RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.1, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?
A.$8.30
B.$20.75
C.$22.50
D.$42.75
Answer: A.$8.30
Explanation: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .
A= 2O
S= 2G
A= 2S
A= 4G
A+O+S+G = 90
=>A + A/2 + A/2 +A/4 = 90
=> 9A/4 = 90
=> A = 40
O = 20
S = 20
G = 10
Cost of each candy = .1 $
Mininum amount of money required to guarantee that you would buy at least three of each type of candy
We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .
Total = 83 candies
Amount required = 83 * .1 = 8.30 $
Answer A
Question: A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?
A.8 days
B.11 days
C.21 days
D.22 days
Answer: A.8 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
Option 'A'
Question: If x is less than y by 20% then y exceed x by:
A.33.33%
B.25%
C.75%
D.66.66%
Answer: B.25%
Explanation: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 20%)
=> 20/(100-20)*100
=25%
ANSWER:B
Question: A can do a piece of work in 4 days. B can do it in 8 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
A.22 days
B.8 days
C.67 days
D.1 days
Answer: B.8 days
Explanation: C = 1/2 - 1/4 - 1/8 = 1/8
=> 8 days
Answer:B
Question: What is the least common multiple of 15, 22 and 24?
A.60
B.120
C.240
D.1320
Answer: D.1320
Explanation: Let us first write the numbers in the form of prime factors:
15 = 3*5
22 = 2*11
24 = 2 * 17^1
The LCM would be the largest powers of the prime numbers from all these three numbers.
Hence LCM = 1320
Option D
Question: It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 160 pages?
A.12
B.18
C.48
D.20
Answer: C.48
Explanation: If it takes 4 more minutes for A to print 40 pages than it takes B,
it takes 5 more minutes for A to print 50 pages than it takes B.
Thus if b is the number of minutes than B takes to print 50 pages,
we can write:
1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)
6(2b+5)=b(b+5)
b^2-7b-30=0
(b-10)(b+3)=0
b=10
Thus it takes A 15 minutes to print 50 pages and 15*160/50=48 minutes to print 160 pages (ANSWER C)
Question: Last year Sandy saved 6% of her annual salary. This year, she made 10% more money than last year, and she saved 9% of her salary. The amount saved this year was what percent of the amount she saved last year?
A.140%
B.152%
C.165%
D.176%
Answer: C.165%
Explanation: Let last year's salary be x.
Last year, Sandy save 0.06x
This year, Sandy saved 0.09*1.1x = 0.099x
0.099x / 0.06x = 99/60 = 1.65 = 165%
The answer is C.
Question: A boy is travelling from his home to school at 4 km/hr and reached 7 min late. Next day he traveled at 8 km/hr and reached 8 min early. Distance between home and school?
A.2km
B.3km
C.4km
D.5km
Answer: A.2km
Explanation: Let the distance be x
T1 = x/4 hr
T2 = x/8hr
Difference in time = 7+8 = 15 =1/4hr
x/4-x/8= 1/4
x/8=1/4
x =2 km
Answer is A
Question: In an exam, Dibi scored 25 percent, Balan scored 38 percent and Cristen 23 percent. The maximum score awarded in the exam is 1200. Find the average mark scored by all the three boys?
A.322
B.342
C.344
D.328
Answer: C.344
Explanation: Average mark scored by all the three boys =
[25/100 (1200) +38 /100 (1200) + 23/100 (1200)] / 3
300+456+276= 344
Answer: C
Question: Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?
A.Rs. 13, Rs. 19
B.Rs. 13, Rs. 17
C.Rs. 13, Rs. 12
D.Rs. 13, Rs. 11
Answer: B.Rs. 13, Rs. 17
Explanation: Explanation:
Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.
Then, 2x + 3y = 77 ...(i) and
3x + 2y = 73 ...(ii)
Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.
Putting y = 17 in (i), we get: x = 13.
