RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A black box contains eight marbles, of which three are red, and the rest are blue. A white box contains five marbles, of which two are red, and the rest are blue. If two marbles are chosen from the black box at random, and one marble is chosen from the white box at random, what is the probability that all marbles will be blue?
A.3/14
B.3/8
C.5/13
D.8/13
Answer: A.3/14
Explanation: From the prompt we know about 2 boxes and the marbles within each:
The black box contains
3 red
5 blue
8 total
The white box contains
2 red
3 blue
5 total
We're told to pull 2 marbles from the black box and 1 marble from the white box. We're asked for the probability that ALL marbles pulled will be BLUE.
Let's start with the 1st marble you pull from the black box....
The probability that it's blue is 5/8
Once you pull that first marble, there's 1 fewer blue marble in the black box.
When you grab the 2nd marble from the black box....
The probability that it's blue is 4/7
For the 3rd marble, we pull from the white box.
The probability that it's blue is 3/5
Now, we multiply the results: (5/8)(4/7)(3/5) = 3/14
A
Question: How many kilograms of sugar costing Rs/.9 per kg must be mixed with 27kg of sugar costing Rs.7 per kg so that there may ba gain of 10% by selling the mixture at Rs.9.24 per kg
A.22
B.63
C.88
D.26
Answer: B.63
Explanation: i. If S.P and gain are given, C.P =        PxS gain . %100 100 Rs. ii. The rule of allegation  Required ratio is cheaper quantity : dearer quantity = (d-m) : (m-c) Answer with Explanation: Step I : S.P of 1 kg of mixture = Rs. 9.24 Gain = 10%
 C.P of 1 kg of mixture =        24.9 10100 100 x = Rs. 8.40  Mean price = Rs. 8.40/- Step (ii) By the rule of allegation vi. C.P of 1 kg of sugar of I kind (p) = 900 vii. C.P of 1 kg of sugar of II kind (p) = 700 viii. Mean price (p) = 840 ix. d – m = 900 - 840 = 60 x. m – c = 840 – 700 = 140  Required ratio = 140 : 60 = 7 : 3 Step (iii) Let x kg of sugar of I kind be mixed with 27 kg of II kind
 7 : 3 = x : 27  7/3 = x/27  x = 7/3 x 27 = 63 kg.
Answer:B
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The ratio between the total expenditure on Taxes for all the years and the total expenditure on Fuel and Transport for all the years respectively is approximately?
A.10:13
B.15:18
C.5:8
D.15:21
Answer: A.10:13
Explanation: Required ratio
=	[	(83 + 108 + 74 + 88 + 98)	]
(98 + 112 + 101 + 133 + 142)
=	[	451	]
586
=	1
1.3
=	10/ 13
Answer is A
Question: The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle?
A.300 square meters
B.400 square meters
C.500 square meters
D.600 square meters
Answer: A.300 square meters
Explanation: If L and W be the original length and width of the rectangle and its area is given by
L ? W
After increase the length becomes 2 L and the width becomes 3 W. The area is then given by (2 L) ? (3 W) and is known. Hence
(2 L) ? (3 W) = 1800
Solve the above equation to find L ? W
6 L ? W = 1800
L ? W = 1800 / 6 = 300 square meters , area of original rectangle
correct answer A
Question: John bought a total of 20 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 20 mangoes and oranges that John originally purchased was 69 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?
A.4
B.5
C.6
D.7
Answer: B.5
Explanation: Let number of mangoes be x, number of oranges be 12-x
0.80x +(20-x)0.60/20 = 0.69
solving for x, we get x = 9 --> Mangoes 9, Oranges 11
Now, number of oranges to be returned be y
0.80*9 + (11-y)*0.60/20-y = 0.72
solving for y, y = 5
Ans: B
Question: P cycles at a speed of 4 m/s for the first 8 seconds, 5 m/s for the next 8 seconds, 6 m/s for the next 8 and so on. Q cycles at a constant speed of 6.5 m/s throughout. If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?
