RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A car started running at a speed of 36 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
A.45 km
B.76 km
C.25 km
D.15 km
Answer: A.45 km
Explanation: A
45 km
The total distance covered by the car in the first 10 hours = 36 + 38 + 40 + 42 + 44 + 46 + 48+ 50 + 52 + 54= sum of 10 terms in AP whose first term is 36 and last term is 54 = 10/2 [36 + 54] = 450 km.
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
A.5/26
B.5/78
C.5/21
D.5/56
Answer: A.5/26
Explanation: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252
= 5/21
Answer:A
Question: Kristy, Amy, and Blair are going on a cross-country road trip from Washington to Maine. The total driving time is 48 hours. Each driver will drive 6 hours daily and in the remaining hours of the day the group will sight-see and explore. They will sleep in the car when they are not driving. They all have driver's licenses, but Amy is scared of driving in unfamiliar places and would prefer not to take the wheel. How much sooner would the group arrive in Maine, in hours, if Amy chose to drive, compared to just Kristy and Blair?
A.12
B.24.76
C.31.92
D.36.92
Answer: C.31.92
Explanation: All three girls calculation: 3 girls x 6 hours = 18 hours of driving per day, 6 nondriving hours/day
48 total trip hours divided by 18 daily driving hours = 2.67 days / driving rotations
2.67 x 24 (hours in one day) = 64.08 total hours for road trip
2 girls calculation: 2 girls x 6 hours = 12 hours of driving per day, 12 nondriving hours/day
48 total trip hours divided by 12 daily driving hours = 4 days / driving rotations
4 x 24 (hours in one day) = 96 total hours for road trip
FINAL ANSWER: 96 hours (2 girls total) minus 64.08 (3 girls total) = ANSWER C: The group would arrive in Maine 31.92 hours sooner if all three drove.
Question: P, Q and R can do a work in 10 , 12 and 15 days respectively. What is the share ratio of P, Q and R respectively?
A.6 : 5 : 7
B.6 : 5 : 4
C.6 : 5 : 3
D.6 : 4 : 5
Answer: B.6 : 5 : 4
Explanation: The ratio of their working rates = 1/10 : 1/12 : 1/15 = 6 : 5 : 4.
Answer: B
Question: A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 30 percent, what is the discount rate on mysteries?
A.17.18%
B.12%
C.13%
D.14%
Answer: A.17.18%
Explanation: Let B be the discount on biographies and M be the discount on mysteries
So., B + M = 0.30 -----(1)
And
(20*5 + 12*3) - (20*5*(1-B) + 12*3*(1-M)) = 19
--> 100(1-(1-B)) + 36(1-(1-M) = 19
100B + 36M = 19 ------(2)
Solving 12., we get M = 0.1718 = 17.18
A
Question: Amar started a business investing Rs. 34000/-. After 3 months, Vamsi joined him with a capital of Rs. 40000/-. At the end of the year, they make a profit of Rs. 17040/-. What will be Amar’s share in the profit?
A.Rs. 9025/-
B.Rs. 9052.5/-
C.Rs. 9503.5/-
D.Rs. 9504.5/-
Answer: B.Rs. 9052.5/-
Explanation: Explanation:
Amar : Vamsi = (34000 * 12 : 40000 * 9)
= 408000 : 360000
= 408 : 300
= 51 : 45
Amar’s share = 17040 * 51/91 = 177.5 * 51 = Rs. 9052.5/-
Answer: Option B
Question: If the greatest common divisor of (n+2)!, (n-1)!, and (n+4)! is 120, what is the value of n?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: Notice that:
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
So, the smallest factorial must be 5! for the GCD to be 120
The smallest of the three factorials is (n-1)!
So, we need (n-1)! to equal 5!
This means that n = 6
If n = 6, then (n+2)!, (n-1)!, and (n+4)! become 8!, 5! and 10!
Let's CONFIRM this conclusion
8! = (1)(2)(3)(4)(5)(6)(7)(8) = (120)(6)(7)(8)
5! = (1)(2)(3)(4)(5) = 120
10! = (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) = (120)(6)(7)(8)(9)(10)
As you can see, 120 is a divisor of all three factorials.
In fact, 120 is the GREATEST COMMON divisor of all three factorials.
Answer: C
Question: The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?
A.16:00.
B.18:00
C.20:00
D.22:00.
