically asks you to calculate the surface area of the cube.
Volume of the cube = x^3
This means each side of the cube = x
Hence area of each side = x^2
Total surfaces in a cube = 6
Total surface area = 6*x2
Correct Option: D
Answer: (D) 6x^2
Question: If x is a positive integer, which of the following must be odd?
(A) x+1
(B) x^2+x
(C) x^2+x+9
(D) x^2−1
(E) 3x^2−3
Rationale: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 9 = ODD
Hence C.
Answer: (C) x^2+x+9
Question: The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 10 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 35
(B) 30
(C) 25
(D) Data inadequate
(E) None of these.
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 60 and C - P = 10 M + C / 2 = [(M + P) + (C - P)] / 2 = (60 + 10) / 2 = 35.
ANSWER:A
Answer: (A) 35
Question: A train 325 m long passed a pole in 25 sec. How long will it take to pass a platform 900 m long?
(A) 76 sec
(B) 94 sec
(C) 87 sec
(D) 75 sec
(E) 96 sec
Rationale: Speed = 325/25 = 13 m/sec.
Required time = (325 + 900)/13
= 94 sec.
Answer:B
Answer: (B) 94 sec
Question: 48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 41% of respondents did not use M. 38% used N. What percent of respondents used only N?
(A) 19.5%
(B) 21.5%
(C) 20%
(D) 15.5%
(E) 17.5%
Rationale: From the question, we can summarize the information as follows:
N Not N
M X
Not M Ans y 41
38 100
Then we can set a system of 3 equations 3 unknowns described below:
X + Y = 48
X + Ans = 38
Y + Ans = 41
Sum up all three equations to get 2X + 2Y + 2Ans = 127
Divide both sides by 2 to get X + Y + Ans = 63.5
Replace X + Y with 48 to get 48 + Ans = 63.5
Substract 48 from both sides to get Ans = 63.5 - 48 = 15.5
The answer must be D.
Answer: (D) 15.5%
Question: A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: D=2S
H=2D =4S
C+S+2S+4S=13;C+7S=13
2S+4S=6S =6
S=1
C=6
ANSWER:C
Answer: (C) 6
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 12 days. If both of them work together, then the number of days required to complete the work is?
(A) 5.5 days
(B) 6.5 days
(C) 7.5 days
(D) 8.5 days
(E) 9.5 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 = 10 Ã— 12/22 = 5.5 days.
A)
Answer: (A) 5.5 days
Question: Two bullet trains of equal lengths take 8 seconds and 15 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(A) 13 sec.
(B) 10.4 sec.
(C) 12 sec.
(D) 17 sec.
(E) 19 sec.
Rationale: Speed of the first bullet train = 120/8 m/sec = 15 m/sec.
Speed of the second bullet train = 120/15 m/sec = 8 m/sec.
Relative speed = (15 + 8) = 23 m/sec.
Required time = (120 + 120)/23 sec = 10.4 sec.
B
Answer: (B) 10.4 sec.
Question: Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 30 items in the same time Machine Z produces 38 items. If machine Y takes 19 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?
(A) 6
(B) 9
(C) 9 1/2
(D) 15
(E) 13 1/2
Rationale: rate z/rate y=38/30
time z/time y=30/38
30/38*19= 15 minutes
D
Answer: (D) 15
Question: If the annual increase in the population of a town is 10% and the present number of people is 15000, what will the population be in 2 years?
(A) 12100
(B) 15240
(C) 18150
(D) 18452
(E) 19002
Rationale: The required population is = 15000 (1 + 10/100)^2
= 15000 * 11/10 * 11/10
= 18150
Answer is C
Answer: (C) 18150
Question: Machine A and machine B are each used to manufacture 550 sprockets. It takes machine A 10 hours longer to produce 550 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
(A) 6
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: Machine B: Takes x hours to produce 550 sprockets
Machine A: Takes (x+10) hours to produce 550 sprockets
Machine B: In 1 hour, B makes 550/x sprockets
Machine A: In 1 hour, A makes 550/(x+10) sprockets
Equating:
1.1(550/(x+10)) = 550/x
605/(x+10) = 550/x
605x = 550x+5500
55x = 5500
x = 100
A makes 550/(110) = 5 sprockets per hour
Answer : B
Answer: (B) 5
Question: R and S start walking each other at 10 AM at the speeds of 3 km/h and 4 km/h respectively. They were initially 17.5 km apart. At what time do they meet?
