mathewhe/aqua_rat huggingface dataset:
Question: An empty pool being filled with water at a constant rate takes 8hours to fill to 2/5 of its capacity.how much more time will it take to finish filling the pool?
(A) 5hr 30min
(B) 5hr 20min
(C) 4hr 48min
(D) 3 hr 12min
(E) 2hr 40 min
Rationale: As pool is filled to 2/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).
Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 5 hours 30 minutes.
Answer: A.
Answer: (A) 5hr 30min
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 5,000, how much money did investors B and C earn in total?
(A) $15,000
(B) $4,900
(C) $5,600
(D) $9,500
(E) $10,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 5000
5x = 5000=>x=1000
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x =15*1000= 15,000
Answer A
Answer: (A) $15,000
Question: If 18!/3^x is an integer, what is the greatest possible value of x?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: 18 - 3*3*2
15 - 5*3
12 - 4*3
9 - 3*3
6 - 2*3
3 - 1*3
Hence max of 3^8 is allowed. IMO E.
Answer: (E) 8
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 24 on Wednesday, what would be the value of D calculated on the following Saturday?
(A) 3450
(B) 3860
(C) 4220
(D) 4670
(E) 5040
Rationale: On Saturday, the value would be 7*6*5*24 = 5040
The answer is E.
Answer: (E) 5040
Question: When the positive integer A is divided by 4 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 4 and 7, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?
(A) 12
(B) 24
(C) 28
(D) 16
(E) 30
Rationale: A = 4k+3 = 7j+4
B = 4m+3 = 7n+4
A-B = 4(k-m) = 7(j-n)
Thus A-B is a multiple of 4 and 7, so it is multiple of 28.
The answer is C.
Answer: (C) 28
Question: Prizes totaling $75,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
(A) (a) $5,000
(B) (b) $10,000
(C) (c) $15,000
(D) (d) $24,000
(E) (e) $65,000
Rationale: The highest prize cannot possibly be less than 1/3rd of 75,000 (because in this case the sum of 3 prizes would be less than 75,000) and cannot be more than 75,000.
Answer: E.
Answer: (E) (e) $65,000
Question: If the sum of a set of 5 different positive prime numbers is 94, what is the difference between larger 2 prime numbers between them?
(A) 11
(B) 12
(C) 23
(D) 17
(E) 13
Rationale: All prime numbers apart from 2 are odd.
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even
We are given 5 different prime numbers, whose sum is 94 i.e even
If we include 2, we will have 4 odd prime numbers and one even.
This sum would be odd
If we exclude 2, we will have 5 odd numbers.
This sum would be even
Hence 2 is included.
The possible 5 no. are = 11+7+2+43+31 = 94
difference between larger 2 prime numbers between them = 43 - 31 = 12
Ans - B
Answer: (B) 12
Question: If the height of an equilateral triangle RBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔRBC is how many times as long as a leg of the right triangle DEF?
(A) (√2)/(√3)
(B) (√3)/(√2)
(C) √2
(D) (2√2)/(√3)
(E) 2/(√3)
Rationale: Side of the equilateral triangle RBC = 2m ----> height = m * sqtr(2)
Hipotenuse of the right triangle RBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)
Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D
Answer: (D) (2√2)/(√3)
Question: There are two numbers. If 40% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) 3/7
(B) 5/8
(C) 6
(D) 6/7
(E) 7
Rationale: Let the two numbers be x and y.
40/100 * x + y = 5/4y
=> 2/5 x = 1/4 y => x/y = 5/8
B)
Answer: (B) 5/8
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
(A) Rs.240
(B) Rs.350
(C) Rs.340
(D) Rs.390
(E) Rs.370
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
ANSWER IS A
Answer: (A) Rs.240
Question: Two cubes of their volumes in the ratio 64 : 1331. The ratio of their surface area is:
(A) 1.5:5
(B) 2:5
(C) 3:5
(D) 4:11
(E) 4:5
Rationale: The ratio of their surface area is
64 : 1331
4 : 11
Answer is D.
Answer: (D) 4:11
Question: 56 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
(A) 33.0
(B) 37.66
(C) 32.1
(D) 31.23
(E) 19
Rationale: Explanation:
Let the two parts be (56 - x) and x.
Then, 10 (56 - x) + 22x = 780
=> 12x = 220
=> x = 20.