Answer: B) Rs. 13, Rs. 17
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
A.4:3
B.8 : 7
C.4 : 1
D.6 : 5
Answer: B.8 : 7
Explanation: Explanation:
Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
ANSWER IS B
Question: Let the polynomials be:
P1(x)=3x2−7x+7,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
A.2x2 + 11x - 7
B.-2x2 - 11x + 9
C.-2x2 - 11x + 6
D.2x2 - 9x + 7
Answer: B.-2x2 - 11x + 9
Explanation: Solution:
P1(x)+P2(x)=(3x2−7x+7)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+7)+(−5x2−4x+2)=
3x2−7x+7−5x2−4x+2=3x2−7x+7−5x2−4x+2=
−2x2−11x+9
Answer B
Question: In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a two on either die, that player wins. What is the probability that a player wins after playing the game once?
A.1/3
B.4/9
C.5/9
D.2/3
Answer: C.5/9
Explanation: We're looking for the number of outcomes that include AT LEAST a 2 or a 5.
#getting a two in the 1st die = {(2,1), (2,2), ...(2,6) }= 6
#getting a two in 2nd die {(3,2), (4,2), ...(6,2) } = 4 [exclude 1,2 and 5,2] since it will be counted twice
#getting a five in 1st die {(5,1), (5,2), ...(5,6) }= 6
#getting a five in 1st die {(2,5), (3,5), ...(6,5) } = 4 [exclude 1,5 and 5,5] since it will be counted twice
Total possibilities = 20
Probability of rolling at least a 2 or a 5 on two dice: 20/36 = 5/9
C
Question: The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. The percentage of slump in business is ?
A.8%
B.1%
C.20%
D.80%
Answer: C.20%
Explanation: Answer
Let the business value change from A to B.
Then, 4% of A = 5% of B
⇒ 4A/100 = 5B/100
⇒ B = 4A/5
∴ change in business = (A - 4A/5) = A/5
Percentage slump in business = {(A/5)/A} x 100 % = 20%
Correct Option: C
Question: Two trains of length 200 m and 300 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
A.70/8
B.70/7
C.70/5
D.70/3
Answer: D.70/3
Explanation: Relative speed = (36 + 72)* 5/18 = 6 * 5 = 30 mps.
The time required = d/s = (200 +200 + 300)/30
= 700/30= 70/3 sec.
Answer: D
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 45.
A.600
B.529
C.612
D.512
Answer: B.529
Explanation: Number of odd numbers between 1 and 45 is (45+1)/2=23
Therefore Sum of odd numbers 23*23= 529
ANSWER: B
Question: Angelina walked 960 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
A.2
B.13
C.24
D.36
Answer: D.36
Explanation: let the speed be X...
so time taken from home to grocery= 960/x..
the speed to gym = 2x..
so time taken = 480/2x=240/x..
its given 960/x-240/x=40..
720/x=40..
x=18m/secs..
so grocery to gym=2*18=36m/s...
D
Question: Tough and Tricky questions: Combinations.
Three students - 2 boys and 1 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
A.2
B.4
C.72
D.240
Answer: B.4
Explanation: 2!*1!*2 = 2*1*2 = 4 ways.
Ans. B) 4
Question: What is the remainder when 3^25 is divided by 5?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}
25 has the form 4k+1, so the units digit of 3^25 is 3.
The remainder when dividing by 5 is 3.
The answer is D.
Question: James eats cookies every day. The first day, he eats 2 cookies. He eats 4 more cookies each day after that. What is the average number of cookies he eats per day for the first 2 weeks?
A.32.14
B.45
C.49.28
D.30
Answer: A.32.14
Explanation: 2 weeks = 14 days
Total cookies = 2 + 6 + 10 + ... + (2 + 14(4))
=2 + 6 + 10 + ... + 58
=2(1 + 3 + 5 + ... + 29)
=2(1 + 2 + 3 + ... + 29 - (2 + 4 + ... + 28))
=2 (1 + 2 + ... + 29) - 2(2 + 4 + ... + 28)
=2(1 + 2 + ... + 29) - 2(2)(1 + 2 + ... + 14)
=2(29)(30)/2 - 4(14)(15)/2
=870-420
=450
Average = 450/14
=32.14
Option A
Question: A can do a piece of work in 15 days and B in 20 days. They began the work together but 5 days before the completion of the work, A leaves. The work was completed in?
