mathewhe/aqua_rat huggingface dataset:
Question: Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 110 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from
(A) 30 to 70
(B) 70 to 100
(C) 110 to 130
(D) 130 to 150
(E) 150 to 170
Rationale: if there are 110 students majoring in electrical then there must be 90 person not majoring electrical at all, since both of the student not majoring electrical and mechanical is at least 30, so the number of the student who are not majoring electrical but majoring mechanical will be at least 60.
if there are 150 students majoring in mechanical there must be 50 students who are not majoring mechanical at all, since the number of the student who are not majoring electrical but majoring mechanical will be at least 60, hence the number of students both majoring mechanical and electrical will be at least 150
so there must be at least 150 students who major in both
see the answers option the only possible answer is E !
Answer: (E) 150 to 170
Question: If the selling price of 100 articles is equal to the cost price of 63 articles, then the loss or gain percent is:
(A) 39%
(B) 36%
(C) 35%
(D) 40%
(E) 37%
Rationale: Let C.P. of each article be Re. 1.
Then, C.P. of 100 articles = Rs. 100;
S.P. of 100 articles = Rs. 63.
Loss % = 37/100 * 100 = 37%
ANSWER:E
Answer: (E) 37%
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 12
(B) 25
(C) 50
(D) 10
(E) 82
Rationale: Explanation:
Due to stoppages, it covers 9 km less.
time taken to cover 9 km=(9/54*60)min=10 min
Answer D
Answer: (D) 10
Question: During the break of a football match, the coach will make 3 substitutions. If the team consists of 12 players among which there are 2 forwards, what is the probability that none of the forwards will be substituted?
(A)  21/55
(B)  18/44
(C)  28/55
(D)  28/44
(E)  36/55
Rationale: Required probability = no. of favorable outcome/ total no. of outcomes
out of 12 players any 3 can be selected in 12C3 ways
after removing 2 forwards any 3 players can be selected from the remaining 9 players in 9C3 ways
thus required probability = 9C3/12C3 =21/55=A
Answer: (A)  21/55
Question: 529 is a perfect square. When x is added to the square root of 529, the result is also a perfect square. What is x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 529 is 23*23
here
A 23+1 = 24
B 23+2 = 25
C 23+3 = 26
D 23+4 = 27
E 23+5= 28
so, B is the only addition that gives a perfect square. so x=3
then the answer is B
Answer: (B) 2
Question: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 3 times his original investment. What is the value of n?
(A) 50 years
(B) 25 years
(C) 12 years 6 months
(D) 37 years 6 months
(E) 40 years
Rationale: Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $300.
Therefore, the Simple Interest earned =300 - 100 = $200.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 200 = (100 * n * 8) / 100
Or 8n = 200
Or n = 25 years.
correct choice is (B)
Answer: (B) 25 years
Question: Which of the following can be a perimeter r of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
(A) I only
(B) III only
(C) II and III only
(D) I, II, and III
(E) Not I, II, or III
Rationale: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: r>0.
Answer is D.
Answer: (D) I, II, and III
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5
(B) 2.9
(C) 2.4
(D) 2.8
(E) 2.1
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer:A:
Answer: (A) 2.5
Question: A tradesman by means of his false balance defrauds to the extent of 60%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 156%
(B) 147%
(C) 134%
(D) 146%
(E) 183%
Rationale: g% = 60 + 60 + (60*60)/100
= 156%
Answer: A
Answer: (A) 156%
Question: What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x
(A) 56675
(B) 73205
(C) 86543
(D) 98765
(E) 86545
Rationale: (B)
5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205
Answer: (B) 73205
Question: If 120/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer
II. 12/x is an integer
III. 36/x is an integer
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: I think, here we should use the greatest common factor.
The greatest common factor for 144 and 108 is 36.
So 36/x is an integer.
For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions.
Ans is A.
