mathewhe/aqua_rat huggingface dataset:
Question: Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
(A) 65000
(B) 67000
(C) 70000
(D) 72000
(E) 75000
Rationale: Ratio of the profits of Kamal and Kiran
=25000×12:60000×8
=25×12:60×8
=5×3:12×2
=5:4×2
=5:8
Let the total profit =x
Then Kamal received 10x/100=x/10 as commission for managing the business.
Remaining profit =x−x/10=9x/10 which is shared in the ratio 5:8
Total amount received by Kamal =(x/10)+(9x/10)×(5/13)
⇒(x/10)+(9x/10)×(5/13)=58000
⇒x+9x(5/13)=580000
⇒x(1+(45/13))=580000
⇒x(58/13)=580000
⇒x(1/13)=10000
⇒x=130000
Kiran's share = 130000−58000=72000
Answer is D.
Answer: (D) 72000
Question: When 2/3 of the garments in the shipment were inspected, 28 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 90 percent of the garments in the shipment pass?
(A) 10
(B) 9
(C) 13
(D) 7
(E) 5
Rationale: B = 9
2/3x= 30
x=45
for 90% approval we need 41 garments approved.
already approved = 28
we need 13 more.
Answer : C
Answer: (C) 13
Question: According to a recent student poll, 4/6 out of 24 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
(A) 1/14
(B) 4/49
(C) 2/7
(D) 62/69
(E) 13/14
Rationale: 16 students are interested, 8 are not interested
Prob = 1 - 8C2/24C2 = 1 - (8*7/(24*23))=1 - 7/69 = 62/69
Answer : D
Answer: (D) 62/69
Question: If 35% of the 840 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
(A) 546
(B) 550
(C) 555
(D) 532
(E) 515
Rationale: We know 35 % people study biology,therefore the no of people not studying = 100 - 35 = 65%
> Therefore the people not studying biology out of a total 840 people are = 65 % of 840
> (65/100)*840 = 546 people
A
Answer: (A) 546
Question: The current in a river is 5 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?
(A) 69 miles
(B) 88 miles
(C) 93,75 miles
(D) 100 miles
(E) 112 miles
Rationale: Upstream Speed = 20-5=15 mph
Downstream Speed = 20+5 = 25 mph
D/15 + D/25 = 10 hours
Solving for D we get D=93,75
Answer: C
Answer: (C) 93,75 miles
Question: X is the least common multiple of 96,196,300, which number below is not factor of X?
(A) 600
(B) 700
(C) 900
(D) 2100
(E) 4900
Rationale: Factors:
96=2^5, 3^1
196=2^2, 7^2
300= 2^2, 3^1, 5^2
So, I get LCM= 2^5, 3^1, 5^2, 7^2
A. 600=2^3, 3^1, 5^2
B. 700=2^2, 5^2, 7^1
C. 900=2^2, 3^2, 5^2
D. 2100=2^2, 3^1, 5^2, 7^1
E. 4900=2^2, 5^2, 7^2
answer is C
Answer: (C) 900
Question: The sum of three consecutive multiples of 3 is 81. What is the largest number?
(A) 24
(B) 28
(C) 30
(D) 32
(E) 35
Rationale: Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 81
9x = 72
x = 8
Largest number = 3x + 6 = 30.
Answer : C
Answer: (C) 30
Question: How many three letter words are formed using the letters of the word MARRIAGE?
(A) 326
(B) 429
(C) 226
(D) 336
(E) 280
Rationale: The number of letters in the given word is eight.
The number of three letter words that can be formed using these four letters is 8P3
= 8 * 7* 6 = 336.
Answer: D
Answer: (D) 336
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 227
(B) 2689
(C) 342
(D) 787
(E) 191
Rationale: 400*(90/100)*(95/100)
= 342
Answer: C
Answer: (C) 342
Question: How long does a train 120 m long travelling at 60 kmph takes to cross a bridge of 170 m in length?
(A) 15.8 sec
(B) 14.9 sec
(C) 12.4 sec
(D) 16.8 sec
(E) 17.4 sec
Rationale: E
17.4 sec
D = 120 + 170 = 290 m
S = 60 * 5/18 = 50/3
T = 290 * 3/50 = 17.4 sec
Answer is E
Answer: (E) 17.4 sec
Question: One ball will drop from a certain height. The height it will reach after rebounding from the floor is 50 percent of the previous height. The total travel is 260cm when it touches the floor on third time. What is the value of the original height?