A.15 3/7 days
B.11 3/7 days
C.12 3/7 days
D.19 3/7 days
Answer: B.11 3/7 days
Explanation: B
11 3/7 days
(x – 5)/15 + x/20 = 1
x = 11 3/7 days
Question: Real-estate salesman Z is selling a house at a 20 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 20 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 20 percent discount. Salesman Y's final price is what fraction of salesman X's final price?
A.29/32
B.28/31
C.30/31
D.40/41
Answer: A.29/32
Explanation: Let the retail price be = x
Selling price of Z = 0.80x
Selling price of X = 0.80*0.80x = 0.64x
Selling price of Y = ((0.80x + 0.64x)/2)*0.80 = 0.72x * 0.80 = 0.58x
0.58x = k * 0.64x
k = 0.58/0.64 = 58/64=29/32
Answer: A
Question: An article manufactured by a company consists of two parts X and Y. In the process of manufacturing of part X, 9 out 100 parts many be defective. Similarly , 5 out of 100 are likely to be defective in the manufacturer of Y. Calculate the probability that the assembled product will not be defective?
A.0.8647
B.0.8642
C.0.8645
D.0.8628
Answer: C.0.8645
Explanation: Ans: Probability that the part X is nondefective is = 1 - 9/100=.91
Probablity that the part Y is nondefective is = 1 - 5/100=.95
so, Probablity of nondefective product=0.91××0.95=0.8645
Answer:C
Question: A focus group is currently made up of x men and y women. If 2 men and 4 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a woman is selected?
A.x/(x + 2)
B.x/(x + y)
C.(x + 2)/(x + y + 2)
D.(y + 4)/(x + y + 6)
Answer: D.(y + 4)/(x + y + 6)
Explanation: x men
y women
x+2+y+4 is the total
=x+y+6
y+4 is the number of men
so (y + 4)/(x + y + 6)
D. (y + 4)/(x + y + 6)
Question: Two numbers are respectively 35% and 50% more than a third number. The percentage that is first of the second is?
A.90%
B.47%
C.38%
D.52%
Answer: A.90%
Explanation: I II III
135 150 100
150----------135
100-----------? => 90%
Answer:A
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 53 percent of those who attended the meeting were stockholders and 63 percent were employees, what percent were stockholders who were not employees?
A.34
B.35
C.36
D.37
Answer: D.37
Explanation: 53+63=116 so 16% were both stockholders and employees.
The percent who were stockholders but not employees is 53-16=37%
The answer is D.
Question: Two trains 140 m and 160 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.12.9 sec
B.29.0 sec
C.28.9 sec
D.10.8 sec
Answer: D.10.8 sec
Explanation: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer:D
Question: Mixture X contains 60% water and 40% chloride. If 120 gallons of Mixture Y is added to 80 gallons of mixture X in order to produce a solution that contains 75% water and 25% chloride, how many gallons of water must mixture Y contain?
A.100
B.101
C.102
D.103
Answer: C.102
Explanation: 80 gallons of Mix X containing 40% chloride + 120 gallons of Mix Y ----> 25% chloride mixture
wA/wB = (cB - cAvg)/(cAvg - cA)
80/120 = (Y - 25)/(25 - 40)
2 * (-15) = 3 * (Y - 25)
Y = 15
So the concentration of chloride in Mix Y is 15%.
In 120 gallons of mix Y, you will have (85/100)*120 = 102 gallons
ANSWER:C
Question: In a tree, 3/7 of the birds are robins while the rest are bluejays. If 1/3 of the robins are female and 3/5 of the bluejays are female, what fraction of the birds in the tree are male?
A.11/35
B.14/35
C.18/35
D.31/70
Answer: C.18/35
Explanation: The fraction of birds that are male robins is (2/3)(3/7)=2/7.
The fraction of birds that are male bluejays is (2/5)(4/7)=8/35.
The total fraction of male birds is 2/7 + 8/35 = 18/35.
The answer is C.
Question: What will be the CI on a sum of Rs. 25,000 after 3 years at the rate of 12 per year?