Answer: (A) I only
Question: Let N be the greatest number that divides 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: HCF of (4665-1305) , ( 6905-4665) , (6905-1305)
= HCF of 3360 ,2240,5600
= 1120
sum of digits = 4
ANSWER:A
Answer: (A) 4
Question: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/100000 that a person who randomly guesses the answer to each question will be a winner?
(A) 5
(B) 10
(C) 50
(D) 100
(E) 1000
Rationale: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
E.1000
Soln: ans is B
Probability that one question is answered right is 1/2.
Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/100000
n = 1000 satisfies this.
E
Answer: (E) 1000
Question: A and B have less than 6 diamonds each.What is the probability that the sum of diamonds they have is more than 3 but less than 7?
(A) 3/5
(B) 9/25
(C) 4/9
(D) 2/3
(E) 3/2
Rationale: A has 0, 1, 2, 3, 4, or 5 diamonds;
B has 0, 1, 2, 3, 4, or 5 diamonds.
More than 3 but less than 7 = 4, 5, or 6.
4:
{A, B}
{4, 0}
{3, 1}
{2, 2}
{1, 3}
{0, 4}
5:
{A, B}
{5, 0}
{4, 1}
{3, 2}
{2, 3}
{1, 4}
{0, 5}
6:
{A, B}
{5, 1}
{4, 2}
{3, 3}
{2, 4}
{1, 5}
Favorable = 5 + 6 + 5 = 16.
Total = 6*6 = 36
Probability = 16/36 = 4/9.
Answer: C.
Answer: (C) 4/9
Question: Sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6. She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle three cards?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: The cards are stacked so that the colors alternate: R-B-R-B-R-B-R-B-R.
We are also told that the number on each red card divides evenly into the number on each neighboring blue card.
There are two primes in Blue cards: 3 and 5. Their divisors are 1 and 3 AND 1 and 5, respectively. Thus R1 must be between R3 and R5, R3 must be by B3 and R5 must be by B5: 3-3-1-5-5.
Next, add multiple of 3 to the left of 3: 6-3-3-1-5-5.
Add factor of 6 to the left of 6: 2-6-3-3-1-5-5.
Add multiple of 2 to the left of 2: 4-2-6-3-3-1-5-5.
And finally add factor of 4 to the left of 4: 4-4-2-6-3-3-1-5-5.
The sum of the numbers on the middle three cards is 6+3+3=12.
Answer: E.
Answer: (E) 12
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 1.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 99
(B) 72
(C) 48
(D) 96
(E) 22
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 1.9 = 3 km = 3000 m.
Required time = 3000 * 3/125 = 72 sec.
Answer:B
Answer: (B) 72
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
(A) Rs.19828.89
(B) Rs.19828.80
(C) Rs.19878.80
(D) Rs.19825.80
(E) Rs.19828.90
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P
= 2828.80 / (0.08)(2.08) = 1360/0.08 = 17000 Principal + Interest
= Rs.19828.80
Answer:B
Answer: (B) Rs.19828.80
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 55?
(A) 3944
(B) 3740
(C) 7290
(D) 6928
(E) 3729
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 55 = Rs. 3740.
Answer: Option B
Answer: (B) 3740
Question: if length of a rectangle is equal to side of a square and breadth of rectangle is half of length.if area of square is 36 sq.m.calculate the area of rectangle?
(A) 18
(B) 20
(C) 27
(D) 32
(E) 25
Rationale: side of square=√36=6 m.
length=6 m and breadth=3 m
area of rectangle=6*3=18 sq.m
answer A
Answer: (A) 18
Question: Bottle R contains 250 capsules and costs $5.25. Bottle T contains 130 capsules and costs $2.99. What is the difference between the cost per capsule for bottle R and the cost per capsule for bottle T?
(A)  $0.25
(B)  $0.12
(C)  $0.05
(D)  $0.03
(E)  $0.002
Rationale: Cost per capsule in R is 5.25/250=0.525/25=0.021
Cost per capsule in T is 2.99/130=0.023
The difference is 0.002
The answer is E
Answer: (E)  $0.002
Question: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 16 cups of tea are prepared, 8 in one way and 8 in other. Find the different possible ways of presenting these 16 cups to the expert.