(A) 80cm
(B) 90cm
(C) 104cm
(D) 120cm
(E) 130cm
Rationale: when Ball comes down, Then i have indicated the distance covered in green
when Ball goes up, Then i have indicated the distance covered in red
Distance travelled uptil the ball touches the floor 3rd time:h+0.5h+0.5 h+0.5*0.5 h+0.5*0.5 h
h + 2 * 0.5 * h + 2 * 0.25 * h = h (1+2*0.5+2* 0.25) = h (1+1+0.5) = 260
2.5 h = 260
h = 104.
C is the answer.
Answer: (C) 104cm
Question: A train 120 m long passed a pole in 6 sec. How long will it take to pass a platform 360 m long?
(A) 20 sec
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Speed = 120/6
= 20 m/sec.
Required time
= (120 + 360)/20
= 24 sec.
Answer:E
Answer: (E) 24
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family ?
(A) 31( 5/7)
(B) 81( 5/7)
(C) 51( 5/7)
(D) 41( 5/7)
(E) 31( 3/7)
Rationale: Explanation:
Required average = (67 * 2 + 35 * 2 + 6 * 3) / (2 + 2 + 3)
= (134 + 70 + 18) / 7 = 222 / 7 = 31(5/7) years.
Answer: A
Answer: (A) 31( 5/7)
Question: The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 32 ?
(A) 440
(B) 512
(C) 550
(D) 620
(E) 750
Rationale: Large numbers are made in two ways:
Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.
31*2 = 62 (large prime number)
2^6 = 64 (many small prime numbers)
To get a sum as large as 32 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.
You are left with 620 which is 31*2*2*5 (sum greater than 32)
Answer D
Answer: (D) 620
Question: The age of father 8 years ago was twice the age of his son. eight years hence, father's age will be twice that of his son. The ratio of their present ages is:
(A) 5 : 3
(B) 7 : 3
(C) 9 : 2
(D) 7 : 2
(E) 13 : 4
Rationale: Let the ages of father and son 8 years ago be 2x and x years respectively.
Then, (2x + 8) + 8 = 2[(x + 8) + 8]
2x + 16 = 2x + 32
x = 16.
Required ratio = (2x + 8) : (x + 8) = 40 : 24 = 5:3
answer :A
Answer: (A) 5 : 3
Question: Find out the wrong term in the series 1, 10, 100 100, 1000, 100000
(A) 100,000,000
(B) 10,000
(C) 100,000
(D) 10,000,000
(E) 100,000,000,000
Rationale: Explanation:
Each number with in the series is the product of the two numbers that proceed it.
So, if (1 * 10 = 10) , then (1000 * 100000 = 100 000 000 ).
100000000 should replace 100000.
Answer: A )100,000,000
Answer: (A) 100,000,000
Question: If a sum of money trebles itself in 40 years,what is the rate of interest?
(A) 5%
(B) 6%
(C) 4%
(D) 3%
(E) None of these
Rationale: Explanation:
Let the sum of money be Rs.x
After 40 years, this becomes 3x
Simple Interest = 3x - x = 2x
Simple Interest = PRT/100
2x = (x×R×40)/100
2 = (R×40)/100
200 = 40R
R = 5%
Answer: Option A
Answer: (A) 5%
Question: If the average (arithmetic mean) of 4x-5, 8x-6, and 9x+5 is 279, what is the value of x?
(A) 18
(B) 25
(C) 27
(D) 29
(E) 31
Rationale: AM of 4x-5, 8x-6, and 9x+5=4x-5+ 8x-6+9x+5 / 3 = 31x/3
Given that 31x/3 = 279
x = 837/31 =27
x = 27
Answer is C
Answer: (C) 27
Question: Three medical experts, working together at the same constant rate, can write an anatomy textbook in 32 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 6 days?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: Each expert can write 1/96 of the book per day.
To complete the book in 6 days, we need 96/6 = 16 experts, thus 13 more experts are needed.
The answer is D.
Answer: (D) 13
Question: 8 couples attend a dance show in a TV channel. A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is at least 1 couple will be selected is :
(A) 11/13
(B) 12/17
(C) 15/39
(D) 19/31
(E) 21/35
Rationale: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)
= 15/39
C
Answer: (C) 15/39
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 7% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 63.84
(B) 62.6
(C) 62.1
(D) 62.7
(E) 62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(93/100) = 59.375
MP = 63.84
Answer: A
Answer: (A) 63.84
Question: What is the remainder when 54617^(42788234) is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: We need to find the units digit of the number.