(A) 2 : 30 PM
(B) 11 : 30 AM
(C) 1 : 30 PM
(D) 12 : 30 PM
(E) None of these
Rationale: Let after t hours they meet then,
3t + 4t = 17.5 ⇒ t = 25
∴ Time = 10 am + 2.5 h = 12 : 30 am
Answer D
Answer: (D) 12 : 30 PM
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 60 more cows and 30 more buffaloes are brought in, how many days will the fodder last?
(A) 6
(B) 9
(C) 12
(D) 15
(E) 18
Rationale: 2 oxen = 3 buffaloes = 4 cows
Also: 15 buffaloes + 8 oxen + 24 cows
= 10 oxen + 8 oxen + 12 oxen = 30 oxen
There is enough fodder for 1 oxen for 30*24 days.
60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen
The new total is equal to 80 oxen instead of 30 oxen.
30*24 / 80 oxen = 9 days
The answer is B.
Answer: (B) 9
Question: Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 3 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half of the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
(A) 60
(B) 72
(C) 84
(D) 96
(E) 108
Rationale: D is the answer....
D = TS where D=distance, T=Time and S=Speed
To travel half distance, (2+3T) = 8T ==> T = 2/5 ==> 24 minutes
To travel double distance, 2(2+3T) = 8T ==> 2 ==> 120 minutes
Difference, 96 minutes
D
Answer: (D) 96
Question: The area of a sector of a circle of radius 5 cm formed by an arc of length 4 cm is?
(A) 8.78
(B) 8.67
(C) 8.75
(D) 10
(E) 8.28
Rationale: (5 * 4)/2
= 10
Answer:D
Answer: (D) 10
Question: A merchant gets a 5% discount on each meter of fabric he buys after the first 2,000 meters and a 7% discount on every meter after the next 1,500 meters. The price, before discount, of one meter of fabric is $2, what is the total amount of money the merchant spends on 5,500 meters of fabric?
(A) $7,360
(B) $8,540
(C) $9,720
(D) $10,570
(E) $11,680
Rationale: For first 2000 meters he does not get any discount.
The price is 2*2000 = $4000
For next 1500 meters, he gets a 5% discount.
The price is 1.9*1500 = $2850
For the next 1500 meters, he gets a 7% discount.
The price is 1.86*2000 = $3720
The total price is $4000 + $2850 + $3720 = $10,570
The answer is D.
Answer: (D) $10,570
Question: Find (7x + 2y ) / (x-2y) if x/2y = 3/2 ?
(A) 23
(B) 25
(C) 26
(D) 27
(E) 29
Rationale: x/2y=3/2
=>x=6y/2=3y
=>(7x+2y)/(x-2y)=((7*(3y))+2y)/(3y-2y)
=>23y/y=23
ANSWER:A
Answer: (A) 23
Question: If A can finish a work in 12 days and B can finish same work in 15 days.then they together can finish that work in how many days?
(A) 15
(B) 12
(C) 20/3
(D) 8
(E) 10/3
Rationale: A work in 1 hour=1/12,B work in 1 hour=1/15
[A+B] work in 1 hour=[1/12+1/15] = 3/20
Time take by both to finish the work=20/3hour
Answer C
Answer: (C) 20/3
Question: Convert the following units:
(a) 60 cm² in mm²
(A) 600 mm²
(B) 1600 mm²
(C) 6000 mm²
(D) 600 mm²
(E) 6600 mm²
Rationale: 60 cm² in mm²
1 cm = 10 mm
1 cm² = 100 mm²
Therefore, 60 cm² = 60 × 100 mm²
= 6000 mm²
ANSWER : OPTION C
Answer: (C) 6000 mm²
Question: The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 294 sq. cm, what is the length of the rectangle?