(A) 12520
(B) 12870
(C) 13000
(D) 13400
(E) None
Rationale: Solution:
Since, there are 8 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,
[16!/(8!x8!)]= 12870
Answer: Option B
Answer: (B) 12870
Question: Statement: Unemployment allowance should be given to all unemployed Indian youth above 18 yrs of age. Assumptions: 1) There are unemployed youth in India who needs monetary support. 2) The government has sufficient funds to provide allowance to all unemployed youth.
(A) Only assumption I is implicit
(B) Only assumption II is implicit
(C) Either I or II is implicit
(D) Neither I nor II is implicit
(E) Both I and II are implicit
Rationale: I directly follows from the statement and so is implicit. Also, the statement is a suggestion and does not tell about a government policy or its position of funds. So, II is not implicit.
A
Answer: (A) Only assumption I is implicit
Question: A fruit seller sells mangoes at the rate of Rs.6 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 5%
(A) Rs 7.41
(B) Rs 9.81
(C) Rs 10.41
(D) Rs 11.81
(E) None of these
Rationale: Explanation:
85 : 6 = 105 : x
x= (6×105/85)
= Rs 7.41
Option A
Answer: (A) Rs 7.41
Question: Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 45 marks. How many sums did Sandy get correct?
(A) 18
(B) 21
(C) 24
(D) 27
(E) 28
Rationale: Let x be the correct sums and (30-x) be the incorrect sums.
3x - 2(30-x) = 45
5x = 105
x = 21
The answer is B.
Answer: (B) 21
Question: What ratio must a shopkeepermix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.22?
(A) 10 : 7
(B) 9 : 8
(C) 1 : 2
(D) 13 : 11
(E) 14 : 8
Rationale: Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 3 : 6 = 1 :2
Answer: (C) 1 : 2
Question: Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 4 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
(A) $506.00
(B) $726.24
(C) $900.00
(D) $920.24
(E) $926.24
Rationale: If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.
Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;
Total: 200+306+(~420)=~$920.24
Answer: D.
Answer: (D) $920.24
Question: (3+√3+√5)^2-(√3+√5)^2=?
(A) 9+6√3+6√5
(B) 1+2√3+3√5
(C) 1-√3+√5
(D) 1+√3-√5
(E) √3+√5
Rationale: (3+√3+√5)^2-(√3+√5)^2
(3+√3)^2 + 5 +2 (3+√3) (√5) - ( 3 +5 + 2√3√5)
9+ 3+ 6√3 +5 +6 √5 + 2 √15 - 3-5 -2√15
9+6√3+6√5
A is the answer
Answer: (A) 9+6√3+6√5
Question: Mohan went to a shop and bought things worth Rs. 100, out of which 90 Paise went on sales tax on taxable purchases. If the tax rate was 9%, then what was the cost of the tax free items?
(A) 89.1
(B) 88.1
(C) 79.1
(D) 80.1
(E) 85.1
Rationale: Total cost of the items he purchased = Rs.100
Given that out of this Rs.100, 90 Paise is given as tax
=> Total tax incurred = 90 Paise = Rs.90/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (100−90/100−x)9/100 = 90/100
⇒ 9(100−0.9−x) = 90
⇒ (100 − 0.9 − x) = 10
⇒ x = 100 − 0.9 − 10 = 89.1
A)
Answer: (A) 89.1
Question: Reeya obtained 65, 67, 76, 82 and 85 out of 100 in different subjects, What will be the average
(A) 70
(B) 75
(C) 80
(D) 85
(E) 60
Rationale: Explanation:
(65+67+76+82+855)=75
Answer: Option B
Answer: (B) 75
Question: On a map, 1 centimeter represents 25 kilometers. Two cities 425 kilometers apart would be separated on the map by how many centimeters?
(A) 25
(B) 17
(C) 19
(D) 310
(E) 280
Rationale: X=425/25= 17
Answer: B
Answer: (B) 17
Question: Three numbers are in the ratio 5 : 6 : 8. The sum of its longest and smallest numbers equals the sum of the third number and 49. Find the third number?