Bigger part = (56 - x) = 37.66.
Answer: B) 37.66
Answer: (B) 37.66
Question: A man purchases the milk at Rs. x/litre and sells it at Rs. 2x/liter stillhe mixes 2liters water with every 6liters of pure milk. What is the profit %?
(A) 100.12%
(B) 123.16%
(C) 154.66%
(D) 166.66%
(E) None
Rationale: Let the cost price of 1 litre pure milk be Re.1, then
\inline \begin{Bmatrix} 6 & litres(milk) & \rightarrow & CP=Rs.6\\ 2 & litres(water) & \rightarrow & CP=Rs.0 \end{Bmatrix}\rightarrow CP=Rs.6 only
and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16
Profit %= 166.66%
D
Answer: (D) 166.66%
Question: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity E of the pool?
(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters
Rationale: D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
Answer: (D) 12000 cubic meters
Question: The probability of pulling a black ball out o f a glass is 1/X. The probability of pulling a black ball out of a glass and breaking the glass is 1/Y. What is the probability of breaking the glass?
(A) 1/(XY).
(B) Y/X
(C) X by Y
(D) 1/(X+Y).
(E) 1/(X-Y).
Rationale: pulling a black ball out of a glass and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a black ball out of a glass = P(a) and Prob of breaking the glass= P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer should be C.
Answer: (C) X by Y
Question: Krista, a personal trainer, is buying energy drinks for her clients. If she has $20 on hand, which of the following options could Krista NOT buy if:
Rock Star = $2.00
Red Bull = $3.25
Monster = $2.50
NOs = 1.25
(A) 5 Rock Stars, 2 Red Bulls, 1 Monster & 1 NO's (20.25)
(B) 8 Monster's (17.50)
(C) 1 Rockstar, 4 Red Bulls & 4 No's (20)
(D) 10 Rock Stars (20)
(E) 8 No's (20)
Rationale: The Correct Answer would exceed the $20 Krista had on hand.
A= $20.25 (exceeds budget by 25 cents)
B= $20
C= $20
D= $20
E= $20
The Correct answer is A
Answer: (A) 5 Rock Stars, 2 Red Bulls, 1 Monster & 1 NO's (20.25)
Question: two friends deepak and rajeev have agreed to meet at a definite spot on a particular day between 9pm and 10pm. the first person to come waits for some time and leaves.If the other one does not turn up by that time.If Deepak comes first,he waits for 45minutes and if Rajeev comes first,he waits for 15minutes.What is the probability of meeting between Deepak and rajeev if their arrival times are independent of eachother and each person arrives during the indicated period at random?
(A) 3/4
(B) 11/16
(C) 7/8
(D) 3/16
(E) 3/15
Rationale: deepak : 45/60 = 3/4
rajeev : 15/60= 1/4
as these are independent events
total probability = (3/4)*(1/4)
= 3/16
ANSWER:D
Answer: (D) 3/16
Question: The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference q would have been how much?
(A) 40/3
(B) 40
(C) 120
(D) 360
(E) 420
Rationale: CASE 1:
Deposit = $x;
Rate of increase = r.
Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.
Interest yearned in 2 year = (x + xr)r.
The difference q= (x + xr)r - xr = xr^2 = 40.
CASE 2:
Deposit = $x;
Rate of increase = 3r.
Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.
Interest yearned in 2 year = (x + 3xr)3r.
The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.
Answer: D.
Answer: (D) 360
Question: If [[x]] = x^2 + 2x + 4, what is the value of [[6]]?
(A) 3
(B) 52
(C) 15
(D) 19
(E) 25
Rationale: These functions questions might look intimidating, but they just test your knowledge about how well you can substitute values
[[x]] = x^2 + 2x + 4
[[6]] = 6^2 + 2*6 + 4 = 52. Option B
Answer: (B) 52
Question: Look at this series: 21, 9, 21, 11, 21, 13, 21, ... What number should come next?
(A) 14
(B) 15
(C) 21
(D) 23
(E) 24
Rationale: Explanation: In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.
Answer: Option B
Answer: (B) 15
Question: From a container having pure milk, 10% is replaced by water and the process is repeated twice. At the end of the second operation, the milk is?
