mathewhe/aqua_rat huggingface dataset:
Question: The contents of a certain box consist of 24 apples and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be apples?
(A)  24
(B)  26
(C)  30
(D)  46
(E)  50
Rationale: apples = (apples + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B.
Answer: (B)  26
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
(A) 34
(B) 28
(C) 12
(D) 17
(E) 19
Rationale: Explanation:
Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
ANSWER IS B
Answer: (B) 28
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) Rs.3948
(B) Rs.3929
(C) Rs.3927
(D) Rs.3900
(E) Rs.3928
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Answer: (D) Rs.3900
Question: The average of 35 students in a class is 18 years. The average age of 25 students is 20. What is the average age of remaining 10 students?
(A) 17 years
(B) 16 years
(C) 15 years
(D) 14 years
(E) 13 years
Rationale: Sum of the ages of 14 students
= (18 * 35) - (20 * 25) = 630 - 500 = 130
Required average = (130/10) = 13 years.
Answer:E
Answer: (E) 13 years
Question: For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 7 of whom are females, by how much does the index for the females exceed the index for the males in the group?
(A)  0.05
(B)  0.0625
(C)  0.2
(D)  0.3
(E)  0.6
Rationale: Index for females = (20-7)/20 = 13/20 = 0.65
Index for males = (20-13/20 = 7/20 = 0.35
Index for females exceeds males by 0.65 - 0.35 = 0.3
Answer: D
Answer: (D)  0.3
Question: Find the number of square tiles to cover the floor of a room measuring 4.5 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 478
(B) 476
(C) 472
(D) 471
(E) 544
Rationale: 4 * 8 1/2 = 1/4 * 1/4 * x => x
= 544
Answer:E
Answer: (E) 544
Question: In an increasing sequence of 3 consecutive integers, the sum of the first 2 integers is 561. What is last integer in the sequence?
(A)  281
(B)  282
(C)  275
(D)  270
(E)  265
Rationale: Solution:
In solving this problem we must first remember that when we have 3 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
We are given that the sum of the first 2 integers is 560. This means that:
x + x+1 = 561
2x + 1 = 561
2x = 560
x = 280
the last integer can be expressed and simplified as:
x+2 = 280+2
= 282
Answer: B
Answer: (B)  282
Question: A person borrows Rs. 9000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
(A) 100 rs
(B) 150 rs
(C) 160 rs
(D) 180 rs
(E) 200 rs
Rationale: Gain in 2 years =
[(9000*6*2)/100]-[(9000*4*2)/100]
1080-720=360
Gain in 1 year =(360/2)=180 rs
ANSWER:D
Answer: (D) 180 rs
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 276. What is their H.C.F.?
(A) 18
(B) 23
(C) 28
(D) 32
(E) 36
Rationale: Let the numbers be 2x, 3x, and 4x.
LCM of 2x, 3x and 4x is 12x.
12x = 276
x = 23
HCF of 2x, 3x and 4x = x = 23
The answer is B.
Answer: (B) 23
Question: David decides to attend a base ball game with four friends. If the party of five sits together in five consecutive seats, and David must NOT sit in between two of his friends, how many ways can the five friends be arranged?
(A) 12
(B) 24
(C) 36
(D) 6
(E) 48
Rationale: David have to sit at either of the ends.
If David sits on the left most corner, then other 5 friends can be arranged in 4! = 24
David can also sit on the other end, then another 4! ways we can arrange.
So total number of ways = 24+24 = 48
Answer : E
Answer: (E) 48
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
(A) 1/6
(B) 1/7
(C) 1/8
(D) 1/11
(E) 1/13
Rationale: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
A
Answer: (A) 1/6
Question: If the number of 741,61n, where n represents the ones digit, is a multiple of 3, then the value of n could be which of the following?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.
i.e 7+4+1+6+1+n= multiple of 3
or, 19 + n = multiple of 3.
If n=5, 19 + n =24,which is a multiple of 3.
Hence answer is C.
