mathewhe/aqua_rat huggingface dataset:
Question: A man can row 6 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
(A) 2 km/hr
(B) 12.5 km/hr
(C) 1 2.6 km/hr
(D) 22.5 km/hr
(E) 22.6 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=6
3x = 12
x = 4
i.e., speed upstream = 4 km/hr
Rate of stream = 1/2(2x−x)=x/2=4/2=2 km/hr
Answer is A
Answer: (A) 2 km/hr
Question: 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 50% of the total school population of x students, what is x?
(A) 134
(B) 150
(C) 225
(D) 250
(E) 500
Rationale: 90=x/100*50/100*x=>x^2 = 9*10000/5 = > x = 134
A
Answer: (A) 134
Question: A train 100 m long crosses a platform 125 m long in 1 sec; find the speed of the train?
(A) 810
(B) 700
(C) 930
(D) 100
(E) 200
Rationale: D = 100 + 125 = 225
T = 15
S = 225/1 * 18/5 = 810 kmph
Answer: A
Answer: (A) 810
Question: If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss.
(A) $70
(B) $40
(C) $50
(D) $30
(E) $80
Rationale: C
$50
Cost of 20 lollipops = $90
Sold each lollipop for $2
So he sold 20 lollipops for $(20 × 2) = $40
Loss = $(90 – 40) = $50
Therefore, loss = $ 50.
Answer: (C) $50
Question: Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Solution:
Four
three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.
Answer D
Answer: (D) 4
Question: If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+5 ?
(A) -1
(B) -2
(C) -3
(D) 6
(E) -5
Rationale: let we put values. a=1, b=3, c=5
5-3-1=1
1+5 =6
Answer :D
Answer: (D) 6
Question: Kim bought a total of $1.82 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 3-cent stamps, what is the least number of 1-cent stamps she could have bought?
(A) 25
(B) 32
(C) 45
(D) 60
(E) 75
Rationale: Let:
# of 5 and 25 cents stamps = n
# of 10 cent stamps = 2n
# of 1 cent stamps = m
Therefore:
5n + 25n + 10(2n) + m = 182 cents
50n + m = 182
Forleastnumber of 1 cents stamps, maximize 50n. Hence,
50*3 + m = 182
m = 32 i.e. 32 stamps 1 cents each
Answer: B
Answer: (B) 32
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
(A) 2288
(B) 2778
(C) 3000
(D) 212
(E) 28812
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000.Answer: D
Answer: (D) 212
Question: A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes
to cover a distance of 5 km upstream. Find the speed of the current.
(A) 1 km/hr
(B) 2 km/hr
(C) 3 km/hr
(D) 4 km/hr
(E) None of these
Rationale: Explanation:
First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(15334)km/hr=15×415=4km/hrSpeed Downstream = (5212)km/hr=5×25=2km/hrSo
speed of current = 12(4−2)=1km/hr
Answer: A
Answer: (A) 1 km/hr
Question: If 45% of z is 96% of y and y is 75% of x, what percent of x is z?
(A) 200
(B) 160
(C) 100
(D) 65
(E) 50
Rationale: (45/100)z = (96/100)y
and y = (75/100)x i.e. y = (3/4)x
i.e. (45/100)z = (96/100)*(3/4)x
i.e. z = (96*3)x/(45*4)
i.e. z = (1.6)x = (160/100)x
i.e. z is 160% of x
Answer: Option B
Answer: (B) 160
Question: Pipes A and B can fill a tank in 3 and 5 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?
(A) 60/17 hr
(B) 12/19 hr
(C) 20/9 hr
(D) 9/20 hr
(E) 63/19 hr
Rationale: Net part filled in 1 hour = 1/3 + 1/5 - 1/12 = 9/20
The tank will be full in 20/9 hr
Answer is C
Answer: (C) 20/9 hr
Question: The value of (10^8-10^2)/(10^6-10^3) is closest to which of the following?
(A) 1
(B) 10
(C) 10^2
(D) 10^3
(E) 10^4
Rationale: Because the question asks for what value isclosestthe question invites approximation.
Let's look at the numerator:
10^8 - 10^2
10^8 is HUGE compared to 10^2.
So 10^8 - 10^2 is very close to 10^8 itself. (Just as 100 - 0.0001 is very close to 100 itself).
Likewise, 10^6 is HUGE compared to 10^3.
