mathewhe/aqua_rat huggingface dataset:
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.72000 after completion of one year. What will be Jose's share of profit?
(A) 20000
(B) 10000
(C) 25000
(D) 34000
(E) 40000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 72000 = 40000
E
Answer: (E) 40000
Question: 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:
(A) 7 and 4
(B) 7 and 5
(C) 8 and 5
(D) 6 and 4
(E) 5 and 8
Rationale: Let the given number be 476 xy 0.
Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.
And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.
x - y - 3 = 0 y = x - 3
(17 + x + y) = (17 + x + x - 3) = (2x + 14)
x= 2 or x = 8.
x = 8 and y = 5.
ANSWER C
Answer: (C) 8 and 5
Question: A man is 30 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
(A) 23 years
(B) 28 years
(C) 21 years
(D) 20 years
(E) 19 years
Rationale: Let present age of the son =x years
Then, present age the man =(x+30) years
Given that, in 2 years, man's age will be twice the age of his son
â‡’(x+30)+2=2(x+2)
â‡’x=28
ANSWER:B
Answer: (B) 28 years
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
(A) 1200
(B) 2899
(C) 1200
(D) 2781
(E) 2782
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP
= 1200
Answer:C
Answer: (C) 1200
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 9232
(C) 8828
(D) 2387
(E) 2813
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer: A
Answer: (A) 3630
Question: A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 12 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
(A) $54.00
(B) $64.80
(C) $90.00
(D) $100.80
(E) $134.40
Rationale: Correct Answer: E
The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.12 ($1120) = $134.40. The correct answer is E.
Answer: (E) $134.40
Question: At a certain supplier, a machine of type A costs $25,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $0
(B) $11,200
(C) $12,000
(D) $12,800
(E) $13,200
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 66000 = 0
Hence, A.
Answer: (A) $0
Question: In a box, there are 3 grey, 5 brown and 2 yellow pencils. One pen is picked up randomly. What is the probability that it is neither brown nor yellow?
(A) 2/5
(B) 3/5
(C) 3/10
(D) 3/4
(E) 3/11
Rationale: Explanation :
Neither brown nor yellow means the pencils drawn is grey.
Total number of outcomes = (3+5+2) = 10.
Number of Favourable outcomes = 3 = Number of grey pencils.
Hence, Probability of the event = 3/10 = 3/10.
Answer : C
Answer: (C) 3/10
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 840 in 4 years. The rate of interest per annum is?
(A) 6%
(B) 2%
(C) 5%
(D) 9%
(E) 1%
Rationale: S.I. on Rs. 800 for 1 year
= (840 - 800) = Rs. 40 Rate
= (100 * 40)/(800 * 1)
= 5%
Answer:C
Answer: (C) 5%
Question: Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
(A) 450
(B) 754
(C) 456
(D) 123
(E) 729
Rationale: The first ring can be worn in any of the 3 fingers (3 ways).
Similarly each of the remaining 5 rings also can be worn in 3 ways.
Hence total number of ways
=3×3×3×3×3×3=36=729
Ans: E
Answer: (E) 729
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 8 years older than B the present age of B is
(A) 37
(B) 38
(C) 39
(D) 40
(E) 41
Rationale: let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+8
=>2b-b-8 = 30
b=38
so the present age of b is 38 years
ANSWER:B
Answer: (B) 38
Question: If y^2 - x^2 = 2xy, then (x+y)^2 =
(A) x^2
(B) 3x^2
(C) 4xy
(D) 2y^2
(E) -y^2
Rationale: Its B
y^2 -x^2 = 2xy
y^2 = 2xy + x^2
Add y^2 on both sides we get
y^2 +y^2 = x^2+2xy+y^2
2y^2 = (x+y)^2
Correct Option : D
Answer: (D) 2y^2
Question: If 1 persons can do 1 times of a particular work in 1 day, then, 7 persons can do 7 times of that work in
?
(A) 3 days
(B) 1 day
(C) 9 days
(D) 11 days
(E) 15 days
Rationale: That is, 1 person can do one time of the work in 1 day.
Therefore, 7 persons can do 7 times work in the same 1 day itself.
Option 'B'
Answer: (B) 1 day
Question: The speed of a train is 94 kmph. What is the distance covered by it in 12 minutes?