(A) 15 cm
(B) 18 cm
(C) 21 cm
(D) 24 cm
(E) 27 cm
Rationale: 2L+2W = 5W
L = 3W/2
W*L = 294
3W^2/2 = 294
W^2 = 196
W = 14
L = 3(14)/2 = 21
The answer is C.
Answer: (C) 21 cm
Question: A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Let x be the speed of B.
Write the equation:
(480-48)/x (time of B for first heat) - 6 (seconds, time B lost to A first heat) = TIME OF A (in both heats A runs with constant rate, so the time for first and second heats are the same)=(480-144)/x (time of B for second heat) + 2 (seconds, time B won to A second heat)
(480-48)/x-6=(480-144)/x+2
x=12
Answer: A.
Answer: (A) 12
Question: a factory produce certain no of car a day finds that increase in production efficiency by 12 1/2% then they produce 20 cars per day.how many cars produced in a day when their efficiency is 20% less
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: et effi. is x
x+(25x/1000=20
or, x=18(apprx)
now, x-(20% of x)= 18-(20% of 18)=14
ANSWER:C
Answer: (C) 14
Question: The equation relates the values (R - 3)/28 = (S + 8)/35 of two linked currencies, where R is the value in dollars of one currency and S is the value in dollars of the other currency. Which of the following equations can be used to convert dollar values from the R currency to the S currency?
(A) S = (5R - 47)/4
(B) S = (4R + 47)/5
(C) S = (5R + 17)/4
(D) S = (4R - 17)/5
(E) S = 5R/4 - 12
Rationale: R - 3)/28 = (S + 8)/35
(R - 3)/4 = (S + 8)/5
5(R - 3)/4 = s+8.
5R-47/4 = S
Option A.
Answer: (A) S = (5R - 47)/4
Question: Simple interest on a certain sum at a certain annual rate of interest is 1/3 of the sum. If the numbers representing Time is three times the Rate percent , then the Rate is:
(A) 1 1/3 %.
(B) 2 1/3 %.
(C) 3 1/3 %.
(D) 4 1/3 %.
(E) 5 1/3 %.
Rationale: Explanation :
Let sum = x. Then, S.I. = x/3
Let N =3R
[x * 3R * R / 100] = x/3? R^2 = 100/9
R = 10/3 = 3 1/3%.
Hence, Rate = 3 1/3 %.
Answer : C
Answer: (C) 3 1/3 %.
Question: The third smallest prime number is?
(A) 67
(B) 71
(C) 79
(D) 83
(E) 89
Rationale: The third smallest prime number is 79.
C)
Answer: (C) 79
Question: One out of every 2000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?
(A) 450
(B) 900
(C) 90,000
(D) 450,000
(E) 900,000
Rationale: (D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 2000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/2000 = 450/y. Solve for y and you will get the total number of chips in the batch: 900,000.
The answer is (E).
Answer: (E) 900,000
Question: In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg?
(A) 1:3
(B) 3:1
(C) 1:2
(D) 2:1
(E) 3:4
Rationale: Explanation:
=4:2=2:1
ANSWER IS D
Answer: (D) 2:1
Question: Mary has a monthly salary of $1200. She spends $280 per month on food. What percent of her monthly salary does she spend on food?
(A) 22%
(B) 23%
(C) 24%
(D) 25%
(E) 26%
Rationale: Solution to Problem 2:
The part of her salary that is spent on food is $280 out of her monthly salary of $1200
percent = part / whole = 280 / 1200 = 0.23 (rounded to 2 decimal places)
Multiply and divide 0.23 by 100 to convert in percent
percent = 0.23 * 100 / 100 = 23 / 100 = 23%
Answer B
Answer: (B) 23%
Question: If X = the product of four distinct prime numbers, how many factors does X have besides 1 and itself?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Let's take the four primes: 2, 3, 5 and 7 --> each of the 4 primes will be a factor of the product
All the possible combinations of the four primes will be factors (10 possible combinations):
2x3
2x5
2x7
3x5
3x7
5x7
2x3x5
2x3x7
2x5x7
3x5x7
Thus, in total there are 10 + 4 = 14 factors.