(A) A)54
(B) B)75
(C) C)48
(D) D)42
(E) E)63
Rationale: Let the numbers be 5x, 6x, 8x.
Largest number = 8x.
Smallest number = 5x.
Third number = 6x.
8x + 5x = 6x + 49
7x = 49 =>x=7
6x=42=> third number is 42.
Answer:D
Answer: (D) D)42
Question: The total of 336 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is
(A) 238
(B) 277
(C) 278
(D) 260
(E) 288
Rationale: Explanation:
Let the number of 20 paise coins be x. Then the no of 25 paise coins = (336 - x).
0.20 * (x) + 0.25 (336 - x) = 71 => x = 260..
Answer: D) 260
Answer: (D) 260
Question: A train running at the speed of 60 km/hr crosses a pole in 18 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 300 metres
(E) 180 metres
Rationale: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50 x 18/3 m = 300 m.
ANSWER : OPTION D
Answer: (D) 300 metres
Question: In a game of billiards, A can give B 30 points in 80 and he can give C 40 points in 80. How many points can B give C in a game of 100?
(A) 23
(B) 24
(C) 25
(D) 20
(E) 28
Rationale: A scores 80 while B score 50 and C scores 40.
The number of points that C scores when B scores 100 = (100 * 40)/50 = 80.
In a game of 100 points, B gives (100 - 80) = 20 points to C
Answer:D
Answer: (D) 20
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 17 km/hr
(B) 18 km/hr
(C) 60 km/hr
(D) 16 km/hr
(E) 11 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5
= 60 km/hr.
Answer: C
Answer: (C) 60 km/hr
Question: An urn contains 8 black and 2 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
(A) 1/5
(B) 28/45
(C) 2/5
(D) 3/5
(E) 2/7
Rationale: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 8/10
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 7 black balls and two white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 7/9
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 8/10 × 7/9 = 28/45
B
Answer: (B) 28/45
Question: If × stands for 'addition', ÷ stands for 'subtraction', + stands for 'multiplication' and-stands for 'division', then 20 × 8 ÷ 8 - 4 + 2 = ?
(A) 33
(B) 77
(C) 24
(D) 23
(E) 21
Rationale: Explanation:
By the Given data , We have the expression:
20 + 8 - 8 ÷ 4 × 2 = 20 + 8 - 2 × 2 = 20 + 8 - 4 = 24
Answer: C) 24
Answer: (C) 24
Question: In March, Kurt ran an average of 1.5 miles an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?
(A) 3590/60^2
(B) 2410/60^2
(C) 2390/60^2
(D) 3586/60
(E) 60^2/3590
Rationale: 1500 in 3600 sec
1000 in x sec
x = 2400
In june = 2400-10 = 2390
so 2390 / 60 * 60
2390/60^2
ANSWER:C
Answer: (C) 2390/60^2
Question: Which fraction should be added to:
1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ....... + 1/(31 Ã— 32)
so that the result is equal to 1?
(A) 11/32
(B) 13/32
(C) 15/32
(D) 17/32
(E) 19/32
Rationale: The given expression
= 1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ...... + 1/(31 Ã— 32)
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .......... + (1/31 - 1/32)
= 1/2 - 1/32 = 15/32
Thus, the fraction we should add = 1 - 15/32 = 17/32
The answer is D.
Answer: (D) 17/32
Question: In a renowned city, the average birth rate is 4 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
(A) 86,400
(B) 172,800
(C) 468,830
(D) 338,200
(E) 259,200
Rationale: Every 2 seconds, 2 persons are added (4-2). Every second 1 person are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 1 = 86400
Option A
Answer: (A) 86,400
Question: In what time will a train 200 m long cross an electric pole, it its speed be 216 km/hr?