(A) 15 kmph
(B) 11 kmph
(C) 88 kmph
(D) 19 kmph
(E) 12 kmph
Rationale: 94 * 12/60
= 18.8 kmph
Answer:D
Answer: (D) 19 kmph
Question: 5, 9, 17, 29, 45, ?
(A) 65
(B) 56
(C) 74
(D) 57
(E) 32
Rationale: The pattern is + 4, + 8, + 12, + 16, ....
Answer : A.
Answer: (A) 65
Question: What is the two-digit number? I. The difference between the two-digit number and the number formed by interchanging the digits is 27. II. The difference between the two digits is 3. III. The digit at unit's place is less than that at ten's place by 3.
(A) I and II
(B) II and III only
(C) all
(D) Even with all I, II and III, answer cannot be give.
(E) I and either II or III
Rationale: Let the tens and units digit be x and y respectively.
I. (10x + y) - (10y + x) x - y = 3.
II. x - y = 3.
III. x - y = 3.
Thus, even all the given three statements together do not give the answer.
Correct answer is (D).
Answer: (D) Even with all I, II and III, answer cannot be give.
Question: During a two-week period, the price of an ounce of silver increased by 10 percent by the end of the first week and then decreased by 10 percent of this new price by the end of the second week. If the price of silver was x dollars per ounce at the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period?
(A) 0.97x
(B) 0.98x
(C) 0.99x
(D) x
(E) 1.01x
Rationale: The price at the end is 0.9(1.1x)=0.99x
The answer is C.
Answer: (C) 0.99x
Question: In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a one or five on either die, that player wins. What is the probability that a player wins after playing the game once?
(A) 1/3
(B) 4/9
(C) 3/4
(D) 2/3
(E) 5/9
Rationale: We're looking for the number of outcomes that include AT LEAST a 1 or a 5.
#getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6
#getting a one in 2nd die {(2,1), (3,1), ...(6,1) } = 4 [exclude 1,1 and 5,1] since it will be counted twice
#getting a five in 1st die {(5,1), (5,2), ...(5,6) }= 6
#getting a five in 1st die {(2,5), (3,5), ...(6,5) } = 4 [exclude 1,5 and 5,5] since it will be counted twice
Total possibilities = 20
Probability of rolling at least a 1 or a 5 on two dice: 20/36 = 5/9
E
Answer: (E) 5/9
Question: By selling an article at Rs.600, a profit of 60% is made. Find its cost price?
(A) 228
(B) 267
(C) 375
(D) 480
(E) 811
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+60)]
= 600 * [100/160] = Rs.375
Answer: C
Answer: (C) 375
Question: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose?
(A) (10 + 10/143 )min
(B) (10 + 10/843 )min
(C) (10 + 19/143 )min
(D) (90 + 10/143 )min
(E) (10 + 10/193 )min
Rationale: In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour hand.
55 minutes are gained in 60 min.
60 min. are gained in [(60/55) * 60] min = min.
But they are together after 65 min.
Therefore, gain in 65 minutes = = min.
Gain in 24 hours = = 1440/143 min.
Therefore, the clock gains (10 + 10/143 )minutes in 24 hours.
Answer: A) (10 + 10/143 )min
Answer: (A) (10 + 10/143 )min
Question: If d is the mean of x, y, and z, what is the mean of x + 5, y + 5, z + 5 ?
(A) d
(B) 3d
(C) 15d
(D) d + 5
(E) d + 15
Rationale: If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case mean will increase by 5 as we are adding 5 to each term in a set --> Mean =d + 5.
Answer: D.
Answer: (D) d + 5
Question: The remainder of the division of a number by 63 is 27. What will be the remainder when that number is divided by 8?
Please explain
(A) 4
(B) 5
(C) 6
(D) 2
(E) 8
Rationale: The easiest way to solve this question is by plugging in a number. Here are the steps I followed:
1) Choose a number X that when divided by 63 gives you 27 as a remainder. So I did x = 63 + 27 = 90. (90/63 = 1R27)
2) Divide that number by 8. 90/8 = 11R2
Since the remainder is 2, the correct answer is choice D.
Answer: (D) 2
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.29
(B) 2.88
(C) 2.2
(D) 2.12
(E) 2.25
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: (B) 2.88
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two visitors will buy a pack of candy?