Answer: B.18:00
Explanation: Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 3 hours
Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 6 hours
Time taken by both buses to meet again in St. Louis will be LCM of 3 and 6 = 6
If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours
Answer B
Question: A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes?
A.35:1
B.Either ;35:1
C.Either 70;35:1
D.Either 55;45:1
Answer: B.Either ;35:1
Explanation: Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans.
Either ;35:1
B)
Question: Let A be the event that a randomly selected two digit number is divisible by 2 and let B be the event that a randomly selected two digit number is divisible by 10. What is P(A and B)?
A.1/20
B.1/15
C.1/12
D.1/8
Answer: A.1/20
Explanation: P(A and B) = 1/2*1/10 = 1/20
The answer is A.
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
A.65 sec
B.16 sec
C.18 sec
D.13 sec
Answer: B.16 sec
Explanation: Speed = 63 * 5/18 = 35/2 m/sec
Time taken
= 280 * 2/35
= 16 sec
Answer:B
Question: Shaun is starting a new diet plan that offers him the choice of fruit or yogurt for breakfast, 6 different entrees for lunch, and 9 different entrees for dinner. If Shaun chooses an Italian entree for lunch, he always chooses an Italian entree for dinner. If Shaun chooses a Chinese entree for lunch, he never chooses a Chinese entree for dinner. If there are 2 Italian entrees and 2 Chinese entrees among the lunch choices, and 3 Italian entrees and 3 Chinese entrees among the dinner choices, from how many different daily menus can Shaun choose?
A.24
B.36
C.72
D.90
Answer: C.72
Explanation: Let the Breakfast set be {F , Y}
Lunch be {I ,I , C,C , L1,L2}
Dinner be {I,I,I , C,C,C, D1,D2,D3}
There are only 2 restrictions, Italian Lunch has to go with Italian Dinner and Chinese Lunch cannot go with Chinese dinner.
So the set of Breakfast, Lunch and Dinner will
{Any BF, Italian Lunch, Italian Dinner } = 2 * 2 * 2
{Any BF, Chinese Lunch, Not Chinese Dinner} = 2 * 2 * 6
{Any BF, Not Italian or Chinese Lunch, Any Dinner} = 2 * 2 * 9
Adding all these gives 72.
Answer is C
Question: What is the smallest no. which must be added to 532869 so as to obtain a sum which is divisible by 9?
A.9
B.2
C.1
D.3
Answer: D.3
Explanation: For 532869 , 5+3+2+8+6+9=33
3 must be added to 532869 to make it divisible by 9.
Now ,5+3+2+8+7+2=27=> 27 is a multiple of 9 and hence 532869 is also divisible by 9
D
Question: In a division sum, the remainder is 8 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is:
A.200
B.251
C.250
D.262
Answer: B.251
Explanation: Diver = (8*3)+3 = 27
3* Quotient = 27
Quotient = 9
Dividend = (Divisor * Quotient) + Remainder
Dividend = (27 * 9) + 8 = 251
B
Question: Six bells commence tolling together and toll at intervals of 2,4,6,8,10 and 12 seconds respectively. in 30 m9nutes,how many times do they toll together ?
A.4
B.10
C.15
D.16
Answer: D.16
Explanation: Solution
L.C.M. of 2,4,6,8,10,12 is 120.
So, the bells will toll together after every 120 seconds, i.e., 2 minutes
In 30 minutes, they will toll together left [ ( 30/2 )+ 1 ] = 16 times. Answer D
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
A.33772
B.26782
C.26788
D.13500
Answer: D.13500
Explanation: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer: D
Question: What annual payment will discharge a debt of Rs. 1125 due in 2 years at the rate of 5% compound interest?
A.993.2
B.551.25
C.534.33
D.605.03
Answer: D.605.03
Explanation: Explanation:
Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1125
820x + 1125 * 441
x = 605.03
So, value of each installment = Rs. 605.03
Answer: Option D
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?
A.Rs.12
B.Rs.16
C.Rs.14
D.Rs.10
Answer: C.Rs.14
Explanation: Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]
= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400
= Rs. [(1/6)8(1/100)*8400] = Rs. 14.
Answer is C.
Question: If 0.5% of A =80 paise, then the value of A is ?
