RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: On a game show, a contestant spins three different wheels; each wheel is numbered 1 to 10. What is the probability that the contestant will spin all tens?
A.1/3
B.1/2
C.1/50
D.1/1,000
Answer: D.1/1,000
Explanation: All 10s:
1st wheel = 10 = 1/10
2nd wheel = 10 = 1/10
3rd wheel = 10 = 1/10
(1/10)(1/10)(1/10) = 1/1,000
Answer: D
Question: John Purchased 1300 large bottles at $1.89 per bottle and 750 small bottles at $1.38 per bottle. What was the approximate average price paid per bottle?
A.$1.63
B.$1.64
C.$1.68
D.$1.70
Answer: D.$1.70
Explanation: (1300*1.89+750*1.38)/(1300+750) =~1.70
Option (D)
Question: In 4 years, Raj's father age twice as raj, Two years ago, Raj's mother's age twice as raj. If Raj is 32yrs old in eight yrs from now, what is the age of Raj's mother and father?
A.27
B.36
C.28
D.46
Answer: C.28
Explanation: Raj present age = 32 - 8 = 24.
After 4 years Raj's age is 28. and Raj's fathers age is 28 x 2 = 56, and his present age is 52.
Two years ago, Raj's age is 22. and his mother's age is 22 x 2 = 44. His mother's present age = 46
Answer:C
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
A.100
B.250
C.260
D.416
Answer: D.416
Explanation: Explanation:
Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 × 32 = 416.
Answer: D
Question: R-R-G-G-G-Y-Y-B-R-R-G-G-G-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?
A.63
B.64
C.65
D.66
Answer: A.63
Explanation: The repeated pattern R-R-G-G-G-Y-Y-B has 8 beads.
But the missing section includes R-R-G-G-G-Y-Y at the end.
Thus the number of beads in the missing section has the form 8k + 7.
The answer is A.
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
A.46
B.82
C.45
D.43
Answer: A.46
Explanation: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.
Answer:A
Question: Which of the following CANNOT be the least common multiple of two positive integers x and y
A.xy
B.x
C.x - xy
D.y
Answer: C.x - xy
Explanation: The least common multiple of two positive integers cannot be less than either of them. Therefore, since x - xy is less than x, it cannot be the LCM of a x and y.
Answer: C
Question: I chose a number and divide it by 8. Then I subtracted 160 from the result and got 12. What was the number I chose?
A.1376
B.1800
C.1400
D.2500
Answer: A.1376
Explanation: Let x be the number I chose, then
x/8−160=12
x/8=172
x=1376
Answer is A.
Question: Raman's salary was decreased by 50% and subsequently increased by 50%. How much percent does he loss
A.75
B.65
C.45
D.25
Answer: D.25
Explanation: Explanation:
Let the origianl salary = Rs. 100
It will be 150% of (50% of 100)
= (150/100) * (50/100) * 100 = 75
So New salary is 75, It means his loss is 25%
Answer: Option D
Question: Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
A.$1500
B.$1750
C.$2000
D.$2500
Answer: D.$2500
Explanation: Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 months = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404
Substitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...
Hence, D
Question: An article is bought for Rs.675 and sold for Rs.1080, find the gain percent?
A.33 1/9%
B.60%
C.33 1/3%
D.33 2/3%
Answer: B.60%
Explanation: 675 ---- 405
100 ---- ? => 60%
Answer: B
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 2:3. The first number is:
A.A)27
B.B)98
C.C)34
D.D)35
Answer: A.A)27
Explanation: (3x-9):(5x-9) = 2:3
x = 9 => 3x = 27
Answer:A
Question: The mean of 30 values was 150. It was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean. Find the correct mean.
A.151
B.149
C.152
D.148
Answer: A.151
Explanation: Corrected mean = 150×30−135+165/30
= 4500−135+165/30
=4530/30=151
Answer A
Question: A set of data consists of the following 7 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
A.-1 and 9
B.4 and 4
C.3 and 5
D.2 and 6
Answer: C.3 and 5
Explanation: If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.
Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.