A.43.4 m
B.56.6 m
C.32.1 m
D.P cannot give a lead as Q is always ahead of P
Answer: C.32.1 m
Explanation: DETAILED SOLUTION
Distance covered by P in 8 sec = 4 * 8 = 32 m
Distance covered by P in 16 sec = 32 + 5 *8 = 72 m
Distance covered by P in 24 sec = 72 + 6 * 8 = 120 m
Distance covered by P in 32 sec = 120 + 7 * 8 = 176 m
Distance covered by P in 40 sec = 176 + 8 * 8 = 240 m
Distance covered by P in 48 sec = 240 + 9 * 8 = 312 m
Total distance in 48 sec = 312m
To cover balance 86 m with speed = 10 m/sec, time taken = 86/10 = 8.6 sec
So P would finish 400 m in 48 + 8.6 = 56.6 seconds.
In 56.6 seconds, Q cycles 56.6 * 6.5 = 367.9 m or B should have a 32.1 m lead to result in a dead heat.
CORRECT ANSWER C
Question: The value of	0.1 x 0.1 x 0.1 + 0.02 x 0.02 x 0.02	is:
0.2 x 0.2 x 0.2 + 0.04 x 0.04 x 0.04
A.0.0125
B.0.125
C.0.25
D.0.5
Answer: B.0.125
Explanation: Explanation:
Given expression =	(0.1)3 + (0.02)3=1= 0.125
23 [(0.1)3 + (0.02)3]	=8
Answer- B
Question: What is the area of a square field whose diagonal of length 18 m?
A.120 sq m
B.250 sq m
C.200 sq m
D.180 sq m
Answer: D.180 sq m
Explanation: d2/2 = (18 * 18)/2 = 180
ANSWER:D
Question: Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 800 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
A.16.3
B.13:30
C.14:00
D.15:00
Answer: A.16.3
Explanation: Both Sari and Ken climb in the same direction.
Speed of Sari = 800/2 = 400 meters/hr (since she covers 800 meters in 2 hrs)
Speed of Ken = 500 meters/hr
At 8:00, distance between Ken and Sari is 800 meters. Ken needs to cover this and another 50 meters.
Time he will take = Total distance to be covered/Relative Speed = (800 + 50)/(500 - 400) = 8.5 hrs
Starting from 8:00, in 8.5 hrs, the time will be 16:30
Answer (A)
Question: The number X is 200% of Y. The number Z increased by 200% is 50% of X. What percentage of Z is Y?
A.33.3%
B.100%
C.200%
D.300%
Answer: D.300%
Explanation: Picking Numbers:
Start with Z as question asks in terms of Z.
Let Z =100, thus, X=600 and Y=300 from question stems.
Hence Y is 300% of Z.
Ans D.
Question: A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 9 salespeople on staff, how many different arrangements of winners are possible?
A.1,728
B.1,440
C.1,320
D.504
Answer: D.504
Explanation: [quote=Bunuel]A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 9 salespeople on staff, how many different arrangements of winners are possible?
9*8*7
=504
Answer : D
Question: Mr. Hernandez, who was a resident of State X for only 8 months last year, had a taxable income of $22,500 for the year. If the state tax rate were 6 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year?
A. $900
B. $720
C. $600
D. $300
Answer: A. $900
Explanation: Total tax for the year = 22,500 x 6% = 1350
As stated Annual tax is prorated as per the duration of stay.
Prorated Tax = 1350 (8/12) = 900
Answer A
Question: A bowl has only 2 apples and 2 bananas. If one piece of fruit is selected from the bowl at random, and a second piece is selected from the bowl without replacing the first, what is the probability that both pieces of fruit chosen are apples?
A.1/10
B.1/6
C.2/9
D.2/5
Answer: B.1/6
Explanation: 2/4 * 1/3
=1/6
B. 1/6
Question: If A and B get profits of Rs.15,000 and Rs.5,000 respectively at the end of year then ratio of their investments are
A.4:1
B.1:4
C.3:1
D.2:3
Answer: C.3:1
Explanation: Ratio = 15000/5000 = 3 : 1
Answer : C
Question: Find the area of trapezium whose parallel sides are 22 cm and 18 cm long, and the distance between them is 15 cm.