(A) 2.5 sec
(B) 2.8 sec
(C) 8.5 sec
(D) 3.3 sec
(E) 4.5 sec
Rationale: Speed = 216 * 5/18
= 60 m/sec
Time taken = 200/60
= 3.3 sec.
Answer:D
Answer: (D) 3.3 sec
Question: A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 25 payments is to be $500; each of the remaining payments is to be $100 more than each of the first 25 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
(A) 500
(B) 450
(C) 552
(D) 600
(E) 400
Rationale: Total = 500(25) + 600(27)
Number of installments = 52
Average = Total/Number of installments = 552 approximately
Answer: C
Answer: (C) 552
Question: In the first week of the Year, Rancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Rancy saved during the 52 weeks?
(A) $1,326
(B) $1,352
(C) $1,378
(D) $2,652
(E) $2,756
Rationale: In the first week of the Year, Rancy saved $1.If you don't recall the formula, there is one method:
1 + 2 + 3 + 4 + 5 ........ + 26 + 27 + ............ + 48 + 50 + 51 + 52
Sum of 1stlast digit = 1 + 52 = 53
Sum of 2nd2nd last digit = 2 + 51 = 53
Sum of 3rd3rd last digit = 3 + 50 = 53
.
.
.
.
This is repeated 26 times
So, 26 * 53 = 1378
Answer = C
Answer: (C) $1,378
Question: A truck covers a distance of 200 metres in 1 minute whereas a bus covers a distance of 100kms in 50minutes. The ratio of their speeds is?
(A) 2:3
(B) 1:5
(C) ratio 1:10
(D) 9:13
(E) 7:15
Rationale: Ratio of speeds = (200/60) 18/5 : 60*100/50 = 12:120 = 1:10
Answer is C
Answer: (C) ratio 1:10
Question: A circular logo is enlarged to fit the lid of a jar. The new diameter is 10 per cent larger than the original. By what percentage has the area of the logo increased?
(A) 50
(B) 80
(C) 100
(D) 125
(E) 21
Rationale: Let old diameter be 4 , so radius is 2
Old area = 4π
New diameter is 4.4 , so radius is 2.2
New area = 4.84π
Increase in area is 0.84π
% increase in area = 0.84/4*100
So, % increase is 21%
Answer will be (E)
Answer: (E) 21
Question: Two pipes P and Q can fill a cistern in 12 and 13 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 1/8
(B) 1/4
(C) 2/4
(D) 1/4
(E) 3/4
Rationale: 3/12 + x/13
= 1
x= 7 3/4
Answer: E
Answer: (E) 3/4
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer?
(A) Rs.4268
(B) Rs.4290
(C) Rs.4566
(D) Rs.4266
(E) Rs.4208
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs.4266
Answer:D
Answer: (D) Rs.4266
Question: Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ?
(A) 47-43
(B) 47+43
(C) (47^43)+(43^47)
(D) None of these
(E) (47^2)+(43^2)
Rationale: When n is odd, (xn + an) is always divisible by (x + a).
Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43).
Option B
Answer: (B) 47+43
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical B present and inversely proportional to the concentration of chemical A present. If the concentration of chemical B present is increased by 100 percent, which of the following is closest to the percent change in the the concentration of chemical B required to keep the reaction rate unchanged.
(A) 100 % decrease
(B) 60% decrease
(C) 40% decrease
(D) 30% increase
(E) 50% increase
Rationale: Let's say here is the formula of how B and A affects the reaction speed:
rate = B^2/A
After the concentration A is increased by 100%, the percentage of A
become 2A, to keep 'rate' the same, need to have B^2 being doubled.
Which means A increased by 2^(1/2) times.
Answer : C
Answer: (C) 40% decrease
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
(A) 1/7
(B) 1/8
(C) 1/5
(D) 1/1
(E) 1/2
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability
= 1/5
Answer:C
Answer: (C) 1/5
Question: In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fell ill for the next five daysreducing the daily avg for the month to 58 sets/day . The average production per day for day last 5days is ?
(A) 30
(B) 42
(C) 48
(D) 50
(E) 54
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Answer: (C) 48