Answer: (C) 5
Question: If a-b= 8 and a^2+b^2=164, find the value of ab
(A) 10
(B) 12
(C) 50
(D) 18
(E) 19
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 164 - 64 = 100
=> ab = 50
ANSWER: C
Answer: (C) 50
Question: In a office work is distribute between p persons. If 1/3 members are absent then work increased for each person is?
(A) 13.28%
(B) 14%
(C) 15%
(D) 16%
(E) 50%
Rationale: let total % of work is 100%
total person=p
1/3 person are absent of total person . so absent person is 1/3p ie p/3.
left person is, p-p/3=2p/3.
p person do the work 100%
1 person do the work 100*p%
2p/3 person do the work (100*p*3)/2p%=150%
work increased for each person is=(150-100)%=50%
ANSWER:E
Answer: (E) 50%
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 2/3
(C) 3/5
(D) 4/7
(E) 4/9
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: (A) 1/2
Question: A certain college party is attended by both male and female students. The ratio of male to female students is 4 to 5. If 12 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 64
(B) 72
(C) 80
(D) 88
(E) 96
Rationale: The ratio is 4:5 = 8:10, so there are 8k males and 10k females.
If 12 males left, the ratio would be 1:2 = 5:10, so there would be 5k males and 10k females.
8k-5k = 12
k = 4
8k + 10k = 32 + 40 = 72
The answer is B.
Answer: (B) 72
Question: Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
(A) 5 min
(B) 9 min
(C) 10 min
(D) 15 min
(E) 20 min
Rationale: Explanation:
Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9
ANSWER IS B
Answer: (B) 9 min
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 3 m, the volume of the box (in m3) is:
(A) 3780
(B) 5120
(C) 6420
(D) 8960
(E) 7960
Rationale: Clearly, l = (48 - 6)m = 42 m,
b = (36 -6)m = 30 m,
h = 8 m.
Volume of the box = (42 x 30 x 3) m3 = 3780 m3. Answer: Option A
Answer: (A) 3780
Question: A and B are integers. The expression (A+1)(B+1) is even. What can be said about A and B?
(A) They are both even numbers.
(B) At least one of them is even
(C) At least one of them is odd.
(D) They are both odd.
(E) Nothing can be said surly on A and B
Rationale: Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (A+1) or (B+1) needs to be Even
So either A or B needs to be odd
Or At Least one of them is odd.
ANSWER:C
Answer: (C) At least one of them is odd.
Question: Using only the digits from 0 to 6 , how many 5 digit codes can be constructed, if the first digit can not be 4 and no digits is used more than once ?
(A) 1800
(B) 2160
(C) 7776
(D) 720
(E) 820
Rationale: 5*6*5*4*3 = 1800
ANSWER:A
Answer: (A) 1800
Question: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 550-mile journey? Assume that the train makes no intermediate stops.
(A) 8
(B) 8.5
(C) 9
(D) 9.5
(E) 10
Rationale: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 550-mile journey? Assume that the train makes no intermediate stops.
I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)
Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
7 70 280
8 80 360
9 90 450
10 100 550
It takes a total of nine hours to cover the 550 mile distance.
ANSWER: E
Answer: (E) 10
Question: Group A has 1 boys and 2 girls, group B has 3 boys and 2 girls and group C has 2 boys and 5 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?
(A) 3/41
(B) 152/18
(C) 29/105
(D) 219/315
(E) 202/735
Rationale: Group A has 1 boy and 2 girls; 3
Group B has 3 boys and 2 girls; 5
Group C has 2 boys and 5 girls. 7
Selected group should have one girl and two boys.
Girl from A, boy from B, boy from C: 2/3*3/5*2/7 = 4/35;
Boy from A, girl from B, boy from C: 1/3*2/5*2/7 = 4/105;
Boy from A, boy from B, girl from C: 2/7*3/5*5/7 = 6/49.
Sum = 4/35 + 4/105 + 6/49 = 202/735.
Answer: E.
Answer: (E) 202/735
Question: How much is 50% of 40 is greater than 4/5 of 25?