So 10^6- 10^3 is very close to 10^6.
So we have:
10^8/10^6
or 10^(8-6) = 10^2.
Choose C.
Answer: (C) 10^2
Question: A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
(A) 7500
(B) 7528
(C) 2789
(D) 2668
(E) 2088
Rationale: P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8 = Rs.7500
Answer: A
Answer: (A) 7500
Question: What is the average of three tenths and five thousandths
(A) 0.2022
(B) 0.3325
(C) 0.1525
(D) 0.2012
(E) 0.2114
Rationale: Explanation:
three tenths = 0.3
Five thousandths = 0.005
The average is (0.3 + 0.005)/2 = 0.1525
Answer: C
Answer: (C) 0.1525
Question: A , B , and C started a partnership business by investing $45,000 , $63,000 , and $72,000 respectively. At the end of the year, the profit was distributed among them. If C's share of profit is $24,000, what is the total profit?
(A) $48,000
(B) $52,000
(C) $56,000
(D) $60,000
(E) $64,000
Rationale: A:B:C = 45000:63000:72000 which is a ratio of 5:7:8.
Let the total profit be x.
x * 8/20 = 24000
x = 24000*20/8 = 60,000.
The answer is D.
Answer: (D) $60,000
Question: Which of the following is not divisible by 8?
(A) 10032
(B) 21192
(C) 47816
(D) 91232
(E) 72034
Rationale: Divisibility rule of 8: Last three digits of the number should be divisible by 8
Option A: 10032, last three digits = 032. Divisible by 8
Option B: 21192, last three digits = 192. Divisible by 8
Option C: 47816, last three digits = 816. Divisible by 8
Option D: 91232, last three digits = 232. Divisible by 8
Option E: 72034, last three digits = 034. Not divisible by 8. Hence 72034 is not divisible by 8
Answer: (E) 72034
Question: At garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 25th lowest price among the prices of the items sold, how many items were sold at the garage sale?
(A) 33
(B) 34
(C) 35
(D) 39
(E) 37
Rationale: 14+24+1= 39
Answer: D
Answer: (D) 39
Question: A 4 digit number 8a43 is added to another 4 digit number 3121 to give a 5 digit number 11b64, which is divisible by 11, then (a+b)=?
(A) 3
(B) 4
(C) 7
(D) 5
(E) 9
Rationale: Solution: a+1=b
=> b-a=1.
and 11b64 is divisible by 11
=> (4+b+1)-(6+1)=0
=> b-2=0
=> b=2.
so, a=1
=>(a+b)= 3.
Answer A
Answer: (A) 3
Question: A man sitting in a train which is travelling at 80 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?
(A) 52 kmph.
(B) 62 kmph.
(C) 72 kmph.
(D) 80 kmph.
(E) 32 kmph.
Rationale: Solution
Relative Speed	= (280 / 9)m/sec
= (280/9 x 18/5)
= 112 kmph.
Speed of the train	= (112 - 80)kmph
= 32 kmph.
Answer E
Answer: (E) 32 kmph.
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 12.8 kmph
(B) 23.9 kmph
(C) 21.9 kmph
(D) 12.5 kmph
(E) 13.8 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b)
= 7
Solving the equation, the speed of man in still water is
12.5 kmph.
Answer: D
Answer: (D) 12.5 kmph
Question: A women has 3 purse and 4 paper. In how many ways can he put the paper in her purse?
(A) 78
(B) 80
(C) 81
(D) 82
(E) 85
Rationale: First paper can be put in 3 ways, similarly second, third and forth paper also can be put in 3 ways.
So total number of ways = 3 x 3 x 3 x 3 = 34 = 81
C
Answer: (C) 81
Question: 19 persons went to a hotel for a combined dinner party. 13 of them spent Rs 79 each for the dinner and the rest spent Rs 4 more than the average expenditure of all the 19. What was the total money spent by them?
(A) Rs1628.40
(B) Rs1536
(C) Rs1492
(D) Rs1498
(E) none of these
Rationale: (13*79)+(6(x+4)) = 19x
1027 + 6x + 24 = 19x
1051 = 13x
x = 1051/13
total money = 19x = 1536
ANSWER:B
Answer: (B) Rs1536
Question: If 10 gallons of grape juice are added to 50 gallons of a mixture, which contains 10 percent grape juice then what percent of the resulting mixture is grape juice?
