mathewhe/aqua_rat huggingface dataset:
Question: A 300 m long train crosses a platform in 36 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 286 m
(B) 350 m
(C) 277 m
(D) 278 m
(E) 300 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/36 = 50/3
x = 300 m.
Answer:E
Answer: (E) 300 m
Question: Albert borrowed a total of $ 6000 from Brian and Milton. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1494 as total interest. What is the interest paid to Brian at the end of three years?
(A) 491
(B) 481
(C) 471
(D) 441
(E) 445
Rationale: Let x be the amount borrowed form Brian. So amount borrowed form Milton = 6000-x.
1494 = 21/100x + 27/100(6000-x)
=>x = 2100.
Interest paid = 3*7/100*2100 = 441.
D
Answer: (D) 441
Question: Find the average of first 5000 natural numbers?
(A) 2500
(B) 2500.5
(C) 2145.5
(D) 2005.5
(E) 2560
Rationale: Sum of first 100 natural numbers = 5000*5001/2 = 12502500
Required average = 12502500/5000 = 2500.5
Answer is B
Answer: (B) 2500.5
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age five years back was?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 16 years
(E) 18 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
C
Answer: (C) 14 years
Question: In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) 125
(B) 627
(C) 153
(D) 721
(E) 159
Rationale: 44 + 28 + 10 = 82%
100 – 82 = 18%
850 * 18/100 = 153
Answer:C
Answer: (C) 153
Question: 8, 12, 18, 27, 40.5, (...)
(A) 60
(B) 60.75
(C) 58
(D) 89
(E) 88
Rationale: 8
(8×3)÷ 2 = 12
(12×3)÷ 2 = 18
(18×3)÷ 2 = 27
(27×3)÷ 2 = 40.5
(40.5×3)÷ 2 = 60.75
Answer is B
Answer: (B) 60.75
Question: If x≠4 and (x^2 - 16)/(2y) = (x - 4)/4, then in terms of y, x = ?
(A) (y - 8)/2
(B) (y - 3)/2
(C) y - 3
(D) y - 6
(E) (y + 6)/2
Rationale: Since (x^2 – 16)=(x-4)(x+4) the original equation can be changed into 4*(x-4)(x+4) = 2y *(x-4).
By cancelling 2(x-3) (we can do it because x≠4) we get :
2*(x+4)=y.
So x=(y-8)/2. So the answer is A).
Answer: (A) (y - 8)/2
Question: Rectangular tile each of size 50cm by 40cm must be laid horizontally on a rectangular floor of size 120cm by 150cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
(A) 9
(B) 15
(C) 12
(D) 11
(E) 10
Rationale: Area of tile = 50*40 = 2000
Area of floor = 120*150= 18000
No of tiles = 18000/2000 =9
So, the no of tile = 9
ANSWER:A
Answer: (A) 9
Question: Total of the ages of A, B and C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2: 3. What is the age of B at present
(A) 20
(B) 25
(C) 15
(D) 27
(E) 30
Rationale: 10 yrs ago is x,2x and 3x
10+2x+10+3x+10=90 hence x =10
B's present age = 2x+10 = 30 yrs
ANSWER E
Answer: (E) 30
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 2989
(B) 2765
(C) 5550
(D) 2989
(E) 9772
Rationale: Total production of salt by the company in that year
= 5000 + 5100 + 5200 + .... + 6100 = 66600.
Average monthly production of salt for that year
= 66600/12
= 5550.
Answer:C
Answer: (C) 5550
Question: In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage Q of those asked favoured more than one of the 3 proposals.
(A)  10
(B)  12
(C)  17
(D)  22
(E)  30
Rationale: Bunuel, my answer for exactly 2 people was 17 and this was my approach:
100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to
Q=100%=(50+30+20)-(at least 2 people)-5%+22%.C
Answer: (C)  17
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) Rs. 5725
(B) Rs. 5275
(C) Rs. 6275
(D) Rs. 6725
(E) None of these
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
ANSWER:D
Answer: (D) Rs. 6725
Question: A river 2m deep and 45 m wide is flowing at the rate of 6 kmph the amount of water that runs into the sea per minute is?
(A) 4500 M3
(B) 4580 M3
(C) 9000 M3
(D) 4900 M3
(E) 4700 M3
Rationale: Explanation:
(6000 * 2 * 45)/60 = 9000 M3
Answer: Option C
Answer: (C) 9000 M3
Question: The present ratio of students to teachers at a certain school is 45 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?