A.Rs. 170
B.Rs. 160
C.Rs. 1.70
D.Rs. 4.25
Answer: B.Rs. 160
Explanation: Answer
∵ 0.5/100 of A = 80/100
∴ A = Rs. (80 / 0.5) = Rs. 160
Correct Option: B
Question: In the Biotechnology class of 2000, there were X graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is X equal to?
A.69.
B.71
C.73
D.75
Answer: C.73
Explanation: Graduates got job = 32
Graduates continued to second degree = 45
Graduates got job and continued to second degree = 13
Graduates didn't get job and didn't continue to second degree = 9
Job	No Job	Total
Second Degree 13	32	45
No Second Degree	19	9	28
Total	32	41	X
Therefore X = 73
Answer C
Question: The original price of a car was $30,000. Because the car owner thought he could get more money for the car, he set a new price by increasing the original price of the car by 5%. After a week, the car had not sold, so the owner discounted the new price by 5%, and the car was finally sold. What price was the car sold for?
A.$29,915
B.$29,925
C.$29,935
D.$29,945
Answer: B.$29,925
Explanation: The car was sold for (0.95)(1.05)($30,000)=$29,925.
The answer is B.
Question: Points M(7,2) and N(5,14) lie on the xy - plane. What is the midpoint of line segment MN?
A.(5,0)
B.(6,8)
C.(0, (136^(1/2))/2)
D.(3/2,0)
Answer: B.(6,8)
Explanation: The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states:
• The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints.
• Likewise, the y-coordinate is the average of the y-coordinates of the endpoints.
So, x=(7+5)/2=6 and y=(2+14)/2=8 --> coordinates of the midpoint are (6, 8).
Answer: B.
Question: Missing number in the series
4 9 20 43 90 185 376?
A.175
B.185
C.759
D.195
Answer: C.759
Explanation: 4*2+1=9
9*2+2=20
20*2+3=43
43*2+4=90
90*2+5=185
185*2+6=376
376*2+7=759
ANSWER:C
Question: The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 1024 feet squared, what is the difference between the length and the width of the roof?
A.38.
B.40.
C.42.
D.48.
Answer: D.48.
Explanation: Let the width= x
x*4x=1024
x^2= 256
x= 16
Length= 4*16=64
difference= 64-16= 48
D is the answer
Question: At present the age of the father is 3 times that of the age of the son. Three years hence the father's age would be 2 times that of his son. Find the present age of the father?
A.18years
B.12years
C.20years
D.16years
Answer: A.18years
Explanation: Age of the son = (3-1)*3 / (3-2) = 6 years
Age of the father = 6*3 = 18 years
Answer is A
Question: Pat and Cara begin running at the same time and they start at the same place on a straight path. Pat runs at 9 miles per hour, and Cara runs at 5 miles per hour. After 10 minutes, Pat stops to stretch. If it takes Pat 20 minutes to stretch and Cara continues to run during this time, how many minutes will it take Pat to catch up to Cara?
A.12
B.15
C.18
D.21
Answer: B.15
Explanation: In 10 minutes, Pat runs 1.5 miles.
In 30 minutes, Cara runs 2.5 miles.
Pat can catch Cara at a rate of 4 miles per hour.
Since Cara is ahead by 1 mile, it will take Pat 1 / 4 = 0.25 hours = 15 minutes to catch Cara.
the answer is B.
Question: Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age?
A.12 years
B.13 years
C.15 years
D.14 years
Answer: D.14 years
Explanation: Let MTomy's present age be 'x' years.
x+ 16 = 3(x- 4)
=> 2x = 28 => x = 14 years.
D
Question: Suppose son name is 120,his brother name is 150 and his mother name is 190.find out his father's name???
A.220
B.210
C.230
D.240
Answer: A.220
Explanation: since difference between all name is =30
so father's name will be 190+30=220.
ANSWER:A
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
A.19 kmph
B.24 kmph
C.17 kmph
D.12 kmph
Answer: B.24 kmph
Explanation: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.
Answer:B
Question: Tommy has a lot of Lego blocks, but only green and red blocks. There are four times as many green blocks as there are red blocks. If Tommy has Y Lego blocks, how many red blocks are there, in terms of Y.