(A) 50%
(B) 60%
(C) 55%
(D) 75%
(E) 81%
Rationale: Let the total quantity of original milk = 1000gm
Milk after 1st operation = 90% of 1000 = 900gm
Milk after second operation = 90% of 900 = 810gm
Strength of final mixture = 81%
Answer is E
Answer: (E) 81%
Question: If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many V such committees are possible?
(A) 20
(B) 40
(C) V=50
(D) V=80
(E) V=120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: (D) V=80
Question: A train running at the speed of 100 km/hr crosses a pole in 18 seconds. What is the length of the train?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: Speed=(100 * 5/18) m/sec = (250/9) m/sec Length of the train = (Speed x Time) = (250/9 * 18) m
= 500 m.
Answer: C
Answer: (C) 500
Question: Of the diplomats attending a summit conference, 30 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?
(A) 20
(B) 96
(C) 108
(D) 120
(E) 150
Rationale: {Total} = {French} + {Russian} - {Both} + {Neither}
{Total} = 30 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}
Solving gives {Total} = 20.
Answer: A.
Answer: (A) 20
Question: A boat traveled upstream 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average speed of (v+3) miles per hour. If the trip upstream took a half hour longer than the trip downstream, then how many hours did it take the boat to travel downstream?
(A) 2.5
(B) 2.4
(C) 2.3
(D) 2.2
(E) 2.1
Rationale: 90/(V-3) = 90/(V+3) + 0.5 hours
=> 90(V+3) = (V-3) [90 + 0.5 V + 1.5]
90V + 270 = (V-3)(183/2 + V/2)
180V + 540 = (V-3)(183+V)= 183V- 549+ V^2 -3V
V^2 - 1089= 0 => V= 33 miles/hr
=> Time downstream = 90/36 = 30/12= 5/2= 2.5 hrs
ANSWER A 2.5
Answer: (A) 2.5
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
(A) 1/9
(B) 5/9
(C) 7/9
(D) 7/11
(E) None
Rationale: Explanation:
Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂ = 20/36 = 5/9
B)
Answer: (B) 5/9
Question: A certain taxi company charges $2.10 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
(A) 15.6
(B) 16.0
(C) 17.7
(D) 18.7
(E) 19.1
Rationale: A certain taxi company charges $2.10 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
A. 15.60
B. 16.00
C. 17.50
D. 18.70
E. 19.10
1/5 miles = 0.2 miles.
The cost of 8 miles long ride would be $2.10 for the first 0.2 miles plus (8-0.2)/0.2*0.4 = $2.1 + $15.6 = $17.7.
Answer: C.
Answer: (C) 17.7
Question: P and Q together can complete a piece of work in 4 days. If P alone can complete the same work in 20 days, in how many days can Q alone complete that work?
(A) 2
(B) 7
(C) 5
(D) 9
(E) 1
Rationale: Explanation:
(P + Q)'s 1 day's work = 1/4, P's 1 day's work = 1/20
Q's 1 day's work = (1/4 – 1/20) = (4/20) = (1/5)
Hence, Q alone can complete the work in 5 days.
ANSWER: C
Answer: (C) 5
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1275, find the loss %?
(A) 15%
(B) 16%
(C) 17%
(D) 78%
(E) 28%
Rationale: 1500 ---- 225
100 ---- ? => 15%
Answer:A
Answer: (A) 15%
Question: A circular swimming pool is surrounded by a concrete wall 4 feet wide.if the area of the wall is 11/25 of the area of the pool, then the radius of the pool in feet is?
(A) 22
(B) 88
(C) 37
(D) 20
(E) 289
Rationale: Let the radius of the pool be r. Then area of the wall and pool = π(r+4)2π(r+4)2
Area of the pool = π(r)2π(r)2
Area of the wall = π(r+4)2−π(r)2π(r+4)2−π(r)2
Given π(r+4)2−π(r)2π(r+4)2−π(r)2 = 1125(πr2)1125(πr2)
r2+8r+16−r2=1125r2r2+8r+16−r2=1125r2
11r2−200r−400=011r2−200r−400=0
Solving r = 20
Answer:D
Answer: (D) 20
Question: In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
(A) 3/5
(B) 2/3
(C) 3/4
(D) 4/5
(E) 5/6
Rationale: You can use the weighted averages formula for a 10 sec solution.
