RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: When positive integer x is divided by positive integer y, the remainder is 5. If x/y = 96.2, what is the value of y?
A.96
B.75
C.48
D.25
Answer: D.25
Explanation: Guys, one more simple funda.
5/2= 2.5
now .5 x2 =1 is the remainder
25/4 = 6.25
now .25x4=1 is the remainder
32/5=6.4
now.4x5 = 2 is the remainder
given x/y = 96.2 and remainder is 5
So .2 X y = 5
hence y= 25
Ans D
Question: If x⁄2 + 9⁄4 = 5⁄4, what is the value of x?
A.–2
B.–1
C.0
D.1
Answer: A.–2
Explanation: x⁄2 + 9⁄4 = 5⁄4
Let's multiply both sides by 4.
2x + 9 = 5
2x = -4
x = -2
The answer is A.
Question: How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
A.26
B.50
C.1000
D.100
Answer: D.100
Explanation: 1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be ‘n’.
Therefore, using ‘n’ alphabets we can form n * n * n = n3 distinct 3 digit initials.
Note distinct initials is different from initials where the digits are different.
For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This n3 different initials = 1 million
i.e. n3 = 106 (1 million = 106)
=> n3 = (102)3 => n = 102 = 100
Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.
ANSWER D
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280more at the second station it drops one half the new total and takes twelve more .on arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning?
A.288
B.388
C.188
D.258
Answer: A.288
Explanation: Let no of passengers in the beginning be x
After first station no passengers=(x-x/3)+280=2x/3 +280
After second station no passengers =1/2(2x/3+280)+12
½(2x/3+280)+12=248
2x/3+280=2*236
2x/3=192
x=288
Answer is A.
Question: Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
A.5
B.6
C.7
D.8
Answer: A.5
Explanation: Let the present age of P and Q be 3x and 4x respectively.
Ten years ago, P was half of Q in age
=> 2(3x – 10) = (4x – 10)
=> 6x – 20 = 4x – 10
=> 2x = 10
=> x = 5
Answer: A
Question: A school has 120, 192 and 144 students enrolled for its science, arts and commerce courses. All students have to be seated in rooms for an exam such that each room has students of only the same course and also all rooms have equal number of students. What is the least number of rooms needed?
A.11
B.19
C.00
D.27
Answer: B.19
Explanation: We have to find the maximum number which divides all the given numbers so that number of roots get minimized. HCF of 120,192 & 144 is 24. Each room have 24 students of the same course.
Then rooms needed 12024+19224+1442412024+19224+14424 = 5 +8 + 6 = 19
Answer:B
Question: Carlos is 8 years old. In 12 years, how old will he be?
A.17
B.18
C.19
D.20
Answer: D.20
Explanation: 8years + 12years=20 years
answer : D
Question: X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
A.Rs.14400
B.Rs.26400
C.Rs.28400
D.Rs.29400
Answer: A.Rs.14400
Explanation: Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5
Share of X in the profit = 26400 * (6/11) = 2400 * 6 = 14400
Ansewer is A
Question: The sum of two numbers is 18. Their difference is 4. What are the numbers?
A.8,6
B.9,9
C.11,7
D.15,3
Answer: C.11,7
Explanation: Let two numbers be x and y.
Equation (i): x + y = 18
Equation (ii): x - y = 4
Solve system of equations:
2x=22
x=11
y=7
Answer C is correct.
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
A.20:15:15
B.20:15:11
C.20:15:12
D.20:15:19
Answer: C.20:15:12
Explanation: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Question: Bart has $150,512 dollars in his bank account. He wants to split this money evenly among his nine daughters. What is the least amount of money (in whole number of dollars) that he must remove from his account?
A.2
B.3
C.4
D.5
Answer: D.5
Explanation: 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 150,512 = 14 and 9 is divisible by 9.
Hence we need to subtract 5 to this number for it to be divisible by 9
Correct Option: D
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.287
B.277
C.500
D.888
Answer: C.500
Explanation: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (7, 0), (0, -3.5), (-7, 0)?