(A) 14%
(B) 25%
(C) 28%
(D) 34%
(E) 50%
Rationale: OFFICIAL SOLUTION:
If we start with 40 gallons of a mixture that is 10% grape juice, then we have:
50 × 0.10 = 5 gallons of grape juice.
50 × 0.90 = 45 gallons of other components.
If we add 10 gallons of grape juice, we will end up with 15 gallons of grape juice and 45 gallons of other components, and we will have a total of 60 gallons of the mixture.
So 15/60 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 25/100= 25%.
The correct answer is choice (B)
Answer: (B) 25%
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 10 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 40
(B) 44
(C) 48
(D) 55
(E) None of these
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 10)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 10 = 4/9(T - 10)
10T = 990 - 440 => T = 55.
ANSWER:D
Answer: (D) 55
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 1:3. The sum of numbers is:
(A) 28
(B) 30
(C) 40
(D) 50
(E) 64
Rationale: Let the numbers be 1x and 3x.
Then, their L.C.M = 3x. So, 3x = 48 or x = 16.
The numbers are 16 and 48.
Hence, required sum = (16 + 48) = 64.
ANSWER:E
Answer: (E) 64
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 25 years. What is the age of the new member ?
(A) 20 years
(B) 21 years
(C) 40 years
(D) 23 years
(E) 24 years
Rationale: The average age of a group of 5 members is 20 years --> the sum of the ages is 5*20=100;
Two years laterthe sum of the ages of these 5 members would be 100+5*2=110;
Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 25 years then: 25*6=110+x --> x=40.
Answer: C.
Answer: (C) 40 years
Question: A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x?
(A) 5
(B) 4
(C) 3
(D) 7
(E) 6
Rationale: 3+11+7+9+15+13+8+19+17+21+14+x/12=12
137+x/12=12
137+x=144
x=144-137=7
Option D
Answer: (D) 7
Question: Every year an amount increases by 1/9th of itself. How much will it be after two years if its present value is Rs.64000?
(A) 81000
(B) 81007
(C) 81008
(D) 79012.3
(E) 81022
Rationale: 64000* 10/9 * 10/9 = 79012.3
Answer:D
Answer: (D) 79012.3
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 12,000?
(A) 50,000
(B) 750,000
(C) 850,000
(D) 7,500,000
(E) 2,400,000,000
Rationale: number of cars sold = x=800000-50y
y=12000
x=800000-600000=200000
revenue from 50000 cars=12000*200000=2400000000
Answer E
Answer: (E) 2,400,000,000
Question: certain office 1/3 of the workers are women ½ of the women are married and 1/3 of the married women have children if ¾ of the men are married and 2/3 of the married men have children what part of workers are without children?
(A) 11/8 of all workers
(B) 1/18 of all workers
(C) 11/18 of all workers
(D) 13/18 of all workers
(E) 4/18 of all workers
Rationale: Let the total no of workers be x
No of women =x/3
No of men =x-(x/3)=2x/3
No of women having children =1/3 of ½ ofx/3=x/18
No of men having children=2/3 of ¾ of2x/3=x/3
No of workers having children = x/8 +x/3=7x/18
Workers having no children=x-7x/18=11x/18=11/18 of all workers
Option C is answer
Answer: (C) 11/18 of all workers
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 12 minutes and the second alone would have done it in 8 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
(A) 4 4/5min
(B) 3 2/5min
(C) 3 3/5min
(D) 3 4/5min
(E) 3 min
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(1/12+1/8)=(5/24)
So both punctures will make the type flat in
(24/5)mins=4 4/5mins
Option A
Answer: (A) 4 4/5min
Question: (0.96)(power 3) - (0.1)(power 3)/ (0.96)(power 2) + 0.096 + (0.1)(power 2) is:
(A) 0.86
(B) 0.68
(C) 0.96
(D) 0.69
(E) 0.76
Rationale: Given expression
= (0.96) (power 3) - (0.1)(power 3) / (0.96)(power 2) + (0.96 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.96 - 0.1)
= 0.86
Answer is A.
Answer: (A) 0.86
Question: What is the value of the following expression?