ANSWER:E
Answer: (E) 14
Question: What should come in place of the question mark (?) in the following equation?
12400 + 6899 = 610+ ?
(A) 12345
(B) 56894
(C) 18689
(D) 23478
(E) 94561
Rationale: 12400 + 6899 = 610+ ?
12400 + 6899 – 610 = 18689
Answer C
Answer: (C) 18689
Question: A person can row at 9 kmph and still water. He takes 8 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 60 km
(B) 87 km
(C) 38 km
(D) 67 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 8.5
=> x/10 + x/8 = 17/2 => (4x + 5x)/40 = 17/2 => x
= 38 km.
Answer:C
Answer: (C) 38 km
Question: The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
(A) Rs.10176
(B) Rs.10287
(C) Rs.10560
(D) Rs.10227
(E) Rs.11827
Rationale: Explanation:
Let the rate of interest be R% p.a.
4400{[1 + R/100]2 - 1} = 11193.60
[1 + R/100]2 = (44000 + 11193.60)/44000
[1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625
[1 + R/100]2 = 784/625 = (28/25)2
1 + R/100 = 28/25
R/100 = 3/25
Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100
=Rs.10560
Answer: C
Answer: (C) Rs.10560
Question: A test has 120 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?
(A) 11
(B) 13
(C) 15
(D) 17
(E) 19
Rationale: A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points.
Let C be the number of correct answers and let I be the number of incorrect answers.
To get 40 points, a test taker must have at least 40 correct answers. Then C=> 40.
For every correct question above 40, the test taker has 4 incorrect answers.
Then, the I = 4*(C - 40).
Also, I + C <= 120. Thus 5C <= 280 and so C <= 56.
Then 40 <= C <= 56 and C can have 17 possible values.
The answer is D.
Answer: (D) 17
Question: A man can reach certain place in 50hours. If he reduces his speed by 1/10th, he goes 400km less in time. Find his speed?
(A) 20km/hr
(B) 30km/hr
(C) 40km/hr
(D) 80km/hr
(E) 60km/hr
Rationale: Let the speed be x km/hr
50x-50* 9/10 *x = 400
50x - 45x = 400
5x = 400
x = 80km/hr
Answer is D
Answer: (D) 80km/hr
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
(A) Rs.147
(B) Rs.148
(C) Rs.144
(D) Rs.129
(E) Rs.112
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6
= Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100
= (120 * 120)/100
= Rs.144
Answer:C
Answer: (C) Rs.144
Question: The sum of the ages of 5 children born at the intervals of 3 year each is 60 year. what is the age of the eldest child ?
(A) 4 year
(B) 18 year
(C) 10 year
(D) None of these
(E) 9 year
Rationale: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 60 â‡” 5 x = 30 â‡” x= 6.
âˆ´ Age of the eldest child = x +12= 6 +12 =18 years. Answer B
Answer: (B) 18 year
Question: There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) Rs. 34
(B) Rs. 39
(C) Rs. 42
(D) Rs. 48
(E) Rs. 49
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
Answer: (C) Rs. 42
Question: Total number of people attending a party is 600. 70% of the men are wearing black shirt and rest are wearing red. If 60% of the total people are women then how many men are wearing red shirts?
(A) 168
(B) 72
(C) 56
(D) 170
(E) 60
Rationale: Number of woman in the party = 0.60*600 = 360
number of men in the party = 600-360 = 240
% of men wearing red shirts = 100-70 = 30%
number of men wearing red shirt = 0.30*240 = 72. B is the correct answer
Answer: (B) 72