A.56
B.88
C.112
D.49
Answer: D.49
Explanation: Area of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 7+7= 14
Length of 2nd diagonal= 3.5+3.5= 7
Area= 1/2*14*7= 49
D is the answer
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.2 kmph.
B.4 kmph.
C.5 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: Pipe P can fill a tank in 3 hours, pipe Q in 9 hours and pipe R in 18 hours. If all the pipes are open, in how many hours will the tank be filled?
A.2 hours
B.2.4 hours
C.3 hours
D.3.5 hours
Answer: A.2 hours
Explanation: Explanation:
Part filled by (P + Q + R) in 1 hour = (1/3 + 1/9 + 1/18) = 1/2
All the three pipes together will fill the tank = 2/1 = 2 hours
ANSWER A
Question: 120 is what percent of 80?
A.0.2%
B.2%
C.5%
D.150%
Answer: D.150%
Explanation: 120= x*80/100
x = 150%
Ans; D
Question: 1393 x 1393 = ?
A.A)1951609
B.B)1951601
C.C)1940449
D.D)1951603
Answer: C.C)1940449
Explanation: 1393 x 1393	= (1393)2
= (1400 - 7)2
= (1400)2 + (7)2 - (2 x 1400 x 7)
= 1960000 + 49 - 19600
= 1960049 - 19600
= 1940449.
Answer:C
Question: A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 375,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
A.a) 500
B.b) 750
C.c) 1,000
D.d) 1,250
Answer: D.d) 1,250
Explanation: Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 375,000 = 93,750
So required ratio = 93,750/75 =1,250
Answer D
Question: In a certain company, a third of the workers do not have a retirement plan. 40% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
A.80
B.95
C.105
D.137
Answer: D.137
Explanation: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.
Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.
Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.
Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.
If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.
Cavg = (60*1 + 40*2)/3 = 140/3% are men
Total = 120*300/140 = 257
No. of women = 257 - 120 = 137
D
Question: The average speed of a car decreased by 3 miles per hour every successive 8-minutes interval. If the car traveled 4.4 miles in the fifth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8 minute interval?
A.45
B.48
C.51
D.54
Answer: A.45
Explanation: (4.4 miles / 8 minutes)*60 minutes/hour = 33 mph
Let x be the original speed.
x - 4(3) = 33
x = 45 mph
The answer is A.
Question: The initial price of an article is Rs.4000 which increases 40% increse in its price in the first year,a 20% decrease in the second year and a 20% increase in the next year. What is the final price of the article ?
A.Rs.2928
B.Rs.5928
C.Rs.3928
D.Rs.R4928
Answer: D.Rs.R4928
Explanation: The initial price of the article is Rs.4000. In the 1st year, price of the article = 4000 + 1600 = Rs. 5600. In the 2nd year, price = 5600 - 20% of 5600 = 5600 - 1120 = Rs. 4480.
In the 3rd year, price = 4480 + 10% of 4480 = 4480 + 448 = Rs. 4928
Required price = = Rs.4928.
Answer:D
Question: If x and y are integers and 4^(x-4) = 4^(y+4), what is y in terms of x?
A.x - 8
B.x - 5
C.x - 2
D.x + 2
Answer: A.x - 8
Explanation: Answer: A
4^(x-4) = 4^(y+4)
Since the base is the same, I isolated the equations and solved for y.
x-4 = y+4
y=x-8
Question: A girl has 12 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?
A.A)100
B.B)102
C.C)108
D.D)144
Answer: D.D)144
Explanation: The girl can select one jeans in 12 ways.
The girl can select one shirt in 12 ways.
The number of ways in which he can select one jeans and one shirt is 12 * 12 = 144 ways.
D
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 4 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
A.20cm
B.25cm
C.26cm
D.100/3cm
Answer: D.100/3cm
Explanation: Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 5) (x + 4) - 2x * x = 75 => 3x - 25 = 75 => x = 100/3.
Length of the rectangle = 100/3 cm.
Answer: Option D
Question: The number 243 has been divided into three parts in such a way that one third of the first part, fourth of the second part and half of the third part are equal. Determine the largest part.