A.227
B.299
C.300
D.161
Answer: C.300
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (22 + 18) * (15)
= 300 cm2
Answer: C
Question: What is the square root of 169?
A.8
B.16
C.13
D.42
Answer: C.13
Explanation: 13X13 = 169
ANSWER C
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.896?
A.1000
B.800
C.2889
D.2777
Answer: B.800
Explanation: 896 = P [1 + (5*12/5)/100]
P= 800
Answer: B
Question: There are a red, yellow, blue and green tennis balls respectively in a set. How many subsets of these balls can I get without using the green ball?
A.9
B.7
C.8
D.6
Answer: C.8
Explanation: This is a combination solution
Since we have 3 different kinds of Balls other than the green ball we can take any ball from the set of 3 to make a subset as follows.
3C1 +3C2 + 3C3 = 7
Plus the one set that is null that is the Set having no element in it which is 3C0 =1
= 7 + 1 = 8
C = 8
Question: If x = a/3 + b/3^2 + c/3^3, where a, b, and c are each equal to 0 or 1, then x could be each of the following EXCEPT:
A.1/27
B.1/9
C.4/27
D.2/9
Answer: D.2/9
Explanation: x = a/3 + b/3^2 + c/3^3
= a/3 + b/9 + c/27
= (9a + 3b + c ) /27
Depending on whether a, b and c take 0 or 1 , the numerator can take 1 , 3 , 4 and 12
3/27 = 1/9
12/27 = 4/9
Answer D
Question: A part-time employee’s hourly wage was increased by 50%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
A.9%
B.15%
C.25%
D.33%
Answer: D.33%
Explanation: Let's plug in somenicenumbers and see what's needed.
Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 50% wage increase, the employee makes $1.50/hour
We want the employee's income to remain at $100/week.
So, we want ($1.50/hour)(new # of hours) = $100
Divide both sides by 1.50 to get:
new # of hours = 100/1.50
≈ 67 hours
So, the number of hours decreases from 100 hours to (approximately) 67 hours.
This represents a 33% decrease (approximately) .
Answer : D
Question: If Ajay drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?
A.38
B.27
C.24
D.19
Answer: C.24
Explanation: Explanation:
Let t be his usual time to reach his office and v be his usual speed.
v = d/t ……….(d is the distance Ajay travels while going to his office)
vt = d
At v1 = 4v/5 ; t1 = t + 6
4v/5 = d/(t + 6)
4v/5* (t + 6) = d
4v/5* (t + 6) = vt
On solving we get,
t = 24 minutes
ANSWER:C
Question: what is the value of (3)^-4 ?
A.1/4
B.1/81
C.1/65
D.1/9
Answer: B.1/81
Explanation: 3^-4= 1/(3)^4= 1/81
ANSWER:B
Question: Rabert’s age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev?
A.10 years.
B.11 years.
C.12 years.
D.13 years.
Answer: A.10 years.
Explanation: Sol. Let Rabert’s present age be x years. Then,
Rabert’s age after 15 years = (x + 15) years.
Rabert’s age 5 years back = (x - 5) years.
∴ x + 15 = 5 (x - 5) ⇔ x + 15 = 5x - 25
⇔ 4x = 40 ⇔ x = 10.
Hence, Rabert’ present age = 10 years.
Answer A
Question: A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
A.54
B.27
C.36
D.57
Answer: C.36
Explanation: 8 minutes are needed to fill 150 bottles. How many groups of 150 bottles are there in 675 bottles?
675 ÷ 150 = 4.5 = 4 and 1/2
For each of these groups 8 minutes are needed. For 4 groups and 1/2
8 × 4 + 4 = 32 + 4 = 36 minutes. (4 is for 1/2 a group that needs half time)
correct answer C
Question: A sum of money triples itself in ten years at simple interest. Find the rate of interest?
A.12 1/2 % p.a.
