mathewhe/aqua_rat huggingface dataset:
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
(A) 128
(B) 130
(C) 132
(D) 143
(E) 145
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: (C) 132
Question: Two trains are moving in the same direction at 144 kmph and 72 kmph. The faster train crosses a man in the slower train in 19 seconds. Find the length of the faster train?
(A) 320
(B) 340
(C) 360
(D) 380
(E) 400
Rationale: Relative speed = (144 - 72) * 5/18 = 4 * 5
= 20 mps.
Distance covered in 19 sec
= 19 * 20
= 380 m.
The length of the faster train
= 380 m.
Answer:D
Answer: (D) 380
Question: Village A	Village B	Village C	Village D	Village E	Village F ;
Village A
Village B
Village C
Village D
Village E
Village F
In the table above, what is the least number of table entries that are needed to show the mileage between each Village and each of the other five Villages?
(A) 16
(B) 15
(C) 18
(D) 20
(E) 22
Rationale: Easy way to go about this problem is we have 6*6 = 36 enteries in table the least number of enteries would be (36 - 6) /2 since 6 enteries represent the distances between same points .
Alternatively this can be solved as combination problem.
Correct Answer B
Answer: (B) 15
Question: Myra drove at an average speed of 30 miles per hour for T hours and then at an average speed of 60 miles/hr for the next T hours. If she made no stops during the trip and reached her destination in 2T hours, what was her average speed in miles per hour for the entire trip?
(A) The average speed is 40 miles per hour.
(B) The average speed is 45 miles per hour.
(C) The average speed is 48 miles per hour.
(D) The average speed is 50 miles per hour.
(E) The average speed is 55 miles per hour.
Rationale: Here, time for which Myra traveled at the two speeds is same.
Average Speed = (a + b)/2 = (30 + 60)/2 = 45 miles per hour
Answer (B)
Answer: (B) The average speed is 45 miles per hour.
Question: If a,b and c are consecutive positive integers and a>b>c. What can be the value of (a^2-b^2)(b^2-c^2)?
(A) 21
(B) 79
(C) 143
(D) 231
(E) 450
Rationale: Since a,b and c are consecutive positive integers and a>b>c, we can write them as (x + 1), x and (x - 1) respectively
(a^2-b^2)(b^2-c^2) can be simplified into (2x + 1)(2x - 1) = 4x^2 - 1
using the options to find the product,
only C. 143 satisfactorily gives us x as an integer
ANSWER:C
Answer: (C) 143
Question: The number N is 5,1H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
(A) 1
(B) 3
(C) 8
(D) 7
(E) 9
Rationale: Integer is divisible by 9 - Sum of digits is divisible by 9
Answer: C
Answer: (C) 8
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
(A) 4
(B) 9
(C) 12
(D) 21
(E) 35
Rationale: More cogs less revolution,..
so
6:14::x:21
(21*6)/14=9
ANSWER:B
Answer: (B) 9
Question: A certain bus driver is paid a regular rate of $20 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $1000 in total compensation, how many total hours did he work that week?
(A) 46
(B) 40
(C) 44
(D) 48
(E) 49
Rationale: For 40 hrs = 40*20=800
Excess = 1000-800=200
For extra hours =.75(20)=15+20=35
Number of extra hrs =200/35=5.71=6 approx.
Total hrs =40+6=46
Answer A 46
Answer: (A) 46
Question: If a and b are odd integers, which of the following is an even integer?
(A) 2ab+a
(B) 2ab-b
(C) 2ab+a+b
(D) 2ab+2a+b
(E) 2ab+2a+3b
Rationale: 2ab+a+b=even+odd+odd=even
The answer is C.
Answer: (C) 2ab+a+b
Question: How many digits are required to number a book containing 260 pages?
(A) 784
(B) 672
(C) 492
(D) 372
(E) 300
Rationale: 9 pages from 1 to 9 will require 9 digits.
90 pages from 10 to 99 will require 90*2=180 digits.
260-(90+9)=161 pages will require 161*3=483 digits.
The total number of digits is 9+180+483=672.
The answer is B.
Answer: (B) 672
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?
(A) 10
(B) 20
(C) 30
(D) 43
(E) 50
Rationale: His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.25-1)* 100 = 20
B
Answer: (B) 20
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 40 seconds. Its length is?
(A) 188 m
(B) 876 m
(C) 251 m
(D) 100 m
(E) 145 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 40 = x / 15
x = 100 m.
Answer: D
Answer: (D) 100 m
Question: A bag contains 12white and 18black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 31/145
(B) 36/145
(C) 32/145
(D) 36/147
(E) None
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 9 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?
(A)  4y
(B)  5y
(C)  6y
(D)  17y
(E)  9y
Rationale: Let $x be the advance that both receive = 2x
Amount earned per hour by John and Mary = x/9 and x/8
Mary gives $y to John to make the wages earned equal
Hence John wage per hr = (x+y)10 which is now equal to Mary's wage (x-y)/8
Solve (x+y)9 = (x-y)/8
8x + 8y = 9x -9y
x = 17y
Ans. D
Answer: (D)  17y
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current ?