(A) 0
(B) 67
(C) 88
(D) 12
(E) 66
Rationale: (50/100) * 40 – (4/5) * 25
= 0
Answer: A
Answer: (A) 0
Question: A person distributed 10% of his income to his 2 children each. He deposited 20% of his income to his wife's account. He donated 10% of remaining amount to an orphan house.Finally he has $500. Find his total income?
(A) $900
(B) $1000
(C) $1200
(D) $1150
(E) $1500
Rationale: 2 children got = 2*10% = 20%
wife got = 20%
orphan house = 10%
total = 20+20+10= 50%
remaining = 100-50 = 50%
50% = 500
100% = 500*100/50 = $1000
Answer is B
Answer: (B) $1000
Question: If a new town has 300 residents, and the population doubles every 10 years, what will be its population after 75 years?
(A) 6034 residents
(B) 9051 residents
(C) 54306 residents
(D) 15075 residents
(E) 18102 residents
Rationale: 300*2^(75/10)=300*2^7.5=100*181.02=54306
The answer is C.
Answer: (C) 54306 residents
Question: 3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 15/7 days
(B) 15/4 days
(C) 17/4 days
(D) 15/6 days
(E) 12/4 days
Rationale: 3M = 6W ---- 20 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 20 32 -----?
6 * 20 = 32 * x => x = 15/4 days Answer: B
Answer: (B) 15/4 days
Question: Find the area, diameter = 12m.
(A) 113.00 square meter
(B) 113.04 square meter
(C) 113.08 square meter
(D) 113.24 square meter
(E) 113.43 square meter
Rationale: Diameter = 12 meter.
Radius = diameter/2.
= 12/2.
= 6 meter.
Area of a circle = πr2.
Here, pi (π) = 3.14 meter, radius (r) = 6.
Area of a circle = 3.14 × 6 × 6..
= 3.14 × 36.
= 113.04 square meter or 113.04 m2. ANSWER : B
Answer: (B) 113.04 square meter
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1200 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 1200 more than that by the previous schema, his sales were worth?
(A) 12028
(B) 12000
(C) 12019
(D) 16000
(E) 12012
Rationale: [1200 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 16000
Answer: D
Answer: (D) 16000
Question: The speed of a boat in still water is 24 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 15 minutes is
(A) 1.6 km
(B) 2 km
(C) 3.6 km
(D) 6.75 km
(E) None of these
Rationale: Explanation:
Speed downstreams	=(24 + 3)kmph
= 27 kmph.
Distance travelled	= (27 x 15/60)km
= 6.75 km
Option D
Answer: (D) 6.75 km
Question: Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 48456, how much amount per month would he have spent on clothes and transport?
(A) 4038
(B) 8076
(C) 9691.2
(D) 4845.6
(E) None of these
Rationale: ∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month
∵ Amount, spent on clothes and transport
= 48456⁄12 = 4038
Answer A
Answer: (A) 4038
Question: A Japanese rock band made ¥3 million on their first album with sales of ¥12 million, and made ¥5 million on their second album with sales of ¥30 million. By approximately what percent did the ratio of profit to sales decrease from the first album to second album?
(A) 24%
(B) 27%
(C) 30%
(D) 33%
(E) 36%
Rationale: Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of profits to sales. The first ratio will be for the first album, and the second ratio will be for the next album. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First album
profit/sales = 3/12 = 1/4
Second album
profit/sales = 5/30 =1/6
We can simplify each ratio by multiplying each by the LCM of the two denominators, which is 12. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First album
profit/sales = (1/4) x 12 = 3
Next 2 Million
profit/sales = (1/6) x 12 = 2
We can plug 3 and 2 into our percent change formula:
(2 – 3)/3 x 100
=-1/3 x 100 so approximately a 33% decrease.
Answer D.
Answer: (D) 33%
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
(A) 15
(B) 19
(C) 14
(D) 18
(E) 16
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer:C
Answer: (C) 14
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 800 m long?