(1/ (2^2 – 1)) + (1/ (4^2 – 1)) + (1/ (6^2 – 1)) + .... + (1/ (18^2 – 1))
(A) a. 9/19
(B) b. 10/19
(C) c. 10/21
(D) d. 11/21
(E) e. 11/19
Rationale: it can be written into
1/3+1/15+ 1/35.....1/323
i.e
1/3+1/2*(1/3-1/5)+1/2*(1/5-1/7).... til last term - 1/2*(1/19)
all terms from 1/5 .. to second last term get cancelled
left with
1/3+1/6-1/42=1/2-1/38=18/38=9/19
A
Answer: (A) a. 9/19
Question: Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 30 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
(A) 20
(B) 34
(C) 30
(D) 40
(E) 46
Rationale: Nice question +1
We have that X/24 - (60-X)/2R = 30
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 30
Hence answer is C
Answer: (C) 30
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 10 years?
(A) 6%
(B) 2%
(C) 4%
(D) 5%
(E) 3%
Rationale: 150 = (750*10*R)/100
R = 2%
Answer: B
Answer: (B) 2%
Question: A and B go around a circular track of length 900m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
(A) 120 sec
(B) 165 sec
(C) 186 sec
(D) 180 sec
(E) 168 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 900/ (36 * 5/18) , 900/ (54 * 5 /18) }
= LCM (90, 60)
=180 sec.
Answer:D
Answer: (D) 180 sec
Question: If 7^n is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of n?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: So the question just means that we have to find all the multiples of 7 between 1 to 100
there are 14 multiples of 7 ( 7 - 98)
But 49 and 98 contain two 7's as factors
so we have to add 14 + 2 = 16
ANSWER:E
Answer: (E) 16
Question: There are 200 female managers in a certain company. Find the total number T of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
(A) 300
(B) T=400
(C) T=500
(D) 600
(E) None of these
Rationale: {Managers} = {Female Managers} + {Male Managers};
We are told that the total number of managers in the company is 2/5 of all the employees , thus {Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively.
Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200;
Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500.
Answer: C.
Answer: (C) T=500
Question: The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
(A) 2/9
(B) 3/2
(C) 3/8
(D) 3/4
(E) 3/1
Rationale: Let the earnings of P and Q be 9x and 10x respectively.
New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]
=> 9*(1 + 1/4)/10*(1 - 1/4)
=> 9/10 * (5/4)/(3/4) = 3/2
Answer:B
Answer: (B) 3/2
Question: If (3/2)x - 3 = 15
what is the value of x ?
(A) -12
(B) 12
(C) -1/12
(D) 1/12
(E) 3
Rationale: (3/2)x - 3 = 15
=> 3x-6=30
=>3x = 36
=> x=12
Answer: B
Answer: (B) 12
Question: A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 2 specified cars. In how many ways cars can be arranged?
(A) 1210
(B) 650
(C) 1500
(D) 1640
(E) 1440
Rationale: we arranged 2 specified cars in 2 slots = 2!
remaining 6 cars in 6 slots = 6!
number of ways = 2!*6! = 1440
correct option is E
Answer: (E) 1440
Question: Robex traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different.
(A) z=3x
(B) x=3z
(C) y=2x
(D) x=2y
(E) y=3x
Rationale: Robex Travelled for x,y and for z min.
Total Time : x + y + z
Which is equal to : 3y
Equating both sides we get
x+y+z = 3y
=> x+z =2y ........ Eqn 1
Looking out at options
D Says x =2y
Using it in Eqn 1
2y + z = 2y
=> Z = 0 mins, Which I guess is not possible.
The Ans isD
Answer: (D) x=2y
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) 275
(B) 270
(C) 279
(D) 263
(E) 271
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
Answer is B.
Answer: (B) 270
Question: If 20% of a = b, then b% of 20 is the same as:
(A) 4% of a
(B) 5% of a
(C) 20% of a
(D) 30% of a
(E) None of these
Rationale: Explanation:
20% of a = b =	(20/100)a=b.
b% of 20 =(b/100 x 20)=((20/100)a x 1/100 x 20)=(4/100)a=4% of a.
ANSWER IS A
Answer: (A) 4% of a
Question: Calculate how long it will take a swimmer to swim a distance of 12km against the current of a river which flows at 1.2 km/hr, given that he can swim in still water at 5km/h
(A) 3.26
(B) 3.16
(C) 2.34
(D) 3.98
(E) 3.17
Rationale: swim in still water at = 5
speed of river= 1.2
US = 5 - 1.2= 3.8
Distance = 12
T = 12/3.8 = 3.16
Answer: B
Answer: (B) 3.16
Question: A train running at 1/6 of its own speed reached a place in 24 hours. How much time could be saved if the train would have run at its own speed?