A.Rs. 10100
B.Rs. 10110
C.Rs. 10123.20
D.Rs. 10135.50
Answer: C.Rs. 10123.20
Explanation: Amount
= Rs. 25000 x 1 + 12 3
100
= Rs. 25000 x 28 x 28 x 28
25 25 25
= Rs. 35123.20
C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20
C
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.11 minutes
B.17 minutes
C.18 minutes
D.10 minutes
Answer: D.10 minutes
Explanation: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer: D:
Question: A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 mins and 24 seconds. If the second blast occurred exactly 30 mins after the first, how many meters was he from the site when he heard the second blast? ( speed of sound = 330 m/s)
A.6810
B.7920
C.9030
D.10,140
Answer: B.7920
Explanation: The distance the sound traveled to the man is 24*330 = 7920 meters
The answer is B.
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.15of money?
A.1500
B.1528
C.2796
D.2650
Answer: A.1500
Explanation: P = 15(100/10)2 => P
= 1500
Answer:A
Question: 9 friends decided to divide the hotel bill evenly. If the bill was $124.15 dollars, how much money did they pay if 1 cent is the smallest unit?
A.$124.11
B.$124.12
C.$124.13
D.$124.14
Answer: A.$124.11
Explanation: This is equivalent to finding the first number that is divisible by 9 that occurs after 12415.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 12415 = 13 and 9 is divisible by 9.
Hence, we need to remove 4 to this number for it to be divisible by 9
Correct Option: A
Question: When the positive integer y is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer z is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of y-z?
A. 12
B. 24
C. 35
D. 16
Answer: C. 35
Explanation: If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:
n = 5y + 3
n = 7z + 4
I will need to check for the smallest such number.
I put z= 1. n = 11. Is it of the form 5y + 3? No.
Put z= 2. n = 18. Is it of the form 5y + 3? Yes.
When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.
Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder
Next will be 35*2 + 18
and so on...
Difference between such numbers will be a multiple of 35 so your answer is 35.
your answer is C
Question: In how many different number of ways 1 boys and 3 girls can sit on a bench?
A.720
B.730
C.740
D.24
Answer: D.24
Explanation: npn = n!
4p4 = 4 × 3 × 2 × 1 = 24
D
Question: Lucy deposited $62500 in an investment fund that provided 8 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $5100?
A.0.5
B.24
C.93
D.63
Answer: C.93
Explanation: A = P + I = 62500 + 5100 = 67600
67600 = 62500(1 + 8/4*100)^(4t)
(676/625) = (102/100)^(4t)
t =7 7/9 yrs = 93 months
Answer: C
Question: The current birth rate per thousand is 32, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by?
A.2.0%
B.3.2%
C.3.9%
D.4%
Answer: A.2.0%
Explanation: Net growth on 1000 = 32-10 = 20
Net growth on 100 = 20*100/1000 = 2.0%
Answer is A
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
A.227
B.247
C.200
D.277
Answer: C.200
Explanation: 2(l + 100) = 600 => l = 200 m
Answer:C
Question: A man performs 2/15 of total journey by train,9/20 by tonga and the remaining 10 kms on foot. total journey is ?
A.30
B.20
C.24
D.21
Answer: C.24
Explanation: 1-((2/15)+9/20)=1-35/60=25/60=5/12
5/12 of x=10km(Remaining)
x=10*12/5=24
ANSWER:C
Question: How many 7 digit number are there having the digit 3 three times & the digit 5 four times?
A.7!/(3!)(5!)
B.3^3 * 5^5
C.77
D.35
Answer: D.35
Explanation: Explanation :
7!/3!*4!=35
Answer : D
Question: A family has two children. find the probability that both the children are boys given that at least
one of them is a boy?
A.1/3
B.1/5
C.1/7
D.1/11
Answer: A.1/3
Explanation: Let b stand for boy and g for boy. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are boys’
F : ‘at least one of the child is a boy’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A)
Question: If two distinct positive divisors of 64 are randomly selected, what is the probability that their sum will be less than 32?
A.1/3
B.1/2
C.5/7
D.10/21
Answer: D.10/21
Explanation: list the distinct positive factors: 1,2,4,8,16,32,64
selecting 2 from this list = 7C2 = 21
as per the given condition there sum has to be less than 32
picking any 2 numbers from our list of first five numbers will render the sum less than 32 in any case
selecting 2 number from 5 numbers = 5C2 = 10
proability = 10/21
correct answer - D
Question: 21, 9, 21, 11, 21, 13, 21, ?