(A) 0.343
(B) 0.147
(C) 0.189
(D) 0.063
(E) 0.027
Rationale: 0.3*0.3*0.7 is equivalent to saying the the first person picks candy and second person picks candy and third person doesn't pick candy.
however this is a different case compared to
0.3*0.7*0.3 is equivalent to saying the the first person picks candy and second person doesn't pick candy and third person picks candy.
which in turn is a different case compared to
0.7*0.3*0.3 (I'll skip the verbose comments)
Hence the answer is 3*(0.3*0.3*0.7)=0.189
ANSWER C
Answer: (C) 0.189
Question: Which of the following is closest to the difference between sum R of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
(A) 2.82
(B) 2.72
(C) 1.82
(D) 1.72
(E) 0.82
Rationale: Sum R of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:
1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.
Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5
Product of all proper fractions in the form y/(y+1), where y is a positive digit:
1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.
Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7
Closest is 1.72
Answer (D).
Answer: (D) 1.72
Question: If a - b = 4 and a2 + b2 = 18, find the value of ab.
(A) 9
(B) 1
(C) 2
(D) 18
(E) 19
Rationale: 2ab = (a2 + b2) - (a - b)2
= 18 - 16 = 2
ab = 1.
Answer: B
Answer: (B) 1
Question: Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 60 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?
(A) 1 hour
(B) 1 hour 10 minutes
(C) 2 hours 30 minutes
(D) 2 hours
(E) 2 hours 10 minutes
Rationale: Both cars leave at the same time
Both cars travel at constant speed
Stealing a useful piece of information from Paragkan:
If two objects A and B start from opposite points and, after having met en route, reach their respective destinations in a and b mins (or any other measure of time) respectively, then the ratio of their speeds
ratio of speed: (a/b) = sq. rt(b/a)
sq. rt(b/a)
sq. rt(90/60)
sq. rt(3/2)
So, for every three units of distance A travels, B travels two. Because we know the ratio of speed and the time it took B to travel the distance A hasn't yet covered, we can find the time it took A to cover the distance B did in 90 minutes.
90*(2/3)where represents the lesser amount of time it took A to travel the distance B did in 90 minutes.
= 60 minutes.
Therefore, A took 60 minutes to travel the first portion then 60 minutes to travel the distance B did in 90 minutes. A spent (60+60)=120 minutes on the road.
D. 2 hours
Answer: (D) 2 hours
Question: The marked price of an article is 10% higher than the cost price. A discount of 10% is given on the marked price. In this kind of sale, the seller:
(A) bears no loss, no gain
(B) gains 1%
(C) loses 1%
(D) None of these
(E) Can't be determine
Rationale: Let C.P.=Rs. 100. Then, marked price=Rs. 110.
S.P=90% of Rs. 110=Rs. 99. So, loss=1%
ANSWER:C
Answer: (C) loses 1%
Question: The sale price sarees listed for Rs.400 after successive discount is 30% and 20% is?
(A) 297
(B) 879
(C) 342
(D) 762
(E) 224
Rationale: 400*(70/100)*(80/100)
= 224
Answer: E
Answer: (E) 224
Question: A shopkeeper sold an book offering a discount of 5% and earned a profit of 30%. What would have been the percentage of profit earned if no discount was offered?
(A) 140
(B) 120
(C) 130
(D) 136.8
(E) 150
Rationale: Let C.P. be $100.
Then, S.P. = $130
Let marked price be $x. Then, 95/100 x = 130
x = 13000/95 = $136.8
Now, S.P. = $136.8, C.P. = $100
Profit % = 136.8%.
D
Answer: (D) 136.8
Question: How many digits 2^200 has?
(A) 31
(B) 61
(C) 50
(D) 99
(E) 101
Rationale: 2^10 = 1.024 * 10^3 => 2^100 = (1.024)^10 * 10^60
therefore 61 digits would be my best guess
B
Answer: (B) 61
Question: Enzo is flying to Austria on vacation. He wants to bring several pairs of shoes with him. He knows each shoe's individual weight (x = weight as an integer). Choose an equation, that Enzo can use later in another equation, to find how many pairs of shoes he can take on his trip. So, this equation must result in an even number. What equation is true?
(A) 2x + 1 = even
(B) (2x + 1)(2x + 1) = even
(C) (1/2)(4x + 2) = even
(D) (1/2)(4x + 2)(2x + 1) = even
(E) (2x)(2x + 1) = even
Rationale: Divisible by 2 (Parity Mathematics) states: an even number is an integer of the form n = 2k, where k is an integer; an odd number is an integer of the form n = 2k + 1.