No of females/No of males = (50 - 42)/(42 - 40 ) = 4/1
No of females as a fraction of total employees = 4/(4+1) = 4/5;
ANSWER:D
Answer: (D) 4/5
Question: The weight of a glass of jar is 30% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar?
(A) 1/5
(B) 1/3
(C) 2/5
(D) 1/2
(E) 3/7
Rationale: Let weight of jar filled with beans = 100 g
Weight of jar = 30 g
Weight of coffee beans = 70 g
Weight of jar and remaining beans = 60 g
Weight of remaining beans = 30 g
Fraction remaining = 30/70 = 3/7
Answer is E.
Answer: (E) 3/7
Question: How many ways can 840 be written as the product of two numbers ?
(A) 32
(B) 16
(C) 6
(D) 18
(E) 8
Rationale: factor of 840 = 2*2*2*3*5*7;
Total number of method to select the combination = (3+1)*(1+1)*(1+1)*(1+1)/2!=16
(here we should make attention in one step that a*b and b*a will be considered as 1 case)
ANSWER:B
Answer: (B) 16
Question: A man sells a horse for Rs. 700 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 27
(B) 98
(C) 93.3
(D) 96.2
(E) 90.1
Rationale: CP = SP + 1CP = SP - g
700 + x = 980 - 2x
3x = 280 => x = 93.3
Answer:C
Answer: (C) 93.3
Question: Bookman purchased 40 copies of a new book released recently, 10 of which are hardback and sold for $20 each, and rest are paperback and sold for $10 each. If 14 copies were sold and the total value of the remaining books was 300, how many paperback copies were sold?
(A) 6
(B) 4
(C) 8
(D) 10
(E) 12
Rationale: The bookman had 10 hardback ad 40-10=30 paperback copies;
14 copies were sold, hence 40-14=26 copies were left. Let # of paperback copies left be p then 10p+20(26-p)=300 --> 10 p=220 --> p=22
# of paperback copies sold is 30-22=8
Answer: C
Answer: (C) 8
Question: A metallic sheet is of rectangular shape with dimensions 20 m x 25 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 2 m, the volume of the box (in m cube) is:
(A) 4120 m cube
(B) 4140 m cube
(C) 5140 m cube
(D) 1344 m cube
(E) None of these
Rationale: Explanation:
l = (20- 4)m =16 m, [because 2+2=4]
b = (25 -4)m = 21 m,
h = 2 m.
Volume of the box = (16 X 21 X 4) m cube
= 1344 m cube.
Option D
Answer: (D) 1344 m cube
Question: How many integers are there between 15 and 97, inclusive?
(A) 51
(B) 55
(C) 56
(D) 57
(E) 83
Rationale: I guess the easiest way to answer this is -
Say you have two positive integers, x and y where y > x
Then the number of integers between x and y is given by - (y - x) + 1
In this case, it's (97 - 15) + 1 =83. Option E
Answer: (E) 83
Question: A bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey in 3/5th time. what should be its speed to cover the remaining distance in the time left.
(A) 10 kmph speed
(B) 20 kmph
(C) 30 kmph
(D) 40 kmph
(E) 50 kmph
Rationale: A
10 kmph
Time left = 10 - 3/5*10
= 4 hr 10 km/h
speed =40 km /4 hr
=10 kmph
Answer: (A) 10 kmph speed
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand x gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand x gasoline. At this time, what percent of the gasoline in the tank is brand Z?
(A) 50%
(B) 37.5%
(C) 40%
(D) 33%
(E) 25%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) = 3/8 = 37.5%
Answer (B)
Answer: (B) 37.5%
Question: By using the numbers 7, 2, 3, 4 and 6 only once, how many five digit numbers can be made that are divisible by 14?
(A) 12
(B) 48
(C) 42
(D) 6
(E) 24
Rationale: A number to be divisible by 14 must end with 14, 28, 42,56,70,84
So, there are the following cases possible:
736-42 --> the first three digits can be arranged in 3=6 ways.
Total = 6 = 6.
Answer: D.
Answer: (D) 6
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
(A) Rs. 18.20
(B) Rs. 70
(C) Rs. 72
(D) Rs. 88.25
(E) None
Rationale: C.P. = Rs. 100	x 392 = Rs. 1000	x 392 = Rs. 320
122.5	1225
Profit = Rs. (392 - 320) = Rs. 72.