A.108
B.86
C.74
D.92
Answer: A.108
Explanation: Explanation:
It is given that 243 has been divided into 3 numbers x y and z for instance.
Second condition mentioned in the question is:
=> x/3 = y/4 =z/2
Clearly the biggest number is y. So let us solve w.r.t. y.
=> x = 3y/4
=> x =3z/2
=> z = y/2
=> x+y+z = 243
=> y/2 + 3y/4 + y = 243
9y/4 = 243
=> 243*4/9
=> 108
ANSWER A
Question: If a and b are positive integers and x = 9^a and y = 3^b, which of the following is a possible units digit of xy?
A.2
B.4
C.5
D.7
Answer: D.7
Explanation: The units digit of 9^a is either 1 or 9.
The units digit of 3^b is 3, 9, 7, or 1.
We can multiply the units digits together to see that the units digits of xy could be 1, 3, 7, or 9.
The answer is D.
Question: Working together, printer A and printer B would finish the task in 30 minutes. Printer A alone would finish the task in 50 minutes. How many pages does the task contain if printer B prints 3 pages a minute more than printer A ?
A.200
B.400
C.600
D.800
Answer: B.400
Explanation: 30*A + 30*B = x pages
in 30 mins printer A will print = 30/50 * x pages = 3/5*x pages
thus in 30 mins printer printer B will print x - 3/5*x = 2/5*x pages
Also it is given that printer B prints 3 more pages per min that printer A. In 30 mins printer B will print 90 more pages than printer A
thus 3/5*x - 2/5*x = 90 => x = 400 pages
Answer: B
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.19.9
B.19.3
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: Option D
Question: Look at this series: 8, 43, 11, 41, __, 39, 17, ... What number should fill in the blank?
A.8
B.14
C.43
D.44
Answer: B.14
Explanation: Answer: Option B
This is a simple alternating addition and subtraction series. The first series begins with 8 and adds 3; the second begins with 43 and subtracts 2.
Question: {1/(4+√15)}^2 =
A.a. 16+16√15
B.b. 31- 8√15
C.c. 31+ 8√15
D.d. 32- 4√15
Answer: B.b. 31- 8√15
Explanation: 1 / (16 - 8 root15 + 15)
= 1 / (31 + 8 root15)
Multiply numeratordenominator by (31 - 8 root15)
= (31 + 8 root15) / (961-960) = (31 - 8 root15)
Answer = B
Question: Which of these must the factor G of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80
A.1,2 only
B.G=2,3 only
C.G=1,2,3 only
D.G=1,2,3,4 only
Answer: D.G=1,2,3,4 only
Explanation: Let the four variables be a< b< c< d.
Assume a worst case scenario where the a equal to a prime number (hence odd).
therefore
a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)
therefore
each answer choice must be divisible by 2 x 3 x 4 = 24
only 80 is not divisible. Therefore answer = D
Question: If the simple interest on Rs. 2000 is less than the Simple Interest on Rs. 3000 at 5% by Rs. 50, find the time.
A.2.5 year
B.1 year
C.1.5 year
D.2 year
Answer: B.1 year
Explanation: Explanation :
Difference in principal = 3000-2000 = 1000
i.e., Simple Interest on Rs.1000 will be Rs.50
1000×5×T/100=50
50T=50
T=1 year
Answer : Option B
Question: What least number must be added to 3000 to obtain a number exactly divisible by 19 ?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: Sol. On dividing 3000 by 19, we get 17 as remainder.
Number to be added = (19 - 17) = 2.
Option B
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 2x km.
A.16
B.18
C.24
D.19
Answer: A.16
Explanation: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 2x/(x/8) = 16 kmph
Answer: A
Question: If a is a number such that –2 ≤ a ≤ 2, which of the following has the largest possible absolute value?
A.3a – 1
B.x^2 + 1
C.3 – x
D.x – 3
Answer: A.3a – 1
Explanation: Ans is A .. leads to the max value of 7 for a = -2
Question: A woman bought a pack of 36 eggs, but the seller told her that there were 3 rotten eggs in the pack. She forgot it and begun to prepare a recipe that needs 2 eggs. What is the probability that both choosen eggs will be rotten?