B.14 1/2 % p.a.
C.20 % p.a.
D.22 % p.a.
Answer: C.20 % p.a.
Explanation: Let the pricipal be Rs. x, then amount = 3x(where R = rate of interest) => Interest = 3x - x = Rs. 2x
R = (100 * 2x)/(x * 10) = 20 %
ANSWER:C
Question: The banker's discount on Rs.1800 at 16% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?
A.3 months
B.4 months
C.5 months
D.6 months
Answer: A.3 months
Explanation: Solution
S.I on Rs.1800 = T.D on Rs.1872.
P.W on Rs.1872 is Rs.1800.
Rs.72 is S.I on Rs. 1800 at 16%.
Time	=(100x72 / 16x1800)
= 1/4 year
= 3 months.
Answer A
Question: Suppose you roll a 20 sided die twice. What is the probability you will land on the same number for both rolls?
A.1/10
B.1/20
C.1/5
D.1/25
Answer: B.1/20
Explanation: The acceptable rolls work when we roll any double: 11, 22, 33, ... 2020. Those are 20 possibilities. Then the die can fall in 20*20 = 400 ways.
Hence the probability is 20/400
= 1/20
Answer: B
Question: P cando a work in 15 days and Q cando the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
A.2/7
B.3/11
C.8/15
D.7/15
Answer: C.8/15
Explanation: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
C
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
A.22
B.288
C.29
D.60
Answer: D.60
Explanation: 1/2 * d (10 + 6) = 640
d = 80
Answer:D
Question: What will come in place of the x in the following Number series? 49920, 4160, 416, x
A.52
B.3
C.4
D.5
Answer: A.52
Explanation: 49920 /12 = 4160
3840 /10 = 416
416 /8 = 52
A
Question: For an upcoming charity event, a male vocalist has agreed to sing 5 out of 7 “old songs” and 3 out of 6 “new songs.” How many ways can the singer make his selection?
A.25
B.50
C.140
D.480
Answer: C.140
Explanation: =7C5*6C3
=7*6/3*6*5/3
=7*2*2*5
=140
Ans = C
Question: A man walks half of the journey at 4 km/h by cycle does one third of journey at 12 km/h and rides the remainder journey in a horse cart at 9 km/h, thus completing the whole journey in 6 hours and 12 minutes. The length of the journey is
A.36 km
B.1332⁄67 km
C.40 km
D.28 km
Answer: A.36 km
Explanation: Let the length of the journey = x km.
∴ Journey rides by horse cart = x(1 - 1⁄2 - 1⁄3)
= 1⁄6x km
Then, total time taken to complete journey = 31⁄5hr
⇒ t1 + t2 + t3 = 31⁄5
⇒ x⁄2 × 1⁄4 + x⁄3 × 1⁄12 + x⁄(6 × 9) = 31⁄5
⇒ x = 31⁄5 × 216⁄37 = 36.2 km ≈ 36 km
Answer A
Question: 12.1212+17.0005 - 9.1103 = ?
A.20.0015
B.20.0105
C.20.0115
D.20.0114
Answer: D.20.0114
Explanation: Solution
Given expression
=(12.1212+17.0005)-9.1103
= (29.1217 - 9.1103)
=20.0114.
Answer D
Question: If you write down all the numbers from 1 to 25, then how many times do you write 3 ?
A.A)11
B.B)3
C.C)2
D.D)1
Answer: B.B)3
Explanation: Explanation:
Explanation:
Clearly, from 1 to 25, there are ten numbers with 3 as the unit's digit- 3, 13, 23
So, required number =3
Answer: B
Question: A batsman in his 12th innings makes a score of 60 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?
A.38
B.43
C.44
D.45
Answer: A.38
Explanation: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 2) + 60
∴ x = 38
Answer A
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is ?
A.42 sec
B.44 sec
C.46 sec
D.48 sec
Answer: D.48 sec
Explanation: Explanation:
Relative speed = 60 + 90 = 150 km/hr.
= 150 x 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 x 3/125 = 48 sec.