A and C: 2x + 1 = odd
And from Multiplication Rule:
even x even = even
even x odd = even
odd x even = even
odd x odd = odd
So, B and D: odd x odd = odd, but
E: even x odd = even
Answer: E
Answer: (E) (2x)(2x + 1) = even
Question: Before January, the price of a dress was D and the price of a matching pair of shoes was H. In January, the price of the dress increased by 40% and the price of the shoes increased by 50%. In March, Roberta bought both items with a 30% discount. If D = 4H, which of the following represents the amount that Roberta paid?
(A) D + 40
(B) D + H – 1
(C) D + 2H
(D) 4.97H
(E) 1.21D
Rationale: before Discount price was: 1.4D+1.5H
After Discount: 1.4D +1.5H-.42D-.45H
substitute D=4H
final value: 4.97H
Ans Is D :
Answer: (D) 4.97H
Question: The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1430. The perimeter of the plot is?
(A) 126
(B) 156
(C) 190
(D) 321
(E) 220
Rationale: Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1430
X = 50
Required perimeter = 2(50+60) = 220
E
Answer: (E) 220
Question: Compare the rates of two trains, one travelling at 90 km/hr and other is at 50m/s?
(A) 2:1
(B) 1:2
(C) 1:3
(D) 3:1
(E) 2:3
Rationale: speed of the 1st train = 90km/hr
speed of the 2nd train = 50m/s = 50*18/5 = 180km/hr
ratio of the speeds of the train = 90:180 = 1:2
Answer is B
Answer: (B) 1:2
Question: The mean of set U does not exceed mean of any subset of set U. Which of the following must be true about set U?
I. Set U contains only one element
II. All elements in set U are equal
III. The median of set U equals the mean of set U
(A) of the three qualities is necessary
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: The only necessary condition seems to be II.
If all nos are equal.... them mean of any subset is the same.
I is obviously ruled out ( e.g. U = {1,1,1} )
But III, what about 3?
It is not necessary in itself, rather, is automatically implied by II.
All sets that satsify II satisfy III=D
Answer: (D) II and III only
Question: A car travels from P to Q at a constant speed. If its speed were increased by 20km/hr, it would have taken two hour lesser to cover the distance. It would have taken further 30 minutes lesser if the speed was further increased by 10 km/hr. The distance between the two cities
(A) 100 km
(B) 120 km
(C) 150 km
(D) 180 km
(E) None of these
Rationale: Explanation :
Let the distance between two cities = D,
D = x*t (x = usual speed and t is the actual time)
D = (X + 20)*(T -2) and D = (X +30)*(T – 2.5)
Solve the above equation, u will get T = 5 and X = 30, so distance = 30*5 = 150 km
Answer – C
Answer: (C) 150 km
Question: A restaurant spends one third of its monthly budget for rent and one third of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages?
(A) 23.5%
(B) 32.5%
(C) 22.2%
(D) 37.5%
(E) 75%
Rationale: Spend on rent = 1/3
Spend on food and beverage= 1/3 of remaining = 1/3*2/3= 2/9
so 2/9= 22.2%
C is the answer
Answer: (D) 37.5%
Question: The expression (5x+2)/(x+3) is equivalent to which of the following?
(A) (5-2)/3
(B) 5 – (2/3)
(C) 5 – (x)/(x+3)
(D) 5 – (13)/(x+3)
(E) 5 + (17)/(x+3)
Rationale: Easiest way is to pick any number and put in (5x+2)/(x+3). Then check the options with the same number.
I took x=1 and got D as the answer.
Answer: (D) 5 – (13)/(x+3)
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A. 30% B. 35%
(A) 47%
(B) 50%
(C) 40%
(D) 48%
(E) 20%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP
= Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100
= 40%
Answer: C
Answer: (C) 40%
Question: If the cost price is 98% of sp then what is the profit %
(A) 4.07%
(B) 4%
(C) 2.7%
(D) 2.04%
(E) 2.08%
Rationale: Sol. sp=Rs100 : then cp=Rs 98:profit =Rs 2.
Profit={(2/98)*100}%=2.04%
Answer is D.