(A) 4
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: We are given that the ratio of students to teacher is 45 to 1. We can rewrite this using variable multipliers.
students : teachers = 45x : x
We are next given that student enrollment increases by 50 and the number of teachers increases by 5. With this change the new ratio becomes 25 to 1. We can put all this into an equation:
Students/Teachers  25/1 = (45x + 50)/(x + 5)
If we cross multiply we have:
25(x + 5) = 45x + 50
25x + 125 = 45x + 50
3.75 = x
x~4
Since x is the present number of teachers, currently there are 4 teachers.
Answer A.
Answer: (A) 4
Question: If log 27 = 1.431, then the value of log 9 is :
(A) 0.934
(B) 0.945
(C) 0.954
(D) 0.958
(E) None of these
Rationale: Solution
Log 27 = 1.431 ⇒ log (33) = 1.431 ⇒ 3 log 3 = 1.431
⇒ log 3 = 0.477
∴ log 9 = log (32) = 2 log 3 = (2 × 0.477) = 0.954. Answer C
Answer: (C) 0.954
Question: Ram purchased a TV and a DVD Player for Rs. 25000 and Rs. 5000 respectively. He sold the DVD Player at a loss of 4 percent and TV at a profit of 10 percent. Overall he make a.?
(A) 2200
(B) 2500
(C) 2800
(D) 2300
(E) 2000
Rationale: Let the SP of the TV and the DVD Player be Rs. r and Rs. m respectively.
r = 25000(1 + 10/100) = 25000 + 2500
m = 5000(1 - 4/100) = 5000 - 200
Total SP - Total CP = r + m - (25000 + 5000) = 2500 - 200 = Rs. 2300
As this is positive, an overall profit of Rs. 2300 was made.
Answer: D
Answer: (D) 2300
Question: A = 10% of x, B = 10% of y, C = 10% of x + 10% of y. On the basis of the above equalities, what is true in the following?
(A) A is equal to B
(B) A is greater than B
(C) B is greater than A
(D) Relation cannot be established between A and B
(E) None of these
Rationale: The given information gives no indication regarding the comparison of x and y.
Answer D
Answer: (D) Relation cannot be established between A and B
Question: A class consists of 6 boys and 4 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?
(A) 9
(B) 18
(C) 32
(D) 60
(E) 42
Rationale: Easiest way is to treat it like an arrangements question in the following manner:
From the boys we need to select 2 to be clown and pet: This can be done in 6*5 ways
Similarly for the girls, we have 4*3 ways.
Thus total = 30+12 = 42 ways. Thus E is the correct answer.
Answer: (E) 42
Question: If after 100 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
(A) 180 grams
(B) 200 grams
(C) 250 grams
(D) 350 grams
(E) 400 grams
Rationale: The 24% alcohol solution decreases by 1/3 once the 100 grams of water is added so 100/.08 =1250*.16% (2/3 of 24%) is 200 grams, thus answer is B.
Answer: (B) 200 grams
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
(A) 127.6
(B) 127.5
(C) 127.9
(D) 127.8
(E) 127.4
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000
= 127.5 m.
Answer: B
Answer: (B) 127.5
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 80 ways
(B) 87 ways
(C) 30 ways
(D) 28 ways
(E) 82 ways
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Answer: (C) 30 ways
Question: X completes a work in 12 days and Y 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) 10 days
(C) 12 days
(D) 20 days
(E) 40 days
Rationale: If X can complete a work in x days and Y 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.
B)
Answer: (B) 10 days
Question: How many possible integer values are there for x if |7x - 3| < 6 ?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Rationale: Solution: |7x-3| < 6
let 7x=a therefore we have |a-3| < 6 ==> read this as origin is at +3 and we have to move +6 to the right and -6 to the left
(the less than sign represents that the a must be within boundaries )
(3-6)----------3----------(3+6)
now, we have -3<a<9
but a =7x ==> -3<7x<9
dividing all values by +4 we have -0.46 <x < 1,2
Now question says Integer values (not rational ) therefore we have 0,1
Hence 2 B
Answer: (B) Two
Question: A alone can complete a work in 16 days and B alone can do in 12 days. StarƟng with A, they work on
alternate days. The total work will be completed in
(A) 1314
(B) 1312
(C) 1334
(D) 1344
(E) None of these
Rationale: ExplanaƟon:
A's 1 day work = 1/16
B's 1 day work = 1/12
As they are working on alternate day's
So their 2 days work = (1/16)+(1/12)
= 7/48
[here is a small technique, Total work done will be 1, right, then mulƟply numerator Ɵll denominator, as
7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]
Work done in 6 pairs = 6*(7/48) = 7/8
Remaining work = 1-7/8 = 1/8
On 13th day it will A turn,
then remaining work = (1/8)-(1/16) = 1/16
On 14th day it is B turn,
1/12 work done by B in 1 day
1/16 work will be done in (12*1/16) = 3/4 day
So total days =
1334
Answer: C
Answer: (C) 1334
Question: A Jar of marble contains 6 yellow and 4 blue marbles, and no other marbles. If four are pulled out of the jar, one after the other, without being replaced, what is the probability that exactly two of the four marbles will be yellow and two blue.