ANSWER IS D
Question: A train travels 225 km in 3.5 hours and 370 km in 5 hours.find the average speed of train.
A.80 kmph
B.60 kmph
C.70 kmph
D.90 kmph
Answer: C.70 kmph
Explanation: As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 225 + 370 = 595 km
Thus, Total Speed = 8.5 hrs
or,Average Speed = 595/8.5
or, 70kmph.
ANSWER:C
Question: If -4 < x < 5 and -6 < y < 3, which of the following specifies all the possible values of xy?
A.-42 < xy < 21
B.-42 < xy < 24
C.-30 < xy < 24
D.-24 < xy < 21
Answer: C.-30 < xy < 24
Explanation: The least value of xy is a bit more than 5*(-6)=-30 and the largest value of xy is a bit less than (-4)*(-6)=24.
Therefore -30 < xy < 24.
Answer: C.
Question: Salaries of Ravi and Sumit are in the ration 2:3. It the salary of each in increased by $4000, the new ration becomes 40:57, what is Sumit’s present salary?
A.$17000
B.$20000
C.$25500
D.$38000
Answer: D.$38000
Explanation: Let the original salaries of Ravi and Sumit be $2x and $3x respectively.
Then (2x+4000)/(3x+4000)=40/57
57(2x+4000)= 40)(3x+4000)
6x = 68000
3x=34000
Sumit’s present salary = 3x+4000= 34000+4000=$38000
ANSWER : D $38000
Question: An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time S will it take to fill the bucket to full capacity?
A.7/18
B.9/18
C.2
D.18/7
Answer: D.18/7
Explanation: Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank S= 60/7 - 6 = 18/7 mins. ANS D.
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
A.39%
B.20%
C.23%
D.74%
Answer: B.20%
Explanation: 900 ---- 180
100 ---- ? =>
20%
Answer:B
Question: A and B are two partially filled buckets of water. If 7 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 7 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
A.77/5
B.13
C.17
D.21
Answer: A.77/5
Explanation: Let Bucket A be A and Bucket B be B
Scenario 1
A-7 = 1/3 (B+7) ----> 3A-21 =B+7
Scenario 2
B-7 = 1/2 (A+7) -----> 2B-14 = A+7
From Scenario 1, B = 3A-28
Substitute B with this information in Stmt 2
2 (3A-28) -14 = A+7 ------> 6A -56-14 = A+7 ------> 6A- A = 70+7 ---> 5A= 77
A= 77/5, Answer choice A
Question: If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is?
A.100 pi
B.300 pi
C.70 pi
D.90 pi
Answer: A.100 pi
Explanation: 4/3 Ï€ * 10 * 10 * 10 = 8 * 4/3 Ï€r3
r = 5
4Ï€ * 5 * 5 = 100Ï€
ANSWER A
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
A.0
B.1
C.10
D.19
Answer: D.19
Explanation: Average of 20 numbers = 0.
∴ Sum of 20 numbers = (0 × 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (–a).
Answer D
Question: Find the value of 1/(3+1/(3+1/(3-1/3)))
A.25/89
B.26/97
C.27/89
D.10/3
Answer: C.27/89
Explanation: 1/[3 + (1/(3+1/(3 - 1/3)))]
=> 1/[3 + 1/(3 + 1/(8/3))]
=> 1/[3 + 1/(3 + 3/8)]
=> 1/[3 + 8/27]
=> 1/(89/27)
=> 27/89
C)
Question: The total of 35 students in a class is 560 years. The total age of 21 students is 294. What is the total age of remaining 14 students?
A.260
B.270
C.266
D.294
Answer: C.266
Explanation: The total age of 35 students =560 The total age of 21 students =294 The total age of remaining 14 students = (560-294 )=266 Answer : C
Question: If the average of 42, 87, 36, 78, 99, 22, and x is 59, what is x?
