mathewhe/aqua_rat huggingface dataset:
Question: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If w of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
(A)  y/R
(B)  y/(R-x)
(C)  xy/(R-x)
(D)  wy/(R(R-w))
(E)  y/(R(R-x))
Rationale: y/(R-w)- y/R
if we simplify this we get choice D, which is the correct answer.
Answer: (D)  wy/(R(R-w))
Question: If x, y, and z are positive integers such that x^2 + y^2 + z^2 = 64,470, which of the following could be the values of x, y, and z?
I. x = 115, y = 146, z = 173
II. x = 114, y = 142, z = 171
III. x = -115, y = 146, z = 173
(A) I only
(B) II only
(C) III only
(D) I​ and II
(E) I and III
Rationale: 10 sec answer if you know how to find the units digit of a number
The number given is of the form of square, so calculate the units digit - Here your objective is to find the sum where last digit is 0
x = 115, so x^2 will have units digit 5
y = 146, so y^2 will have units digit 6
z = 173, so z^2 will have units digit 9
Calculate the units digit , the units digit will be 0
Here III) option gives x=-115..(115^2) and(-115^2) are equal.
Hence this will be our answer is option E.
Answer: (E) I and III
Question: A and B together can do a piece of work in 30days. A having worked for 16days, B finishes the remaining work alone in 44days. In how many days shall B finish the whole work?
(A) 60
(B) 12
(C) 24
(D) 30
(E) 45
Rationale: Let A's 1day work = x
B's 1day work = y
x+y = 1/30
16x+44y = 1
x = 1/60
y = 1/60
B's 1 day work = 1/60
B alone can finish the job in 60 days
Answer is A
Answer: (A) 60
Question: In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
(A) 28000
(B) 30000
(C) 32000
(D) 33000
(E) None of these
Rationale: Explanation :
Let the number of candidates applied for the examination = x
Given that 5% of the applicants were found ineligible.
It means that 95% of the applicants were eligible (∴ 100% - 5% = 95%)
Hence total eligible candidates = 95x/100
Given that 85% of the eligible candidates belonged to the general category
It means 15% of the eligible candidates belonged to other categories(∴ 100% - 85% = 15%)
Hence Total eligible candidates belonged to other categories
= total eligible candidates × (15/100) = (95x/100) × (15/100)
= (95x × 15)/(100 × 100)
Given that Total eligible candidates belonged to other categories = 4275
⇒ (95x × 15)/(100 × 100) = 4275
⇒ (19x × 15)/(100 × 100) = 855
⇒ (19x × 3)/(100 × 100) = 171
⇒ (x × 3)/(100 × 100) = 9
⇒ x/(100 × 100) = 3
⇒ x = 3 × 100 × 100 = 30000
Answer : Option B
Answer: (B) 30000
Question: P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 5), the remainder is also D. If P/Q = 1020.75 and P/(Q + 5) = 816.6, then which of the following gives the correct set of {D, Q}?
(A) {6, 12}
(B) {6, 15}
(C) {15,20}
(D) {9, 15}
(E) {15, 24}
Rationale: p/q= d=p/q+5
d= .75 q
d= .6(q+5)
we get d = 15 and q = 20. Answer = C.
Answer: (C) {15,20}
Question: When a is divided by b, the quotient is c with remainder 6. What is a in terms of 6, b, and c?
(A) bc+6
(B) bc/6
(C) bc-6
(D) b/c
(E) b-c
Rationale: a/b =c with remainder 6
i.e, a-6 = bc
a= bc+6
Answer : A
Answer: (A) bc+6
Question: How many prime numbers exist between 1 and 20?
(A) 7
(B) 6
(C) 5
(D) 8
(E) 9
Rationale: E)
Answer: (E) 9
Question: All of the positive integers are written in a triangular pattern, beginning with the following
four lines and continuing in the same way:
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
Which number appears directly below 2012?
(A) 2100
(B) 2102
(C) 2104
(D) 2106
(E) 2108
Rationale: Observe that the nth row has 2n- 1 numbers, that each number on the 2nth row is
equal to 2n-2 plus the one above it, and that the last number in the nth row is n2. (The latter
fact may be proved by observing that n2- (n- 1)2 = 2n- 1, the length of the nth row.)