A
B
C
D 9
(A) 1/10
(B) 1/7
(C) 1/6
(D) 3/7
(E) 9/11
Rationale: 4 marbles out of the given 10 are pulled out of the jar, one after the other, without being replaced
The number of possible combinations (total events) = 10C4
We need to find the probability that exactly two of the four marbles will be yellow(out of 6) and two blue( out of 4).
Here the order in which the marbles are removed isn't asked. So no permutation reqd.
The number of possible combinations to such a specific event = 6C2 X 4C2
The Probability of the specific event = [ 6C2 X 4C2 ] / 10C4
= 15 X 6 / 210
= 3/7
Correct Option : D
Answer: (D) 3/7
Question: You collect baseball cards. Suppose you start out with 15. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Rationale: Solution
Start with 15 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 15 + 1 which is 8,
so you're left with 15 - 8 = 7.
Peter takes 1 baseball card from you: 7 - 1 = 6 baseball cards.
Paul triples the number of baseball cards you have: 6 × 3 = 18 baseball cards.
So you have 18 at the end.
Correct answer : B
Answer: (B) 18
Question: A tank contains 10,000 gallons of a solution that is 3 percent sodium chloride by volume. If 4,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A)  1.25%
(B)  5%
(C)  6.25%
(D)  6.67%
(E)  11.7%
Rationale: The remaining solution will be approximately what percent sodium chloride?means:what percent of the remaining solution is sodium chloride. Now, since the remaining solution is 10,000-4,000=6,000 gallons and sodium chloride is 300 gallons (3% of initial solution of 10,000 gallons) then sodium chloride is 300/6,000*100=5% of the remaining solution of 6,000 gallons.
Answer: B.
Answer: (B)  5%
Question: In certain year in Country C, x sets of twins and y sets of triplets were born. If there were z total babies born in Country C in this year, and x and y were both greater than 0, which of the following represents the fraction T of all babies born who were NOT part of a set of twins or triplets?
(A) z - 2x - 3y
(B) (2x+3y)/z
(C) (x+y)/z
(D) 1 - (2x+3y)/z
(E) 1 - (x+y)/z
Rationale: X set of twins implies 2x babies of twin category.
Y set of triplets means 3y babies of triplet category.
Let K be the babies other than twin or triplet category.
Total babies = z = 2x+3y+k.
or K=Z-(2x+3y)
=> Fraction of babies other than twin or triplet categories = K/Z = Z-(2x+3y)/Z.
T= 1- (2x+3y)/Z. Hence answer is D.
Answer: (D) 1 - (2x+3y)/z
Question: Each writer for the local newspaper is paid as follows: a dollars for each of the first s stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits s+ a stories in a month earn than a writer who submits s+ b stories?
(A) (a – b)( a + b + s)
(B) a – b
(C) a^2 – b^2
(D) s( a – b)
(E) as + bs – as
Rationale: total earned for s+a stories =a + a(a+b)
total earned for s+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
=(a+b)(a-b) =a^2-b^2
answer is C
Answer: (C) a^2 – b^2
Question: In a race of 600 metres, A can beat B by 60 metres and in a race of 500 metres, B can beat C by 50 metres. By how many metres will A beat C in a race of 400 metres?
(A) 76 metres
(B) 80 metres
(C) 70 metres
(D) 84 metres
(E) None
Rationale: A runs	B runs	C runs
600 metres race	600m	540 m
500 metres race	500 m	450m
Combing ratio A runs B runs C runs
300metres - 2700meters - 2430metres
Unitary A runs B runs C runs
Method 400mtres - 360 metres - 324 metres
? A beats C by 400-324 = 76 metres.
Answer: A.
Answer: (A) 76 metres
Question: What is the rate percent when the simple interest on Rs.720 amount to Rs.180 in 4 Years?