A.49
B.42
C.59
D.78
Answer: A.49
Explanation: The answer is 49, because:
(42+87+36+78+99+22+x)/7=59
(42+87+36+78+99+22+x)/7 *7 = 59*7
(42+87+36+78+99+22+x)= 413
(42+87+36+78+99+22+x)-364 = 413-364
x = 49,
so the correct answer is A, 49.
Question: Harold works at a resort from the beginning of March to the end of September. During the month of August this past year, he made 2 times the average (arithmetic mean) of his monthly totals in tips for the other months. His total tips for August were what fraction of his total tips for all of the months he worked?
A.1/3
B.2/5
C.1/4
D.1/2
Answer: C.1/4
Explanation: The time from beginning of March to the end of September is 7 months.
If x is the average monthly tip for all months other than August then his August month tip will be 2*x
His total tip for the 7 months = 6*(average tip for the months other than August) + 2x
=8x
August tips as a fraction of total tips = 2x/8x =1/4. So C
Question: How many odd numbers between 10 and 1200 are the squares of integers?
A.12
B.13
C.14
D.15
Answer: D.15
Explanation: The numbers are the squares of 5, 7, 9,...,33 which includes 15 numbers.
The answer is D.
Question: Given an integer x, let f(x) be the sum of the digits of x. Compute the number of positive
integers less than 1000 where f(x) = 2.
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: We do casework on the number of digits:
(a) The number has 1 digit. The only valid number is 2.
(b) The number has 2 digits. The only valid numbers are 11 and 20.
(c) The number has 3 digits. The only valid numbers are 101, 110, and 200.
This gives us 6 numbers.
correct answer C
Question: John has 6 people in his group of friends. How many different ways can he invite one or more of them to his house?
A.56
B.97
C.63
D.65
Answer: C.63
Explanation: John can select one or more of his group of 6
=> Required number of ways = 2^6 – 1= 63.
C
Question: If u and v are negative integers, which of the following statements must be true?
I. (-u)^v is positive.
II. (-u)^(-v) is positive.
III. u^(-v) is positive.
A.None
B.II only
C.I and II
D.I and III
Answer: C.I and II
Explanation: Let's u = -2 and v = -3
I. (-u)^v = (2)^(-3) = 1/(2^3) --> Positive
II. (-u)^(-v) is positive. = 2^3 --> Positive
III. u^(-v) is positive. = -2^3 --> Negative
Answer: C
Question: You have 59 cubic blocks. What is the minimum number that needs to be taken away in order to construct a solid cube with none left over?
A.27
B.43
C.11
D.32
Answer: D.32
Explanation: D
32
The next cube number below 64(4 ×4 ×4) is 27(3 ×3 ×3).
In order to construct a solid cube, therefore, with none left over,
59 – 27 = 32 blocks need to be taken away.
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
A.5/54
B.5/12
C.5/17
D.5/18
Answer: B.5/12
Explanation: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12
Answer: B
Question: For each color copy, Print Shop X charges $1.20 and Print Shop Y charges $1.70. How much greater is the charge for 40 color copies at Print Shop Y than at Print Shop X?
A.$14
B.$16
C.$18
D.$20
Answer: D.$20
Explanation: The difference in the two prices is $1.70 - $1.20 = $0.50 for each color copy.
Each color copy will cost an extra $0.50 at Print Shop Y.
40*$0.50 = $20
The answer is D.
Question: A can finish a work in 9 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A.6
B.3
C.5.5
D.7
Answer: B.3
Explanation: B's 10 day's work = ( 1 x 10 ) = 2 .
15 3
Remaining work = ( 1 - 2 ) = 1 .
3 3
Now, 1 work is done by A in 1 day.
9
Therefore 1 work is done by A in ( 9 x 1 ) = 3 days.
B
Question: The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A
A.A)11
B.B)12
C.C)13
D.D)14
Answer: A.A)11
Explanation: Explanation:
Given that A+B = 11 + B + C
=> A – C = 11 + B – B = 11
=> C is younger than A by 11 years
Answer: Option A
Question: A 140 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
A.228
B.108
C.84
D.188
Answer: C.84
Explanation: S = 140/6 * 18/5 = 84kmph
Answer: C