442 = 1936 and 452 = 2025, so that 2012 is on the 45th row. The number below it will be
larger by (2 * 46- 2), so it will be 2102.
correct answer B
Answer: (B) 2102
Question: The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Rationale: We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.
# of different approximations are possible.
Approach #1:
2*5=10;
3*7=~20 (actually more than 20);
11*19=~200 (actually more than 200);
13*17=~200 (actually more than 200);
2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107
Answer: C.
Approach #2:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107.
Answer: C.
Answer: (C) 10^7
Question: There are 6 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set?
(A) 15
(B) 30
(C) 69
(D) 78
(E) 90
Rationale: We can select from 0 to 6 pens and from 0 to 9 books.
Thus the total possible ways to select objects is 7*10 = 70
We must subtract 1 for the case with 0 pens and 0 books.
The answer is C.
Answer: (C) 69
Question: For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(20)/h(10) ?
(A)  1.8
(B)  60
(C)  6
(D)  18
(E)  3
Rationale: CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then
Mean = Median =(First+Last)/2
and Sum = Mean*Number of terms
h(20) = [(2+20)/2]*9 = 99
h(10) = (2+10)/2]*5 = 30
h(18)/h(10) = (99) / (30) ~ 3
Answer : E
Answer: (E)  3
Question: Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 15hr. If all pipes are opened simultaneously, then the cistern will be filled in
(A) 7.5 hr
(B) 8 hr
(C) 8.57 hr
(D) 10 hr
(E) None of these
Rationale: Solution:
Work done by all the tanks working together in 1 hour.
1/10+1/12−1/15=7/60
Hence, tank will be filled in 60/7=8.57 hour
Option(C)
Answer: (C) 8.57 hr
Question: The population of a town increased from 1,34,800 to 2,42,500 in a decade. The average percent increase of population per year is:
(A) 4.37%
(B) 7.9%
(C) 6.8%
(D) 8.75%
(E) None
Rationale: Explanation: Increase in 10 years = (242500 - 134800) = 107700
Increase% = (107700/134800 x 100)% = 79%.
Required average = (79/10)% = 7.9%.
Answer: Option B
Answer: (B) 7.9%
Question: In a company of 160 employees, 90 are females. A total of 80 employees have advanced degrees and the rest have a college degree only. If 40 employees are males with college degree only, how many employees are females with advanced degrees?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: The number of males is 160-90=70.
The number of males with advanced degrees is 70-40=30.
The number of females with advanced degrees is 80-30=50.
The answer is C.
Answer: (C) 50
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1400. The difference between the profit shares of A and C is?
(A) 288
(B) 560
(C) 155
(D) 600
(E) 441
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1400
=> 5 parts out of 15 parts is Rs. 1400
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1400) = Rs. 560
Answer:B
Answer: (B) 560
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 49 hours and 25 hours respectively. The ratio of their speeds is?
(A) 4:9
(B) 5:7
(C) 4:5
(D) 4:1
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √25 : √49
= 5:7
Answer:B
Answer: (B) 5:7
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age 5 years back was:
(A) 12 years.
(B) 14 years.
(C) 16 years.
(D) 17 years.
(E) 19 years.
Rationale: Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21
Son's age 5 years back (21- 5) = 16 years.
ANSWER :C
Answer: (C) 16 years.
Question: Simplify 3/4 of 6 0 – 8/5 of 60 + ? = 12
(A) 48
(B) 24
(C) 56
(D) 63
(E) 14
Rationale: 60 × 3/4 = 45, 60 × 8/5 = 96
45 – 96 + ? = 12 => 96 + 12 = 108 – 45 = 63
[63 + 45 = 108 – 96 = 12]
Option D
Answer: (D) 63
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
(A) 306.09
(B) 306.05
(C) 306.04
(D) 306.02
(E) 306.01
Rationale: A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer:C
Answer: (C) 306.04
Question: A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income?
(A) 800
(B) 900
(C) 700
(D) 750
(E) 650
Rationale: X * 4/5 * 80/100 = 576
X = 14400/16
X = 900
ANSWER B
Answer: (B) 900
Question: If two positive numbers are in the ratio 1/12 : 1/9, then by what percent is the second number more than the first?