A.3*Y
B.Y/3
C.Y/5
D.Y/4
Answer: C.Y/5
Explanation: Since Y equals the number of blocks, then Y = Green + Red
Since there are four times green blocks as red blocks, then Green = 4*Red
Thus Y = 4*Red + Red, which simplifies to Y=5*Red
Therefore the Red = Y/5
Answer: C
Question: Milk contains 5% water.What quantity of pure milk should be added to 10 litres of milk to reduce this to 2% ?
A.5 litres
B.7 litres
C.15 litres
D.Cannot be determined
Answer: C.15 litres
Explanation: Here required quantity of pure milk = 10×(5−2)/2
= 10×3/2 = 15 litres.
Answer C
Question: How many three letter words are formed using the letters of the word BREAK?
A.A)240
B.B)360
C.C)720
D.D)120
Answer: D.D)120
Explanation: The number of letters in the given word is five.
The number of three letter words that can be formed using these four letters is 5P4
= 5 * 4 * 3*2 = 120.
Answer:D
Question: According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 26, by how much does the temperature in degrees Celsius (C) increase?
A.9
B.14.44
C.47
D.48 3/5
Answer: B.14.44
Explanation: You can plug in values.
C = 5/9*(F-32)
F=32 --> C=0;
F=32+26=58 --> C=5/9*26=14.44.
Increase = 14.44 degrees.
Answer: B.
Question: The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an
integer, how many possible values are there for r?
A. 4
B. 2
C. 2
D. 10
Answer: A. 4
Explanation: r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8.
Answer A
Question: When 100 is divided by positive integer x, the remainder is 3. What is the remainder when 197 is divided by x?
A.2
B.3
C.4
D.6
Answer: B.3
Explanation: if100/x leaves a reminder 3 then (100-3) i.e. 97 is divisible by x
So (100+97)/x leaves a reminder rem(100/x)+rem(97/x)=> 3+0=3
Answer :B
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?
A.50
B.60
C.80
D.100
Answer: A.50
Explanation: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50
1.2x(1/2) + 0.8x(1/2) = 50
=> x =50
Thus proved...option A.
Question: What two-digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5?
A. 95
B. 99
C. 26
D. 73
Answer: B. 99
Explanation: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -13
Thus 2xy +5 = x^2 + y^2 - 13
x^2 + y^2 -2xy = 16
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 99
Thus the answer is B
Question: The length of the room is 4m and width is 5m. Find the cost of paving the floor by slabs at the rate of Rs.200 per sq meter?
A.1000
B.2000
C.4000
D.3000
Answer: C.4000
Explanation: l=4m w=5m
area of the floor = 4 x 5 = 20 sq m
cost of paving = 200 x 20= Rs. 4000
Answer: C
Question: Nina has exactly enough money to purchase 5 widgets. If the cost of each widget were reduced by $1.25, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?
A.$16.7
B.$24
C.$30
D.$36
Answer: A.$16.7
Explanation: A its is.
Let price = X
(x-1.25)8 = 5X
X= 10/3
hence total money = 5*10/3= 16.7
Question: At the beginning of the year, the ratio of boys to girls in high school X was 3 to 4. During the year, 10 boys and twice as many girls transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of boys to girls was 4 to 5, how many boys were there in high school X at the beginning of the year?
A.70
B.120
C.100
D.90
Answer: B.120
Explanation: let the total number of boys and girls at the beginning of the year be 3x and 4x respectively.
now 10 boys and 20 girls are transferred to another school. thus no. of boys and girls students left in the school X are 3x-10 and 4x-20 respectively. the ratio of these boys and girls students = 4/5
thus we have (3x-10)/(4x-20) = 4/5
15x-50= 16x-80
x=30
thus total no. of boys at the beginning of the year =4(30)= 120
Answer is option B
Question: If |m+n|=|m-n|, then m*n must be equal to:
A.-3
B.0
C.-2
D.-4
Answer: B.0
Explanation: Solution 1: Distance perspective
|m-n| = |m+n| ==> The distance of m and n is equal to the distance of m and -n.
<=======(-n)=======0=======(n)======>
Only 0 is the value that has a distance equal to n and -n.
Solution 2:
|m-n| = |m+n| (square both)
m^2 -2mn + n^2 = m^2 + 2mn + n^2
4mn = 0
mn = 0
Answer: B
Question: City A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
A.56
B.57.5
C.58.9
D.61.4
Answer: B.57.5
Explanation: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold?