The units digit of powers of seven repeats 7, 9, 3, and 1 cyclically.
Since 42788234 has the form 4a + 2, the units digit is 9.
Then the remainder when dividing by 5 is 4.
The answer is E.
Answer: (E) 4
Question: A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun four times, approximately what is the probability that the product of the four winning sectors’ integers will be even?
(A) 50%
(B) 67%
(C) 88%
(D) 94%
(E) 98%
Rationale: The only way to have an odd product is if all 4 integers are odd.
P(odd product) = 1/2*1/2*1/2*1/2 = 1/16
P(even product) = 1 - 1/16 = 15/16 which is about 94%
The answer is D.
Answer: (D) 94%
Question: If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. ab > 0
II. ab is even
III. c is even
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II, and III
Rationale: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
II only.letter B
Answer: (B) II only
Question: In a throw of coin what is the probability of getting head.
(A) 1
(B) 2
(C) 1/2
(D) 0
(E) None of these
Rationale: Explanation:
Total cases = [H,T] - 2
Favourable cases = [H] -1
So probability of geƫng head = 1/2
Answer: C
Answer: (C) 1/2
Question: A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If7 were to be added to each score, which of these three statistics would change?
(A) The mean only
(B) The median only
(C) The standard deviation only
(D) The mean and the standard deviation
(E) The mean and the median
Rationale: The correct answer is E.
Answer: (E) The mean and the median
Question: A manufacturer of a certain type of screw rejects any screw whose length is less than 2.44 + 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?
(A) |k + 0.03| > 2.5
(B) |k — 0.03| <= 2.5
(C) |k — 2.5| > 0.03
(D) |k — 2.5| >= 0.06
(E) |k — 2.5| <= 0.03
Rationale: So, let's go through this step by step:
rejects any screw whose length is less than 2.44 + 0.03 centimeters or greater than 2.5 + 0.03 centimeters.
In other words, any screw that is less than: 2.44 + 0.03 =2.47 or greater than 2.50 + 0.03 =2.53 will be rejected.
If k represents the length of a screw
In other words,Kis an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:
2.47 ≤ K ≤ 2.53
You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.
Let's look at (E):
|k — 2.5| <= 0.03
For the positive case: k - 2.5 ≤ 0.03 ===>k ≤ 2.53
For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===>k ≥ 2.47
2.47 ≤ k ≤ 2.53
(E)
Answer: (E) |k — 2.5| <= 0.03
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start?
(A) A)2
(B) B)5
(C) C)7
(D) D)5
(E) E)1
Rationale: Explanation:
|-----------20--------------------|
60 40
D = 20
RS = 60– 40 = 20
T = 20/10 = 1 hours
Answer: Option E
Answer: (E) E)1
Question: Tammy climbed a mountain in two days. She spent a total of 14 hours climbing the mountain. On the second day, she walked at an average speed that was half a kilometer per hour faster, but 2 hours less than what she walked on the first day. If the total distance she climbed during the two days is 52 kilometers, how many W kilometers per hour did Tammy walk on the second day?
(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 6
Rationale: Ans: C
Total time = 14 hrs
Let time traveled during 1st day = x
Let time traveled during 2nd day = x-2
Total time =14
x+x-2 = 14
x=8
speed * time = distance
s*8 + (s+0.5)(8-2) = 52
solving s = 4.5
now speed for 2nd day is 0.5 less than the 1st day which is 4.5
Thus speed for 2nd day = 4
Its simple algebra for s*8 + (s+0.5)(8-2) = 52 but for some reason Im getting 3.5 and not 4.5.
8s+6s+3=52
14s=49
s=3.5
Answer: (C) 4
Question: If p > 1 and q = 2^(p −1), then 4^p =
(A) 16q^2
(B) 4q^2
(C) q^2
(D) q^2/4
(E) q^2/16
Rationale: If p > 1 and q = 2^(p −1), then 4^p
Given p>1, so let's assume p=2
q=2^(p-1) = 2^(2-1) = 2, so q=2
hence, 4^p = 4^2 = 16
only 1 ans. choice can satisfy this:
A) 16q^2 --> clearly > 16
B) 4q^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)
C) q^2 --> clearly < 16
D) q^2/4 --> clearly < 16
E) q^2/16 --> clearly < 16
Ans. B) 4q^2
Answer: (B) 4q^2
Question: A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among five colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)
(A) 7
(B) 10
(C) 15
(D) 17
(E) 20
Rationale: 5C2 = 10
The number of test subjects is 10 + 5 = 15
The answer is C.