(A) 8hrs
(B) 20hrs
(C) 12hrs
(D) 15hrs
(E) 6hrs
Rationale: time taken if run its own speed = 1/6*24 = 4 hrs
Time saved = 24 - 4 = 20 hrs
Answer : B
Answer: (B) 20hrs
Question: An article is bought for Rs.675 and sold for Rs.1000, find the gain percent?
(A) 34%
(B) 44%
(C) 48%
(D) 32%
(E) 46%
Rationale: 675 ---- 325
100 ---- ? =>
=48%
Answer:C
Answer: (C) 48%
Question: The salaries of A and B together amount to $6000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary?
(A) $1000
(B) $1250
(C) $2500
(D) $4500
(E) $5200
Rationale: Let A's salary is x
B's salary = 6000-x
(100-95)% of x = (100-85)% of (6000-x)
x = $4500
Answer is D
Answer: (D) $4500
Question: There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially?
(A) Rs.2008
(B) Rs.2022
(C) Rs.2000
(D) Rs.2029
(E) Rs.2021
Rationale: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 2288
for 114.4 ---> 100 ; 2288 ---> ?
Required price = (2288 * 100)/114.4 = 20 * 100 = Rs.2000.
Answer:C
Answer: (C) Rs.2000
Question: On a weekend, 7 college friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin?
(A) $175
(B) $210
(C) $147
(D) $560
(E) $412
Rationale: Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 7 for all answer choices.
175/7 = 25
210/7 = 30
147/7 = 21
560/7 = 80
412/7 = 58.86
E is not an integer amount.
Answer:E
Answer: (E) $412
Question: which one is odd?
4377
3954
9861
8454
9831
(A) 4377
(B) 3954
(C) 9861
(D) 8454
(E) None
Rationale: Correct Answer : C
sum of digit of all other number is 21, but sum of digit of 9861 is 24
Answer: (C) 9861
Question: The product of two natural numbers is 19. The sum of the reciprocal of its square is
(A) 361/362
(B) 362/361
(C) 360/359
(D) 359/360
(E) None of these
Rationale: Explanation:
Let the number be a and b. Then,
ab = 19 => a = 1, b = 19
So, 1/a2 + 1/b2 = (a2 + b2)/a2b2
= (12 + 192)/(1 x 19)2 = 362/361
Answer: Option B
Answer: (B) 362/361
Question: The crew of a rowing team of 8 members is to be chosen from 12 men (M1, M2, …., M12) and 8 women (W1, W2,…., W8), such that there are two rows, each row occupying one the two sides of the boat and that each side must have 4 members including at least one women. Further it is also known W1 and M7 must be selected for one of its sides while M2, M3 and M10 must be selected for other side. What is the number of ways in which rowing team can be arranged.
(A) 2
(B) 1
(C) 5
(D) 6
(E) 4
Rationale: We need two person for one side and 1 women for the another side. We select that women in 7 ways. Now that second side people can sit in 7x4! ways.
Now for the first side we need two people from the remaining 14. So this can be done in 14C214C2 ways and this side people can sit in 4C2×4!4C2×4! ways.
Again the first group may take any of the two sides. So total ways are 2×7×4!×14C2×4!
Answer:E
Answer: (E) 4
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 30 metres?
(A) 22 seconds
(B) 6 seconds
(C) 7 seconds
(D) 1 seconds
(E) 2 seconds
Rationale: Speed of the boat downstream
= 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 30/5 = 6 seconds.
Answer:B
Answer: (B) 6 seconds
Question: A six-character password consists of three letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 5,040
(B) 2,228,720
(C) 22,226,000
(D) 22,237,440
(E) 22,464,000
Rationale: 4 character password: DLDLLD
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
The letter can be chosen in 25 ways.
The letter can be chosen in 24 ways.
Next digit can be chosen in 8 ways.
This gives us 10*26*9*25*24*8 ways
Now, the letter can also be DDLLLD so there will be another 10*9*26*25*24*8 ways
Total = 10*26*9*25*24*8*2 = 22,464,000 ways
E
Answer: (E) 22,464,000