(A) 6.25
(B) 7.25
(C) 8.25
(D) 9.25
(E) 10.25
Rationale: 180 = (720*4*R)/100
R = 6.25%
Answer: A
Answer: (A) 6.25
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 22 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
(A) 42
(B) 48
(C) 64
(D) 76
(E) 88
Rationale: 200 are sophomores.
The number of freshmen is 600 - 160 - 0.22(800) = 264
The answer is C.
Answer: (C) 64
Question: Given: b2 = ac and ax=by=cz.
Determine the value of y.
(A) 2xz/(x+z)
(B) 8xz/(x+z)
(C) 3xz/(x+z)
(D) 7xz/(x+z)
(E) 5xz/(x+z)
Rationale: Explanation:
No explanation is available for this question!
ANSWER: A
Answer: (A) 2xz/(x+z)
Question: A teacher of 6 students takes 2 of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once. How many times does the teacher go to the zoo?
(A) 12
(B) 51
(C) 13
(D) 15
(E) 17
Rationale: Two students can be selected from 6 in 6C2 =15 ways.
Therefore, the teacher goes to the zoo 15 times.
Ans: D
Answer: (D) 15
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.10000?
(A) 3310
(B) 1879
(C) 2779
(D) 2672
(E) 2782
Rationale: A = 10000(11/10)^3
= 13310
= 10000
----------
3310
Answer: A
Answer: (A) 3310
Question: If the average of 6x and 8y is greater than 100, and x is twice y, what is the least integer value of x ?
(A) 22
(B) 20
(C) 21
(D) 23
(E) 24
Rationale: Substitution can be used in the following way:
Always start with the equation: x = 2y. It is more straight forward to manage as compared to the inequality.
Substitute y = x/2, not the other way because you need to find the minimum value of x. So you can get rid of y.
Now go on to the inequality. So 8y = 8x/2 = 4x
Now average of 6x and 4x is greater than 100. Average of 6x and 4x is 5x. So,
5x > 100
x > 20
Answer : B
Answer: (B) 20
Question: What is the greatest value of positive integer x such that 2^x is a factor of 100^40?
(A) 80
(B) 90
(C) 95
(D) 105
(E) 110
Rationale: Put in simple words, we need to find the highest power of 2 in 100^40
100 = 2^2*5^2
Therefore 100^40 = (2^2*5^2)^40 = 2^80*5^80
Answer : A
Answer: (A) 80
Question: The area of an equilateral triangle is subtracted from its base, and the perimeter is then added to this total, the result is 4. What is the height of the equilateral triangle if its base is 2?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: An eqilateral triangle means all sides are equal; therefore, base = side. The equation is; base - Area + Perimeter = b - A + P = b -1/2bh + 3b, and b = 2. So, 2 - 2/2h + 6 = 4, and 8 - h = 4.
By plugging in the answers we can test the answers quickly; then, 4 is the only possible answer.
Answer: C
Answer: (C) 4
Question: At noon, ship A is 100km west of ship B. Ship A is sailing east at 35 km/hr and ship B is sailing north at 25km/hr. How fast is the distance between the ships changing at 4.00pm.
(A) 35.21 km/hr.
(B) 36.21 km/hr.
(C) 37.21 km/hr.
(D) 39.21 km/hr.
(E) 32.21 km/hr.
Rationale: Let the position of ship B at noon be at the origin
=>ship A has x-coordinate = -100km and B has x-coordinate =0km
At 4.00 p.m., ship A is at x = -100+4*35=40km
and B is at x = 0 and y = 4 * 25 = 100 km
Distance between them at 4.00 p.m. = √[(100)^2 + (40)^2] = 20√(29) km
Distance between the ships,
s^2 = x^2 + y^2
=> 2s ds/dt = 2x dx/dt + 2y dy/dt
=> rate of change of distance between the ships, ds/dt
= (x dx/dt + y dy/dt) / s
= [40 * 35 + 100 * 25] / [20√(29)] km/hr
= (1400 + 2500) / [20√(29)] km/hr
= 195/√(29) km/hr
≈ 36.21 km/hr.
ANSWER:B
Answer: (B) 36.21 km/hr.
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 3 different boat to go and 4 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 40
(C) 18
(D) 12
(E) 16
Rationale: Ans.(D)
Sol. Number of choices to go by ship = 3 Number of choices to return by airline = 4 From, fundamental principle, total number of ways of performing the journey = 3 x 4 = 12 ways
Answer: (D) 12
Question: At 6′o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12′o clock
(A) 47
(B) 76
(C) 28
(D) 66
(E) 11
Rationale: Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 30/5 = 6 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 6 = 66 secs.