Answer: (C) 15
Question: The mass of the sun is approximately 2 × 10^25 kg and the mass of the moon is approximately 8 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?
(A) 4.0 × 10^(−18)
(B) 2.5 × 10^12
(C) 4.0 × 10^18
(D) 2.5 × 10^19
(E) 4.0 × 10^42
Rationale: Mass of sun = x * Mass of moon
x = Mass of sun / Mass of moon = (2 × 10^25) / (8 × 10^12) = 2*2^-3*10^13 = 10^13/4 = 2.5*10^12
Ans. B) 2.5 × 10^12
Answer: (B) 2.5 × 10^12
Question: If C + D = 17 and C and D are positive integers, which of the following is a possible value for 3C + 2D?
(A) 29
(B) -29
(C) 0
(D) -19
(E) 19
Rationale: c + d = 11
3c + 2d = 2c + c + 2d = 2(c+d) + c = 34+ c=c=-34
Now this reults in
c+d=17=-34+d=17=d=51
c=-34;d=51
3c + 2d=3(-34)+2(51)=-102+102=0
3c + 2d= 0
Hence, C is the right answer.
Answer: (C) 0
Question: In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 24 play both table tennis and cricket 30 play. Badminton and cricket and
16 students play all the sports. How many students are there in the class ?
(A) 84
(B) 164
(C) 97
(D) 94
(E) 74
Rationale: total no. of students
= n(B U T U C)= n(B)+n(T)+n(C)-n(B∩T)-n(B∩C)-n(C∩T)+n(B∩T∩C)
= n(B U T U C)= 73+79+75-25-24-30+16
= n(B U T U C)= 164
ANSWER:B
Answer: (B) 164
Question: Two lorries each 350 m long are running in opposite directions on parallel tracks. Their speeds are 40km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 77 sec
(B) 36 sec
(C) 48 sec
(D) 55 sec
(E) 45 sec
Rationale: Relative speed = 40 + 30 = 70 km/hr.
70 * 5/18 = 175/9 m/sec.
Distance covered = 350 + 350 = 200 m.
Required time = 700 * 9/175 = 36 sec.
Answer: B
Answer: (B) 36 sec
Question: In a simultaneous throw of pair of dice .find the probability of getting the total more than 7
(A) 5/2
(B) 4/7
(C) 4/3
(D) 5/12
(E) 2/7
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.
Ans: D
Answer: (D) 5/12
Question: A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hour?
(A) 7 km/hr
(B) 7.2 km/hr
(C) 8 km/hr
(D) 9 km/hr
(E) 11 km/hr
Rationale: Speed = 600	m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x	18 km/hr
5
= 7.2 km/hr
B
Answer: (B) 7.2 km/hr
Question: If 5 people undertook a piece of construction work and finished half the job in 15 days. If two people drop out, then the job will be completed in?
(A) 8 days
(B) 10 days
(C) 18 days
(D) 20 days
(E) 25 days
Rationale: That is, half the work done = 5 × 15 × ½
Then, 5 × 15 × ½ = 3 × ? ×1/2
i.e. 5 × 15 = 3 × ?
therefore, ? (No. days required) = 5 × 15/3 = 25 days.
E)
Answer: (E) 25 days
Question: A firm is comprised of partners and associates in a ratio of 2:63. If 50 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm?
(A) 5
(B) 10
(C) 12
(D) 20
(E) 25
Rationale: The ratio 1:34 = 2:68 so the ratio changed from 2:63 to 2:68.
68-63 = 5 which is 1/10 of the increase in 50 associates.
The ratio changed from 20:630 to 20:680.
Thus the number of partners is 20.
The answer is D.
Answer: (D) 20
Question: Simple interest on a certain sum is 16.2 over 20 of the sum. Find the rate per cent and time, if both are equal.
(A) 8% and 8 years
(B) 6% and 6 years
(C) 9% and 9 years
(D) 12 % and 12 years
(E) None of these
Rationale: 16.2â„20 P = PÃ—RÃ—R/100
â‡’ R2 = 1620â„20 â‡’81=> R = 9%
Also, time = 9 years
Answer C
Answer: (C) 9% and 9 years
Question: A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 55 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)
(A) $15,360
(B) $17,360
(C) $25,560
(D) $21,360
(E) $27,360
Rationale: For every $3 earn above $9360, the recipient loses $1 of benefit.