(A) 266 Sec
(B) 200 Sec
(C) 776 Sec
(D) 166 Sec
(E) 997 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 2000 m
T = D/S
T = 2000/10
T = 200 Sec
Answer: B
Answer: (B) 200 Sec
Question: If y exceeds x by 20%, then x is less than y by?
(A) 16%
(B) 16 1/3 %
(C) 16 2/3 %
(D) 16 3/5 %
(E) None of these
Rationale: Explanation:
X=100	y=120
120------20
100-------? => 16 2/3%
ANSWER IS C
Answer: (C) 16 2/3 %
Question: 3 candidates in an election and received 2500, 5000 and 15000 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 50%
(C) 57%
(D) 66.6%
(E) 65.6%
Rationale: Total number of votes polled = (2500 + 5000 + 15000) = 22500
So, Required percentage = 11628/20400 * 100 = 66.6%
D
Answer: (D) 66.6%
Question: Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 30 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?
(A) 1 hr 30 min
(B) 1 hr 45 min
(C) 2 hr
(D) 2 hr 20 min
(E) 3 hr
Rationale: Sol:
Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time
first equation=> P+M = 1/45
converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3
second equation => M+2M =>1/30
converting it to hrs 3M=1/(30/60) =>1/(1/2) =>2
therefore M= 2/3 and P=2/3
Rate of Perry = 2/3
time= work/rate (work = 1 job)
Time= 1.5 hrs
Answer A
Answer: (A) 1 hr 30 min
Question: Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 13 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?
(A) 37.5 kilometers per hour
(B) 47.6 kilometers per hour
(C) 50 kilometers per hour
(D) 75 kilometers per hour
(E) 100 kilometers per hour
Rationale: Time taken to reach first 40 km is 40/60 = 2/3 hr
Time taken to reach next 40 km is 40/60 = 2/3 hr
Time taken to reach next 20 km is 20/60 = 1/3 hr
Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...
Each stop was of 13min , so two 13min break = 2*13/60 => 13/30 hr
Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+13/30 ) =21/10 hrs
So, Average speed is 100/(21/10) = 47.6km/hour
Answer will be B
Answer: (B) 47.6 kilometers per hour
Question: The function g(p) is defined for integers p such that if p is even, g(p) = p/2 and if p is odd, g(p) = p + 5. Given that g(g(g(g(g(p))))) = 19, how many possible values for p would satisfy this equation?
(A) 1
(B) 5
(C) 7
(D) 8
(E) 11
Rationale: Let me define terms:
in g(p) = R
p is argument, R is result, g() is function,
in g(g(g(g(g(p))))), g1 is inner most, g5 is outermost for identification.
From definition of function g, we can deduce that:
If Result is even then two possibilities for argument = 1 Even 1 Odd
If Result is odd then one possibility for argument = 1 Even
Since final result = 19 = Odd
Possibilities:
g1:1 Even
g2: 1*(Even,Odd ) =1 Even 1 Odd
g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd
g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd
g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8
Ans D it is!
Answer: (D) 8
Question: Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much Q does she have in her account after two years?
(A) $10079.44
(B) Q=$10815.83
(C) $12652.61
(D) $14232.14
(E) $20598.11
Rationale: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%
Hence B the answer
Answer: (B) Q=$10815.83
Question: What is the least value of x. So that 30x55 is divisible by 3?
(A) 4
(B) 5
(C) 1
(D) 2
(E) 7
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
3 + 0+ x + 5 + 5 = 13+ x
Least value of x may be 2
Therefore 13+ 2 = 15 is divisible by 3.
D
Answer: (D) 2
Question: For positive x and y if x/y is n% of y, then what percent must x be of y?
(A) (y × n)%
(B) (n/y)%
(C) (√n)%
(D) (n^2)%
(E) (100 – n)%
Rationale: Solution -
The statement x/y is n% of y means that: x/y = (n / 100) × y
In order to find what percent must x be of y i.e., we need to divide x by y.
x/y %=(n / 100) × y *100 ---->(y*n)%
Therefore x/y is (y*n)%
ANSWER:A
Answer: (A) (y × n)%
Question: A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 800,000?