Answer: (D) 2.04%
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
(A) Rs.8202
(B) Rs.83902
(C) Rs.14372
(D) Rs.14000
(E) Rs.42611
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer:D
Answer: (D) Rs.14000
Question: The average of 64 numbers is 48. If two numbers namely 35 and 45 are discarded, The average of
remaining numbers is?
(A) 35.5
(B) 37.5
(C) 39.5
(D) 34.5
(E) 47.9
Rationale: Total of 50 numbers =64 * 48 = 3072
Average of 62 numbers = 3072-(45+55) / 62
= 2972 / 62 = 47.9
Answer is E.
Answer: (E) 47.9
Question: A certain meter records voltage between 0 and 10 volts inclusive. If the average value of 3 recordings on the meter was 7 volts, what was the smallest possible recording in volts?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: if average of 3 is 7 so sum of 3 should be 21
3 recording can be from 0-10 inclusive
to find one smallest other two should be highest
so, lets assume three var are a,b,c
say a is smallest and give b and c greatest readings say 9 and 9
so a has to be 3
B
Answer: (B) 3
Question: A photo-mat shop charges $0.55 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $52.58 if each film contains 30 photos?
(A) 4 films and 12 photos
(B) 5 films and 6 photos
(C) 5 films and 14 photos
(D) 6 films and 4 photos
(E) 3 films and 28 photos
Rationale: 1st photo = 0.55
Subsequent = 0.55*0.6=0.33
Price of 1 full film=0.55+0.33*35=12.1
Price of 4 full film = 12.1*4=48.4
52.58-48.4=4.18
4.18=0.55+0.33x
x=11
52.58--->3 full films and 1+11=28 photos
Answer: E
Answer: (E) 3 films and 28 photos
Question: In what time will a train 150 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.50 sec
(B) 2.60 sec
(C) 3.75 sec
(D) 2.9 sec
(E) 9.50 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 150/40
= 3.75 sec.
Answer: C
Answer: (C) 3.75 sec
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 20% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 1131000
(B) 979923
(C) 980241
(D) 2356677
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 20/100)(1 - 35/100)(1 + 45/100)
= 1131000
A
Answer: (A) 1131000
Question: An unbiased coin is tossed 5 times. Find the chance that head will appear exactly 3 times.
(A) 18/32
(B) 10/16
(C) 5/16
(D) 5/32
(E) 6/34
Rationale: Explanation :
Reqd probability
= 5C3 x (1/2)3 x (1/2)2
= 5!/3!(5 - 3)! x (1/2)3 x (1/2)2
= 10 x 1/8 x 1/4 = 5/16
Answer : Option C
Answer: (C) 5/16
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
(A) 12 days
(B) 18 days
(C) 32 days
(D) 16 days
(E) 17 days
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer: C
Answer: (C) 32 days
Question: In a garden, 26 trees are planted at equal distances along a yard 800 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
(A) 10
(B) 8
(C) 32
(D) 14
(E) 16
Rationale: 26 trees have 25 gaps between them.
Length of each gap = 800/25 = 32
i.e., distance between two consecutive trees = 32
Answer is C.
Answer: (C) 32
Question: A grocery store bought some apples at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of apples in the two stacks if the store broke even after having sold all of its apples?
(A) 1:7
(B) 1:5
(C) 1:4
(D) 1:2
(E) 2:5
Rationale: To avoid fractions, assume there were 45 apples. So the store bought them for 45/5 = 9 dollars.
To break even, the selling price should be $9 too. 45 mangoes can be split into 1:4, 2:3 or 1:2. So let's try these.
45 split in the ratio 1:4 gives 9 and 36.
9 apples split into 3 apples each will give $3.
36 apples split into 6 apples each will give $6.
They add up to $9 so we have hit the right answer.
Answer (C)
Answer: (C) 1:4
Question: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 60 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
(A) 13
(B) 33
(C) 50
(D) 51
(E) 60
Rationale: Yes, ensure that you understand the relation thoroughly!
Cost per liter = K * Fraction of Spirit
60 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 30 cents. Fraction of spirit is 1/2.
30 = K * (1/2)
K = 60
Cost per liter = 60 * (1/3) (1 part spirit, 2 parts water)
Cost for 3 liters = 60 * (1/3) * 3 = 50 cents
E. 60 cents
Answer: (E) 60