OR
For every $1 loss in the benefit, the recipient earns $3 above $9360
If earning is; 9360+3x
Benefit = 12000-x
Or the vice versa
If benefit is 12000-x, the earning becomes 9360+3x
He lost 50% of the benefit;
Benefit Received= 12000-0.55*12000 = 12000-6600
x=5400
Earning becomes 9360+3x=9360+3*5400=25560
Ans:C
Answer: (C) $25,560
Question: x and y are positive integers of T. If 1/x + 1/y < 2, which of the following must be true?
(A)  x + y > 4
(B)  xy>1
(C)  x/y + y/x < 1
(D)  (x - y)^2 > 0
(E)  None of the above
Rationale: Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B
Answer: (B)  xy>1
Question: If MANGO is written as 41576 and APPLE is written as 17735, then GRAPES would be written as:
(A) 7999340
(B) 7835610
(C) 7226710
(D) 7913350
(E) 7917510
Rationale: E
7917510
All letters whose position in the alphabet is below 10, are being represented by their position number.
All letters whose position is 10 or more, are being represented by their position number minus ten.
Therefore:
G is 7
R is 18-9=9
A is 1
P is 16-9=7
E is 5
S is 19-9=10
Answer: (E) 7917510
Question: A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 1/4rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?
(A) 1/3
(B) 2/9
(C) 9/49
(D) 16/81
(E) 1/6
Rationale: The first thing to notice is that A is faster than B and B is faster than C.
Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.
If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.
Therefore total work done = (2*2) + (1*1) + (1/4*1/4) = 81/16
Proportion of work done by B = (1*1) / (81/16) = 16/81
Hence Answer D.
Answer: (D) 16/81
Question: If the positive integer N is a perfect square, which of the following must be true?
I. The number of distinct factors of N is odd.
II. The sum of the factors of N is odd.
III. The number of distinct prime factors of N is even.
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III
Rationale: SOLN:
1. The number of distinct factors of a perfect square is ALWAYS ODD.
2. The sum of distinct factors of a perfect square is ALWAYS ODD.
3. A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
4. Perfect square always has even powers of its prime factors.
So I and II must be true.
ANSWER:C
Answer: (C) I and II
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 19:2
(B) 18:3
(C) 19:1
(D) 19:5
(E) 19:4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Answer:D
Answer: (D) 19:5
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) Rs.2000
(B) Rs.2029
(C) Rs.2297
(D) Rs.2020
(E) Rs.2293
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: (A) Rs.2000
Question: A person borrowed Rs.500 at the rate of 5% per annum S.I what amount will he pays to clear the debts after 4 years?
(A) 300
(B) 700
(C) 500
(D) 800
(E) 600
Rationale: Explanation:500------>5*4=20%(500)=100500+100=600Answer: Option E
Answer: (E) 600
Question: Find the smallest number which should be multiplied with 1152 to make it a perfect square.
(A) 2
(B) 1
(C) 3
(D) 5
(E) 6
Rationale: 1152 = 2*2*2*2*2*2*2*3*3
Required smallest number = 2
2 is the smallest number which should be multiplied with 1152 to make it a perfect square.
ANSWER:A
Answer: (A) 2
Question: Two trains 140 m and 210 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 12.6 sec
(B) 11.8 sec
(C) 27.7 sec
(D) 10.8 sec
(E) 17.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 210 = 350 m.
Required time = 350 * 9/250 =12.6 sec.
Answer: A
Answer: (A) 12.6 sec
Question: How many integers are between 5 and 96/7, inclusive?
(A) 7
(B) 9
(C) 10
(D) 12
(E) 15
Rationale: 96/7 = 13.xx
We are not concerned about the exact value of 96/7 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 5 and 96/7 would be 5, 6, 7, 8, 9, 10, 11, 12,13
Total number of integers = 9
Option B
Answer: (B) 9
Question: How many zeroes are there at the end of the number N, if N = 60! + 120! ?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: The number of zeroes at the end of 60! will be less than the number of zeroes at the end of 120!
Hence it is sufficient to calculate the number of zeroes at the end of 60!
The number of zeroes = [60/5] + [60/25] + [60/125] = 12 + 2 + 0 = 14
The answer is B.
Answer: (B) 14