C)
Answer: (C) Rs. 72
Question: Points A, B, C, and D, in that order, lie on a line. If AB = 2 cm, AC = 4 cm, and BD = 6 cm, what is CD, in centimeters?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: Putting a value to each point, lets use the following:
A - 0
B - 2 (AB = 2)
C - 4 (AC = 4)
D - 8 (BD = 6)
CD is 8-4 = 4.
Ans D
Answer: (D)  4
Question: The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 8 years ago, the sum of their ages was 76, what will be the age of Charlie 10 years from now?
(A) 17
(B) 25
(C) 45
(D) 47
(E) 50
Rationale: Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.
5x-8 + 8x-8 + 7x-8 = 76
x = 5
Present age of Charlie = 7*5 = 35
Charlie's age 10 years hence = 35+10 = 45
Answer = C
Answer: (C) 45
Question: If M is the set of all consecutive multiples of 9 between 100 and 500, what is the median of M?
(A) 300
(B) 301
(C) 301.5
(D) 302.5
(E) 306
Rationale: Since 100/9 =11.11, 500/9=55.55, M can be written as {9*12, 9*13, ...., 9*54, 9*55}. The number of elements of M is, therefore, 44(=55-12+1). Since the number of elements is even number the median is the average of the 22nd element(=9*33) and 23rd element(=9*34). So the median is (9*33 + 9*34)/2 = 301.5. The answer is C.
Answer: (C) 301.5
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
(A) 9/20
(B) 1/20
(C) 5/20
(D) 8/15
(E) 6/9
Rationale: Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
p(E)=n(E)/n(S)
=9/20
The answer should be A
Answer: (A) 9/20
Question: Anthony and Michael sit on the six-member board of directors for company A. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: Soln: Let the commitees be I and II
Assuming that Anthony and Michael from A go into commitee I, there is just one more place left to be filled in that commitee and it can be taken by any of the 4 remaining people. Thus 4 ways.
Since the Anthony and Michael can also go into commitee II, we get 4 ways for that commitee also.
So in total = 8 ways
Now total number of ways of choosing 3 from 6 people is
= 6C3
= 6 * 5 * 4/3!
= 20 ways
Therefore Probability is = (8 /20) * 100 = 40%
Answer: (C) 40%
Question: A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field?
(A) 10 hours
(B) 20 hours
(C) 30 hours
(D) 40 hours
(E) 50 hours
Rationale: If A and B together can do a piece of work in x days and A alone can do the same work in y days,
then B alone can do the same work in x y/ y – x days.
Therefore, the No. of hours required by B = 10 × 15/ 15 – 10 = 150/5 = 30 hours.
Answer : C
Answer: (C) 30 hours
Question: The product of two numbers is 220 and the sum of their squares is 289. The sum of the number is?
(A) A)23
(B) B)25
(C) C)27
(D) D)31
(E) E)35
Rationale: Let the numbers be x and y.
Then, xy = 220 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 220) = 729
x + y = 27.
Option C
Answer: (C) C)27
Question: find the average of first 20 multiples of 7?
(A) 73.5
(B) 56.4
(C) 25.8
(D) 12.4
(E) 56.9
Rationale: Required average =7(1+2+3+…….+20)/20
=(7*20*21)/(20*2)
=(147/2)=73.5.
Ans: A
Answer: (A) 73.5
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 9 consecutive spaces in a random direction, what is the probability the piece ends no more than 9 spaces from the square numbered 49?
(A) 19%
(B) 29%
(C) 25%
(D) 20%
(E) 15%
Rationale: No more than 9 spaces from 49 means in the rangefrom 49-9=40 to 49+9=58, inclusive. Total numbers in this range 58-40+1=19, the probability favorable/total=19/100
Answer: A
Answer: (A) 19%
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is:
(A) 153601
(B) 153600
(C) 153602
(D) 153603
(E) 153604
Rationale: Perimeter = Distance covered in 8 min. =(12000/60) x 8m = 1600 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m2.
Answer: B
Answer: (B) 153600
Question: The perimeter of a triangle is 48 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 76
(B) 88
(C) 60
(D) 55
(E) 35
Rationale: Area of a triangle = r * s
Where r is the in radius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 48/2 = 60 cm2
Answer:C
Answer: (C) 60