A. 1/210
B. 2/210
C. 3/210
D. 1/119
Answer: A. 1/210
Explanation: There are 3 rotten eggs in a pack of 36. Thus the probability of picking 2 rotten eggs is: (3/36)(2/35) = 1/210. The correct answer is A.
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
A.1/2
B.3/4
C.3/8
D.5/16
Answer: B.3/4
Explanation: n(S)=36
n(E)=27
P(E)=n(S)/n(E)
=27/36
=3/4
Option B
Question: A bag contains 3red, 2blue and 4green balls. If 2 balls are picked at random, what is the probability that both are red?
A.1/12
B.1/13
C.1/14
D.1/15
Answer: A.1/12
Explanation: P(Both are red),
=3C2/9C2=1/12
A
Question: A father is now three times as old as his son. Four years back, he was four times as old as his son. The age of the son (in years) is
A.12
B.15
C.18
D.20
Answer: A.12
Explanation: If father's age is F and son's age is S, then
F=3S
and
F-4 = 4*(S-4)
3S-4 =4S-16
S=12
F=36 years
ANSWER:A
Question: The average age of a husband and a wife is 23 years when they were married THREE years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
A.6
B.5
C.8
D.4
Answer: C.8
Explanation: 26 * 2 = 52
20 * 3 = 60
-----------
8 years.Answer: C
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 5 and 6hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
A.8hrs 25min. (AM)
B.8hrs 54min. (AM)
C.7hrs 45min. (AM)
D.7hrs 15 min. (AM)
Answer: D.7hrs 15 min. (AM)
Explanation: 1 to 2 = 1/5
2 to 3 = 1/5 + 1/6 = 11/30
After 3 AM = 1/5 + 1/6 - 1/2= -4/30
1/5 + 11/30 = 17/30
1 h ---- 4/30
? ----- 17/30
7hrs 15 min. (AM)
Answer:D
Question: If 3^x*4^y = 531,441 and x – y = 12, then x = ?
A.10
B.11
C.12
D.13
Answer: C.12
Explanation: Since 531,441 is an odd number, it is not a multiple of 4.
This means that y must equal zero.
Since x - y = 12 and y = 0, then x = 12.
The answer is C.
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 15 percent, and on day 3, it is discounted an additional 20 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
A.28%
B.40%
C.68%
D.70%
Answer: C.68%
Explanation: Let initial price be 1000
Price in day 1 after 10% discount = 900
Price in day 2 after 15% discount = 765
Price in day 3 after 20% discount = 612
So, Price in day 3 as percentage of the sale price on day 1 will be = 612/900*100 => 68%
Answer will definitely be (C)
Question: How many times hour hand covers full circle in a day?
A.3 times
B.2 times
C.4 times
D.5 times
Answer: B.2 times
Explanation: 2 times
ANSWER:B
Question: A man’s current age is of the age of his father. After 8 years, he will be of the age of his father. What is the age of father at now ?
A.50
B.40
C.33
D.30
Answer: B.40
Explanation: Explanation:
Let, father’s current age is A years.
Then, Man’s current age = years.
2/5A+8=1/2(A+8)= A= 40. Answer: B
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 3 years would be
A.(1.5)^4
B.4(1.5)
C.(1.05)^3
D.1 + (0.05)^4
Answer: C.(1.05)^3
Explanation: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 3 years would be
1(1.05)^3
1.05^3
C. (1.05)^3
Question: Four kids having five rocks each were playing a game in which they need to throw the rock at solid area in the water.
Kid1: Succeeded in throwing three rocks at solid area but one of the rock sunk.
Kid3: His aim was so bad that all rocks got sunk.
Kid4: He was awesome and none of the rocks got sunk.
Kid2 was the winner but was struck by a rock in the head and died.
Who killed Kid2 ?
A.Kid1
B.Kid2
C.Kid3
D.Kid4
Answer: A.Kid1
Explanation: A
Kid1, he was left with one rock.
Question: If a - b = 3 and a(power 2) + b(power 2) = 25, find the value of ab.