A.15
B.17
C.23
D.25
Answer: A.15
Explanation: In this alternating repetition series, the number 21 is interpolated. If you exclude 21, the series increases by 2, beginning with the number 9.
Answer : A.
Question: A is thrice as good a workman as B and therefore is able to finish a job in 50 days less than B. working together, they can do it in
A.days
B.3/4 days
C.days
D.days
Answer: B.3/4 days
Explanation: Explanation:
B = 3A
3A – A =50 days
A = 25days
Then, B = 90 days
(A + B) = 25 × 90/ 120 = 18 3/4 days .
Answer: Option B
Question: Find the odd man out. 1, 27, 216, 512, 1024, 1331
A.1024
B.512
C.27
D.1
Answer: A.1024
Explanation: Explanation :
All given numbers except 1024 are perfect cubes
Answer : Option A
Question: In a group of ducks and cows, the total no.of legs are 24 more than twice the no.of heads. Find the total no.of buffaloes.
A.10
B.12
C.14
D.16
Answer: B.12
Explanation: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Question: 15 business executives and 3 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
A.150
B.131
C.115
D.90
Answer: A.150
Explanation: there are 15 business exec and in each handshake 2 business execs are involved.
hence 15C2=105
Also, each of 15 exec will shake hand with every 3 other chairmen for total of 45 handshake.
total=45+105=150
ANS:A
Question: (18)7 x (5832)-2 ÷ (324)-1 = (18)7
A.5
B.4
C.3
D.2
Answer: C.3
Explanation: Explanation :
(18)7 x (183)-2 ÷ (182)-1
(18)7 x (18)-6 ÷ (18)-2
(18)7-6+2 = (18)3
Answer : Option C
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
A.17 min
B.10 min
C.15 min
D.47 min
Answer: D.47 min
Explanation: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18
=47 min.
Answer:D
Question: How many even number in the range between 8 to 100 inclusive are not divisible by 3
A.15
B.30
C.32
D.33
Answer: C.32
Explanation: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
8,10,12,14...100
using AP formula, we can say 100 = 10 + (n-1) *2
or n=47.
For 6,
12,18,...96
using AP formula, we can say 96 = 12 + (n-1) *6
or n=15.
Hence, only divisible by 2 but not 3 = 47-15 = 32. hence, Answer C
Question: If x < 0 and 0 < y < 1, which of the following has the greatest value C?
A.x^2
B.(xy)^2
C.(x/y)^2
D.x^2/y
Answer: C.(x/y)^2
Explanation: Given, x < 0 and 0 < y < 1
Let, x = -2 and y = 1/2
A. x ^2 = (-2)^2 =4
B. (xy)^2 = (-2*1/2)^2 =1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16
D. x^2/y = (-2)^2 / (1/2) = 4*2 =8
E. x^2*y = (-2)^2*(1/2) =2
Answer: option C
Question: If n is a prime number, which of the following could be true
A.n^n=n
B.n^2/4= is even
C.n^n/4 = 1^(n-1)
D.n^2+n^3= n^5
Answer: C.n^n/4 = 1^(n-1)
Explanation: C should be the answer.
2^2/4 = 1^(2-1)
Question: From a group of 19 astronauts that includes 10 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
A.380
B.370
C.350
D.360
Answer: D.360
Explanation: number of astronauts with previous experience = 10
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group
(10C1)*(9C2)
=10*36= 360
Answer : D
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
A.7 kmph
B.5 kmph
C.3 kmph
D.8 kmph
Answer: D.8 kmph
Explanation: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer: D
Question: the sum of series represented as
1/(1*5) + 1/(5*9) + 1/(9*13) +..... + 1/(221*225) is
A.28/221
B.56/221
C.56/225
D.54/225
Answer: C.56/225
Explanation: 1/(1*5) + 1/(5*9) + 1/(9*13) +..... + 1/(221*225)
=(1/4)*[(5-1)/(1*5) + (9-5)/(5*9) + (13-9)/(9*13) +..... + (225-221)/(221*225)]
=(1/4)*[(1- 1/5)+(1/5 - 1/9)+(1/9 -1/13)+...(1/221 -1/225)]
=(1/4)*(1- 1/225)
=(1/4)*(224/225)
=56/225
ANSWER:C