Answer: D
Answer: (D) 66
Question: What should be the least number to be added to the 2496 number to make it divisible by 5?
(A) 12
(B) 17
(C) 18
(D) 4
(E) 26
Rationale: Answer : 4
Option : D
Answer: (D) 4
Question: In a simultaneous throw of pair of dice .find the probability of getting the total more than 7
(A) 7/9
(B) 5/7
(C) 11/7
(D) 8/9
(E) 5/12
Rationale: Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12
Ans: E
Answer: (E) 5/12
Question: The interest on a certain deposit at 4.5% p.a. is Rs. 202.50 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a ?
(A) Rs. 20.25
(B) Rs. 22.50
(C) Rs. 25
(D) Rs. 42.75
(E) None
Rationale: Solution
S.I=Rs.202.50, R=4.5%, T= 1 Year
principal = Rs (100*202.50 / 4.5*1)= Rs.4500
Now P =Rs.4500, R =5%, T= 1 year
S.I=(4500*5*1/100)= Rs.225
Different in interest = Rs. ( 225- 202.50)= Rs.22.50
Answer B
Answer: (B) Rs. 22.50
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $396 per week. How much does she earn in dollars per hour?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $396 per week
36x =396
x =11
Correct Option : A
Answer: (A) 11
Question: A girl has exactly 6 quarters, 7 dimes, and 10 nickels in her pocket. If she withdraws a number of these coins at random, how many coins would she have to withdraw to ensure that she has at least a 50 percent chance of withdrawing at least one quarter?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: When the probability of NOT drawing a quarter is 50% or less, then the probability of drawing a quarter is at least 50%.
P(not drawing a quarter with 2 coins) = 17/23 * 16/22 = 136/253 > 50%
P(not drawing a quarter with 3 coins) = 136/253 * 15/21 = 680/1771 < 50%
The answer is C.
Answer: (C) 3
Question: What comes next in the series?
16 72 38 94 50 __
(A) 11
(B) 25
(C) 17
(D) 19
(E) sixteen 16
Rationale: E
16
Each number reverses the previous number and adds 1 to each digit. Thus, in the first two terms, 16 reversed is 61, which then changes to 72. In the penultimate term, 50 reversed becomes 05, which in turn becomes 16 - by adding 1 to each digit.
Answer: (E) sixteen 16
Question: A customer purchased a package of ground beef at a cost of $1.96 per pound. For the same amount of money, the customer could have purchased a piece of steak that weighed 30 percent less than the package of ground beef. What was the cost per pound of the steak?
(A) $4.65
(B) $4.10
(C) $3.60
(D) $3.20
(E) $2.80
Rationale: For simplicity, let's assume the customer bought 1 pound of ground beef for $1.96.
Let x be the price per pound for the steak.
Then 0.7x = 196
x = 196/0.7 = $2.80
The answer is E.
Answer: (E) $2.80
Question: A division of a company consists of three men and seven women. If two of these ten employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
(A) 11/45
(B) 7/45
(C) 11/30
(D) 7/30
(E) 7/15
Rationale: The total number of ways to choose two representatives is 10C2=45.
The number of ways to choose two females is 7C2=21.
P(choosing two female representatives)=21/45=7/15
The answer is E.
Answer: (E) 7/15
Question: A room 11 m 47 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
(A) 636
(B) 640
(C) 647
(D) 651
(E) 675
Rationale: Explanation:
Area of the room = (1147 x 777) cm2.
Size of largest square tile = H.C.F. of 1147 cm and 777 cm = 37 cm.
Area of 1 tile = (37 x 37) cm2.
Number of tiles required =(1147×777)/(37×37)=651
Answer: Option D
Answer: (D) 651
Question: The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
(A) 50 m^3
(B) 60 m^3
(C) 70 m^3
(D) 80 m^3
(E) 100 m^3
Rationale: Explanation:
lb = 20 ; lh = 15 ; fh = 12
(lbh)2 = 20 * 15 * 12 => lbh = 60 m^3
B)
Answer: (B) 60 m^3
Question: If 192 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is :
(A) 16
(B) 14
(C) 20
(D) 18
(E) 32
Rationale: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24
:. The smallest part = (192 *4/24) = 32
ANSWER:E
Answer: (E) 32