(A) 60
(B) 100
(C) 160
(D) 240
(E) 300
Rationale: The first digit and last digit are the same so the only possibility is 8.
The second and third digits can be any number from 0 to 9.
The total number of palindromic integers is 1*10*10 = 100
The answer is B.
Answer: (B) 100
Question: An amount of Rs.1560 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?
(A) Rs.390
(B) Rs.368
(C) Rs.380
(D) Rs.360
(E) Rs.311
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of C = 3/13 * 1560 = Rs. 360.
Answer: D
Answer: (D) Rs.360
Question: There are some passengers riding on a bus. At the first stop, half the passengers get off and nobody gets on the bus. This pattern continues as the bus goes to the next stops. If only one passenger gets off at stop number 4, how many passengers were on the bus originally?
(A) 128
(B) 64
(C) 32
(D) 16
(E) 8
Rationale: Before stop 4, there were 2 passengers on the bus.
Before stop 3, there were 4 passengers on the bus.
Before stop 2, there were 8 passengers on the bus.
Before stop 1, there were 16 passengers on the bus.
The answer is D.
Answer: (D) 16
Question: In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 20% of the total number of children in the camp. How many more boys must she bring to make that happen?
(A) 35.
(B) 45.
(C) 40.
(D) 30.
(E) 25.
Rationale: Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to or 20%..
If we add 35 to existing 45 then the count will be 80 and the girls number will be 20 as it.
Now boys are 80% and girls are 20%. ( out of 100 students = 80 boys + 20 girls ).
IMO option A is correct.
Answer: (A) 35.
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability taht the ticket drawn has a number which is a multiple of 3 or 5?
(A) 1/2
(B) 2/5
(C) 8/15
(D) 9/20
(E) None
Rationale: Solution
Here S=(1,2,3,4,5,...,19,20).
Let E=event of getting a multiple of 3 or 5
= (3,6,9,12,15,18,5,10,20)
P(E)= n(E) / n(S)
= 9/20.
Answer D
Answer: (D) 9/20
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.21000. A's share is?
(A) 2999
(B) 2778
(C) 7000
(D) 2889
(E) 6612
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 21000 = 7000
Answer:C
Answer: (C) 7000
Question: The total cost of 100 paper plates and 200 paper cups is $4.50 At the same rates what is the total cost of 20 of the plates and 40 of the cups?
(A) $.90
(B) $1.00
(C) $1.20
(D) $1.50
(E) $1.60
Rationale: U dont need to go through all this
What u have with u is
100 P + 200 C = $4.50
Just divide the equation by 5 and you will get what u are looking for
20P + 40 C = $0.90
Therefore OA is A
Answer: (A) $.90
Question: If two numbers are in the ratio 2:3. If 7 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) A)12
(B) B)14
(C) C)20
(D) D)24
(E) E)26
Rationale: 2:3
2x + 7 : 3x + 7 = 3 : 4
4[2x + 7] = 3[3x + 7]
8x + 28 = 9x + 21
9x - 8x = 28 - 21
x = 7
Then smallest number is = 2
2x = 14
Correct Option B
Answer: (B) B)14
Question: What decimal of an hour is a second ?
(A) 0.00027
(B) 0.00029
(C) 0.00031
(D) 0.00025
(E) 0.00023
Rationale: Required decimal = 1/60x60 = 1/3600 = .00027
Answer is A.
Answer: (A) 0.00027
Question: When the price of an article was reduced by 35% its sale increased by 80%. What was the net effect on the sale?
(A) 17% increase
(B) 44% decrease
(C) 60% increase
(D) 66% increase
(E) 66% decrease
Rationale: if n items are sold for $p each, revenue is $np. If we reduce the price by 35%, the new price is 0.65p. If we increase the number sold by 80%, the new number sold is 1.8n. So the new revenue is (0.65p)(1.8n) = 1.17np, which is 1.17 times the old revenue, so is 17% greater.
ANSWER:A
Answer: (A) 17% increase