1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2
2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8
3. 3 , 5
Distance is - 1.8 and 1.8
4. 2 , 6
Distance is - 0.8 and 0.8
5. 0 , 8
Distnace is - 1.2 and 1.2
Hence from above , we see that adding 3 and 5 , results in a value that would change the SD to the least. Hence C
Question: If A + B means A is the brother of B; A - B means A is the sister of B and A x B means A is the father of B. Which of the following means that C is the son of M?
A.M - N x C + F
B.F - C + N x M
C.N + M - F x C
D.M x N - C + F
Answer: D.M x N - C + F
Explanation: M is the father of N and N is the sister of C.C is brother of F..
so,N and c and F are siblings.
ANSWER:D
Question: A person can swim in still water at 12 km/h. If the speed of water 10 km/h, how many hours will the man take to swim back against the current for 12km?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: M = 12
S = 10
US = 12 - 10 = 2
D = 12
T = 12/2 = 6 Answer:D
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
Answer: D.72000
Explanation: 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.
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
Answer: C.13
Explanation: B = 9
2/3x= 30
x=45
for 90% approval we need 41 garments approved.
already approved = 28
we need 13 more.
Answer : C
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
Answer: D.62/69
Explanation: 16 students are interested, 8 are not interested
Prob = 1 - 8C2/24C2 = 1 - (8*7/(24*23))=1 - 7/69 = 62/69
Answer : D
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
Answer: A.546
Explanation: 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
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
Answer: C.93,75 miles
Explanation: 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
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
Answer: C.900
Explanation: 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
Question: The sum of three consecutive multiples of 3 is 81. What is the largest number?
A.24
B.28
C.30
D.32
Answer: C.30
Explanation: 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
Question: How many three letter words are formed using the letters of the word MARRIAGE?
A.326
B.429
C.226
D.336
Answer: D.336
Explanation: 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
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
Answer: C.342
Explanation: 400*(90/100)*(95/100)
= 342
Answer: C
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
Answer: C.104cm
Explanation: 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.
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)
Answer: A.31( 5/7)
Explanation: Explanation:
Required average = (67 * 2 + 35 * 2 + 6 * 3) / (2 + 2 + 3)
= (134 + 70 + 18) / 7 = 222 / 7 = 31(5/7) years.
Answer: A
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
Answer: D.620
Explanation: 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
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
Answer: A.5 : 3
Explanation: 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
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
Answer: A.100,000,000
Explanation: 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
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%
Answer: A.5%
Explanation: 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
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
Answer: C.27
Explanation: 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
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
Answer: D.13
Explanation: 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.
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
Answer: C.15/39
Explanation: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)
= 15/39
C
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
Answer: A.63.84
Explanation: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(93/100) = 59.375
MP = 63.84
Answer: A
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%
Answer: D.94%
Explanation: 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.
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
Answer: B.II only
Explanation: 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
Question: In a throw of coin what is the probability of getting head.
A.1
B.2
C.1/2
D.0
Answer: C.1/2
Explanation: Explanation:
Total cases = [H,T] - 2
Favourable cases = [H] -1
So probability of geƫng head = 1/2
Answer: C
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
Answer: C.4
Explanation: 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
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
Answer: B.4q^2
Explanation: 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
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
Answer: C.15
Explanation: 5C2 = 10
The number of test subjects is 10 + 5 = 15
The answer is C.
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
Answer: B.2.5 × 10^12
Explanation: 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
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
Answer: C.0
Explanation: 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.
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
Answer: B.164
Explanation: 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
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
Answer: B.36 sec
Explanation: 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
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
Answer: D.5/12
Explanation: 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
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
Answer: B.7.2 km/hr
Explanation: 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
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
Answer: D.20
Explanation: 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.
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
Answer: C.9% and 9 years
Explanation: 16.2â„20 P = PÃ—RÃ—R/100
â‡’ R2 = 1620â„20 â‡’81=> R = 9%
Also, time = 9 years
Answer C
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
Answer: C.$25,560
Explanation: 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
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
Answer: B. xy>1
Explanation: 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
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
Answer: D.16/81
Explanation: 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.
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
Answer: C.I and II
Explanation: 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
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
Answer: D.19:5
Explanation: 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
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
Answer: A.Rs.2000
Explanation: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A