(A) 70%
(B) 90%
(C) 33.33%
(D) 50%
(E) 65%
Rationale: Given ratio = 1/12 : 1/9 = 9 : 12
Let first number be 9x and the second number be 12x.
The second number is more than first number by 3x.
Required percentage = 3x/9x * 100 = 33.33%.
Answer:C
Answer: (C) 33.33%
Question: S = { 1,2,3,5,6,9}
T = { 4,5,6,7,1,3}
what is the probability that x chosen from S and y chosen from T will result x*y = even
(A) 5/9
(B) 3/2
(C) 1/2
(D) 5/6
(E) 6/5
Rationale: p: the probability that x*y is even, then p=1-p(x*y is odd)
p(x*y odd)=p(x odd)*p(y odd)=4/6*4/6=16/36=4/9
And p=1-4/9=5/9
Option: A
Answer: (A) 5/9
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is?
(A) 1/6
(B) 1/7
(C) 1/4
(D) 1/1
(E) 1/9
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7.Answer:B
Answer: (B) 1/7
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 300 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 5
(C) 18
(D) Cannot be determined
(E) None of these
Rationale: let rate = R% and time = R years
Then ( 1200 x R x R /100) = 300
=> 12R2= 300
=> R2= 25
=> R= 5
Answer B
Answer: (B) 5
Question: One pipe can fill a pool four times faster than a second pipe. When both pipes are opened, they fill the pool in eight hours. How long would it take to fill the pool if only the faster pipe is used?
(A) 5 hr
(B) 8 hr
(C) 10 hr
(D) 16 hr
(E) 20 hr
Rationale: fast pipe + slow pipe = together
One pipe fills the pool four times faster than the other pipe so,
hourly fill rates:
1/x + 1/4x = 1/8
Let x = number of hours it would take the fast pipe to fill the pool thus,
x=10 hours
Answer: C
Answer: (C) 10 hr
Question: How many odd numbers are possible between 1 to 1000000000? find out the number of odd number of digits?
(A) 2999
(B) 3500
(C) 4000
(D) 4599
(E) 499999999
Rationale: There are always one odd and one even no. And the question is odd no. Between 1 to 1000000000
So we have to find no. Between 1 to 1000000000 so we should not includes 1
1000000000/2 -1=499999999
ANSWER:E
Answer: (E) 499999999
Question: Which of the following is the Highest Common Factor of 20, 40 and 60?
(A) 8
(B) 10
(C) 6
(D) 20
(E) 12
Rationale: HCF IS2*2*5=20Ans is :D
Answer: (D) 20
Question: Ratio between Rahul and Deepak is 4:2, After 10 Years Rahul age will be 26 years. What is Deepak present age
(A) 14
(B) 15
(C) 12
(D) 22
(E) 8
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 10 = 26 => x = 4
So Deepak age is = 2(4) = 8
Answer: Option E
Answer: (E) 8
Question: The number of female students in a college in the previous year was 520. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year?
(A) 1600
(B) 1720
(C) 1840
(D) 1960
(E) 2080
Rationale: Let x be the number of male students last year. The number of male students this year is 2x.
Let y be the number of female students this year.
x/520 = 2(2x/y)
y = 2080
The answer is E.
Answer: (E) 2080
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 4 minutes?
(A) 36
(B) 54
(C) 216
(D) 216
(E) 324
Rationale: ONE Veggiematik machine can chop 36 carrots in 4 minutes
So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes
In other words, ONE Veggiematik machine can chop 54 carrots in4minutes
So,SIXVeggiematik machines can chop (4)(54) carrots in4minutes
In other words, SIX Veggiematik machines can chop 216 carrots in4minutes
Answer C
Answer: (C) 216
Question: Consider a Number 3.1n4
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
(A) 3
(B) 2
(C) 1
(D) 4
(E) 5
Rationale: In this ques we are given the thousandth digit as 4, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 4, the hundreth digit has to go up by 0, and correspondingly, the tenth digit should remain same.i.e 0-9.say 1
C
Answer: (C) 1
Question: Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the number's sum will be 13?