A.5
B.8
C.4
D.10
Answer: B.8
Explanation: 2ab = (a(power 2) + b(power 2) - (a - b)(power 2)
= 25 - 9 = 16
ab = 8.
Answer is B.
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
A.2281
B.2771
C.1500
D.2777
Answer: C.1500
Explanation: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500
Answer: C
Question: The total number of digits used in numbering the pages of a book having 366 pages is
A.732
B.990
C.1098
D.1305
Answer: B.990
Explanation: Total number of digits
= (No. of digits in 1- digit page nos. + No. of digits in 2-digit page nos. + No. of digits in 3- digit page nos.)
= (1 x 9 + 2 x 90 + 3 x 267) = (9 + 180 + 801) = 990.
ANSWER:B
Question: 6 noun, 3 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this??
A.294
B.310
C.324
D.360
Answer: C.324
Explanation: we have to choose one from each set. 1 from 6 nouns and 1 from 3 verbs and 1 from 3 adjectives.
then we have to arrange 3 different sets in 3! ways.
so,
6c1*3c1*3c1*3!=324
ANSWER:C
Question: A box contains 2 red chips and 2 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
A.1/2
B.4/3
C.7/12
D.2/3
Answer: B.4/3
Explanation: Total selection ways: 4C2=4!/2!2!=6
Selecting one blue chip out of two: 2C1=2!/1!1!=2
Selecting one red chip out of four: 2C1=2!/1!1!=4
Thus, (2C1*2C1)/4C2=(2*4)/6=8/6=4/3=B
Question: What is the probability of getting only 1 head in a single throw of four fair coins?
A.1/2
B.3/8
C.1/4
D.1/5
Answer: C.1/4
Explanation: One possible case is HTTT.
P(HTTT) = 1/2*1/2*1/2*1/2 = 1/16
There are 4C1 = 4 possible cases.
P(1 head) = 4*1/16 = 1/4
The answer is C.
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
A.250
B.280
C.240
D.270
Answer: D.270
Explanation: Explanation:
Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
Answer D
Question: in a class of 25 students, 15 play hockey and 16 play basketball. if there are 4 students who play neither sport, determine the number of students who play both hockey and basketball?
A.10
B.11
C.13
D.14
Answer: A.10
Explanation: Let the number of who play both be x
Number of students who play sports 25-4=21
Use Venn diagram
(15-x)+x+(16-x)=21
Which gives x=10
Answer is A
10 play both sport
Question: How many multiples of 9 are there between 1 and 50, exclusive?
A.5
B.4
C.6
D.7
Answer: A.5
Explanation: 5
multiples of 9 between 1 and 50 exclusive.
from 9 * 1 upto 9*5, (1,2,3,4,5). Hence, 5 multiples !
correct option is A
Question: A certain number of workers can do a work in 85 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
A.75
B.30
C.28
D.24
Answer: A.75
Explanation: number of workers = 10* (85-10)/10 = 75
Answer is A
Question: If two of the four expressions x + y , x + 4y , x - y , and 4x - y are chosen at random, what is the probability that their product will be of the form of x^2-(by)^2, where b is an integer?
A.1/6
B.1/8
C.1/7
D.1/5
Answer: A.1/6
Explanation: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (x+y)(x-y) = x^2 - (1y)^2
If you see any other combination we are always going to have one term of xy since 4x and 4y are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : A
Question: In a Question paper there are 4 multiple choice questions. Each question has 5 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
A.19
B.85
C.120
D.624
Answer: D.624
Explanation: A candidate can answer the test in 5*5*5*5=5^4 number of ways (each question has 5 choices and we have total of 4 questions). Now, out of these cases there will be only one case when the candidate answered all the four questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.
Answer: D.
Question: Rebecca's yearly income is $15,000 and Jimmy's annual income is $18,000. By how much must Rebecca's yearly income increase so that it constitutes 55% of Rebecca and Jimmy's combined income?
A.7000
B.8000
C.9000
D.10000
Answer: A.7000
Explanation: total rebecca = x+15000 ; total = x+15000+18000;
x+15000/x+33000 = 55/100 therefore x =7000
A