A.1,008
B.1,296
C.1,512
D.2,016
Answer: D.2,016
Explanation: We want A, B, and C to be before F, G and H.
Let's deal with this constraint first: consider A, B, and C as one unit {ABC} and F, G and H also as one unit {FGH}. According to the condition we need them to be arranged as {ABC}{FGH}. A, B, and C, within their unit can be arranged in 3! ways, similarly F, G and H , within their unit can also be arranged in 3! ways.
So, we have a line with 6 people XXXXXX. D can take any place in the line so D has 7 options: *X*X*X*X*X*X*.
Now, we have a line with 7 people and E can take any place there, so E has 8 options: *X*X*X*X*X*X*X*.
Total = 3!*3!*7*8 = 2,016.
Answer: D.
Question: In eight years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is seven years older than Ellen, how old is Aaron?
A.1–5
B.1.5–5
C.11–15
D.16–20
Answer: B.1.5–5
Explanation: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'
In ten years, David will be four times as old as Aaron --> d+8 = 4(a+8)
Twenty years ago, David was twice as old as Ellen --> d-16 = 2(e-16)
David is seven years older than Ellen --> d = e + 7
e+7-16 = 2e-32
e-9= 2e-32
e = 23
d = 30
38 = 4a + 32
a = 1.5
Answer: B
Question: If x+y=2z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?
A. 2z+1
B. 3z
C. 5z
D. z
Answer: D. z
Explanation: Pick any number like X=12, Y=10 and Z= 11 so that X+Y=2Z, now then the arithmetic mean will be (12+10+11)/3=11. Now, just look at the answers and put the value of Z there.
(A) 2.11+1=23, no.
(B) 3.11=33,no
(C) 5.11=55, no
(D) 11, it can be the answer, lets check us the other options
(E) (3.2)/2=3, no
so the answer will be D..
Question: If the radius of a cylinder is made 3 times and height is doubled, what is the new volume of the cylinder divided by the old one?
A.18.
B.2.
C.6.
D.4.
Answer: A.18.
Explanation: let v and v' be the original and the changed volume
now
v=pir^2h
v'=pi(3r)^2(2h)
v'=18v
A) 18
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 200 girls, the total number of students in the college is
A.420
B.520
C.620
D.720
Answer: B.520
Explanation: Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 200
=> x = 40
Total students = 8x+5x = 13x = 13(40) = 520
Option B
Question: In an election, candidate Smith won 52% of the total vote in Counties A and S. He won 61% of the vote in County A. If the ratio of people who voted in County A to County S is 3:1, what percent of the vote did candidate Smith win in County S ?
A.A.25%
B.B.27%
C.C.34%
D.D.43%
Answer: A.A.25%
Explanation: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County S
hence answer is A.
Question: The marks obtained by Polly and Sandy are in the ratio 3:5 and those obtained by Sandy and Willy are in the ratio of 3:2. The marks obtained by Polly and Willy are in the ratio of...?
A.3:4
B.5:6
C.7:8
D.9:10
Answer: D.9:10
Explanation: Polly : Sandy = 3:5 = 9:15
Sandy : Willy = 3:2 = 15:10
Polly : Sandy : Willy = 9:15:10
Polly : Willy = 9:10
The answer is D.
Question: A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint W, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
A.2
B.2 1/2
C.3
D.3 1/2
Answer: B.2 1/2
Explanation: Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable.
So correct ans is 2.5 gallons. B
Question: A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?
A.5/8
B.3/4
C.7/8
D.57/64
Answer: C.7/8
Explanation: It would be easier to calculate the probability of opposite event and subtract it from 1.
Opposite event: 0 tail, 1 tail, 6 tails.
Probability of getting no tails: 1/2^6=1/64
Probability of getting 1 tail: 6C1∗1/2^6=6/64, we must multiply by 6C1 or by 6 as tail can occur for any flip from 6, hence in 6 ways;
Probability of getting 6 tails: 1/2^6=1/6^4
P=1−(1/64+6/64+1/64)=56/64=7/8
Answer: C.
Question: Each shelf of a bookcase contains 24 books. If the librarian took out 34 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?
A.A)4
B.B)5
C.C)6
D.D)8
Answer: B.B)5
Explanation: Denoting x the number of the shelves,
we can build an equation: 24x=16(x−1)+22+34
Solving the equation, we get x=5
Answer: B