(A) 3/14
(B) 2/7
(C) 1/3
(D) 1/42
(E) 12/21
Rationale: Both Dice addition result is 13 = (6+7)
Probability that the number on first die is 6 = 1/6
Probability that the number on Second die is 7 = 1/7
Probability that Both Dice addition result is 13 = 1/6 * 1/7 = 1/42
D
Answer: (D) 1/42
Question: In a recent survey, Q people were asked whether they eat after 22:00 O'clock. 25 percent of the people answered positively and 40 percent of the rest were asked, at what time do they get up in the morning. Which of the following expressions represents the number of people who do not eat after 22:00 and were not asked about the time they get up in the morning?
(A) 3Q/20.
(B) Q/10
(C) 5Q/9
(D) 3Q/10
(E) 9Q/20
Rationale: Assume Q=100
100-25=75 people said they ate before 22:00
75*0.4=30 people were asked what time they got up in the morning
25+30=55 people were either asked what time they got up in the morning OR ate after 22:00
100-55=45 or 45% of Q were the number of people who did neither.
E is the equation for 45% of Q.
Answer: E
Answer: (E) 9Q/20
Question: The ratio, by weight, of coffee to sugar to water in a pot of coffee is 7:3:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: The new ratio of coffee to sugar is 3.5:3
The new ratio of coffee to water is 14:15.
The new ratio of coffee to sugar to water is 14:12:15.
If there are 12 grams of sugar, then there are (15/12)*12=15 grams of water.
The answer is D.
Answer: (D) 15
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
(A) 1
(B) 1/2
(C) 2/3
(D) 3/5
(E) 4/7
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(B)
Answer: (B) 1/2
Question: If the area of a circle is 36pi square feet, find its circumference.
(A) 12 pi feet
(B) 28 pi feet
(C) 38 pi feet
(D) 48 pi feet
(E) 58 pi feet
Rationale: The area is given by pi *r* r. Hence
pi * r *r = 36 pi
r * r = 36; hence r = 36 feet
The circumference is given by
2 * pi * r = 2 * pi * 6 = 12 pi feet
correct answer A
Answer: (A) 12 pi feet
Question: There are 5 white balls and 4 black balls in a bag. Second bag contains 7 white balls and 9 black balls. one ball is transferred from first bag to second. a single ball is taken out from second bag. What is the probability that the ball is white.
(A) 2/9
(B) 3/9
(C) 4/9
(D) 5/9
(E) 6/9
Rationale: lets divide this into 2 cases
case 1:When a black ball is transferred from bag 1 to 2
(4/9)*(7/17)=28/153
case 2: When a white ball is transferred from bag 1 to 2
(5/9)*(8/17)=40/153
total probability=(28/153)+(40/153)=4/9
ANSWER:C
Answer: (C) 4/9
Question: When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 5 centimeter. The actual diameter of the tissue, in centimeters, is
(A)  0.005
(B)  0.002
(C)  0.001
(D)  0.0005
(E)  0.0002
Rationale: It is very easy if x is the diameter, then the magnified length is 1000x.
ince 1000x=5 then x=5/1000=0.005.
The answer is A
Answer: (A)  0.005
Question: Two wheels are connected via a conveyor belt. The larger wheel has a 40cm diameter and the smaller wheel has a 32cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per minute in terms of r?
(A) 1280π
(B) 1.25r
(C) 48r
(D) 24r
(E) (64π)/3
Rationale: Interesting to note that the larger wheel has a diameter of 40 (8*5) while the smaller one has a diameter of 32 (8*4)...
If the large wheel has a diameter of 40 and the small wheel, 32, then their circumferences are 40pi and 32pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.25 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.25 = 12.5 revolutions per minute. If the large wheel makes 10 revolutions per minute . Therefore, the smaller wheel would need to make 10*1.25 = 12.5 revolutions per minute.
If r = 10, then the answer choice must be b.
B. 1.25r
Answer: (B) 1.25r
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
(A) 0 sq m
(B) 7 sq m
(C) 5 sq m
(D) 4 sq m
(E) 3 sq m
Rationale: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer:A
Answer: (A) 0 sq m
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 8
(B) 6
(C) 5
(D) 54
(E) 1
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Answer: (B) 6
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?
(A) 18
(B) 82
(C) 40
(D) 27
(E) 29
Rationale: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (83 - 63) => x/2
= 20 => x = 40.
Answer: C
Answer: (C) 40
Question: If the sum and difference of two numbers are 20 and 10 respectively, then the difference of their square is:
(A) 12
(B) 28
(C) 160
(D) 200
(E) 18
Rationale: Let the numbers be x and y.
Then, x + y = 20 and x - y = 8
x2 - y2 = (x + y)(x - y) = 20 * 10 = 200.
ANSWER:D
Answer: (D) 200
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 5% p.a. was Rs.492. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) Rs.4935
(B) Rs.4925
(C) Rs.5390
(D) Rs.5290
(E) Rs.5292
Rationale: Let the sum be Rs.P
P{ [ 1 + 5/100]2 - 1 } = 492
P(5/100)(2 + 5/100) = 492 [a2 - b2 = (a - b) ( a + b)] P =492 / (0.05)(2.05) = 4800. Amount =4800+492=Rs.5292 Answer : E
Answer: (E) Rs.5292
Question: If p<0, which of the following must be true?
(A) –100 < p < 100
(B) p ≤ –1
(C) p ≤ 1
(D) p^2 ≥ 1/4
(E) –100 < p < 0
Rationale: p is a negative number.
A. –100 < p < 100p can be a negative number less than -100
B. p ≤ –1p can be a fraction, in which case it would be greater than -1
C. p ≤ 1must be true since 1 is positive and p is negative
D. p^2 ≥ 1/4not true if p is a negative fraction like -1/5
E. –100 < p < 0p can be a negative number less than -100=C
Answer: (C) p ≤ 1
Question: A man can row with a speed of 12 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?
(A) 22
(B) 28
(C) 20
(D) 82
(E) 23
Rationale: M = 12
S = 11
DS = 12 + 11 = 23. Answer:E
Answer: (E) 23
Question: What is the minimum number of square marbles required to tile a floor of length 2 metres 89 cm and width 3 metres 74 cm?
(A) 176
(B) 187
(C) 374
(D) 748
(E) 546
Rationale: The marbles used to tile the floor are square marbles.
Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble.
As we have to use whole number of marbles, the side of the square should a factor of both 2 m 89 cm and 3m 74. And it should be the highest factor of 2 m 89 cm and 3m 74.
2m 89 cm = 578 cm and 3 m 74 cm = 374 cm.
The HCF of 289 and 374 = 34.
Hence, the side of the square is 17.
The number of such square marbles required,
=289×374/17×17
=374 marbles
Option(C)
Answer: (C) 374
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 1
II. y = 0
III. x = 0
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
Rationale: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer C
Answer: (C) III only
Question: The sum of the numbers is 110. If the first number be twice the second and third number be one-third of the first, then the second number is:
(A) 30
(B) 54
(C) 72
(D) 84
(E) 27
Rationale: Let the second number be x. Then, first number = 2x and third number = 2x/3.
2x + x + 2x/3 = 110
11x/3 = 110
x = 30
ANSWER:A
Answer: (A) 30
Question: If the sides of a triangle are 39 cm, 32 cm and 10 cm, what is its area?
(A) 120
(B) 772
(C) 288
(D) 160
(E) 2848
Rationale: The triangle with sides 39 cm, 32 cm and 10 cm is right angled, where the hypotenuse is 39 cm.
Area of the triangle = 1/2 * 32 * 10 = 160 cm2
Answer: D
Answer: (D) 160
Question: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $250. Find the original price of petrol?
(A) $11
(B) $5
(C) $45
(D) $400
(E) $5.5
Rationale: Price decreased by 10%, so 9/10 times, which means that original gallons bought increased 10/9 times. Since this increase equals to 5 gallons then 45 gallons were bought originally (45*10/9=50 --> increase 5 gallons). Hence original price was 250/45=$5.5
Answer: E.
Answer: (E) $5.5
Question: A train running at the speed of 60 km/hr crosses a pole in 21 sec. What is the length of the train?
(A) 350
(B) 150
(C) 277
(D) 258
(E) 191
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 21 = 350 m
Answer: A
Answer: (A) 350
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 1w widgets.
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets.
Answer : B
Answer: (B) 6