(A) 1 kmph
(B) 3.2 kmph
(C) 1.5 kmph
(D) 2 kmph
(E) 2.5 kmph
Rationale: Explanation:
72 --- 9
? ---- 1
=> Down Stream = 8
45 ---- 9
? ---- 1
=> Up Stream = 5
Speed od current S = ?
S = (8 - 5)/2 = 1.5 kmph.
ANSWER IS C
Answer: (C) 1.5 kmph
Question: Sachin is younger than Rahul by 7 years. If the ratio of their ages is 6:9, find the age of Sachin
(A) 24.5
(B) 14
(C) 24.21
(D) 27
(E) 25
Rationale: Explanation:
If Rahul age is x, then Sachin age is x - 7,
so,
9x - 63 = 6x
3x = 63
x = 21
So Sachin age is 21 - 7 = 14
Answer: B) 14
Answer: (B) 14
Question: The proportion of water to alcohol in Solution A is 5:4 and the proportion of water to alcohol in Solution B is 6:5. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?
(A) 40.9%
(B) 41.9%
(C) 42.9%
(D) 43.9%
(E) 44.9%
Rationale: Let V be the total volume of the new solution.
Then a volume of V/2 was added from each solution A and B.
The amount of alcohol added to the new solution was:
(4/9)(V/2)+(5/11)(V/2)=2V/9+5V/22=89V/198.
The concentration of alcohol is 89/198=44.9%
The answer is E.
Answer: (E) 44.9%
Question: A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is
(A) 7hours 75 mins
(B) 7 hours
(C) 8 hours
(D) 5 hours
(E) 6 hours
Rationale: Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
Answer is A.
Answer: (A) 7hours 75 mins
Question: Two goods trains each 850 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 22 sec
(B) 81.6 sec
(C) 48 sec
(D) 18.3 sec
(E) 9.32 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 850 + 850 = 1700 m.
Required time = 1700 * 6/125 = 81.6 sec.
Answer:B
Answer: (B) 81.6 sec
Question: Sujit incurred a loss of 45% on selling an article for Rs.3850/-. What was the cost price of the article?
(A) Rs.5725/-
(B) Rs.5080/-
(C) Rs.6250/-
(D) Rs.7000/-
(E) None of these
Rationale: Explanation:
45% loss means SP of Rs.3850/- is 55% of CP
:. CP = 3850x100/55 = Rs.7000/-
Answer: Option D
Answer: (D) Rs.7000/-
Question: The sum of the ages of 4 children born at the intervals of 3 years each is 36 years. what is the age of the youngest child ?
(A) 22
(B) 18
(C) 4.5
(D) 99
(E) 38
Rationale: Let x = the youngest child. Each of the other four children will then be x+3, x+6, x+9
We know that the sum of their ages is 36
so, x+(x+3)+(x+6)+(x+9)= 36
therefore The youngest child is 4.5 years old
Answer: C
Answer: (C) 4.5
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.5000?
(A) 1655
(B) 2888
(C) 2776
(D) 2997
(E) 2718
Rationale: A = 5000(11/10)^3
= 6655
= 5000
----------
1655
Answer: A
Answer: (A) 1655
Question: Can you find the missing number in the sequence given below?
10 18 26 11 19 ? 12 20 28 13 21 29
(A) 25
(B) 23
(C) 20
(D) 27
(E) 19
Rationale: Let's break the given series as below:
10 18 26
11 19 ?
12 20 28
13 21 29
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 27
Answer : D
Answer: (D) 27
Question: 2,5,12,31,81,__
(A) 210
(B) 211
(C) 213
(D) 214
(E) 215
Rationale: 12= 5*2+2
31= 12*2+5+2
81= 31*2+12+5+2
Similarly 81*2+31+12+5+2 = 162+50=212
ANSWER:C
Answer: (C) 213
Question: A rectangle PRSU, is divided into two smaller rectangles PQTU, and QRST by the line TQ. PQ = 10 cm. QR = 5 cm and RS = 10 cm. Points A, B, F are within rectangle PQTU, and points C, D, E are within the rectangle QRST. The closest pair of points among the pairs (A, C), (A, D), (A, E), (F, C), (F, D), (F, E), (B, C), (B, D), (B, E) are 10 3 cm apart.
Which of the following statements is necessarily true?
(A) The closest pair of points among the six given points cannot be (F, C)
(B) Distance between A and B is greater than that between F and C.
(C) The closest pair of points among the six given points is (C, D), (D, E), or (C, E).
(D) none of the above
(E) Cannot be determined
Rationale: Explanation :
We have not been given the distances between any two points.
Answer : D
Answer: (D) none of the above
Question: If |x + 2| = 10, what is the sum of all the possible values of x?
(A) -16
(B) -13
(C) -4
(D) -2
(E) 12
Rationale: There will be two cases
x+2 = 10 or x+2 = -10
=> x = 8 or x= -12
sum of both the values will be -12 + 8 = -4
Answer: C
Answer: (C) -4
Question: How many Q ways are there of placing 6 marbles in 4 bowls, if any number of them can be placed in each bowl?
(A) 6C4
(B) 6P4
(C) 4^6
(D) 6^4
(E) 6!
Rationale: Each marble has 4 options, so there are total of Q= 4*4*4*4*4*4=4^6 ways.
Answer: C.
The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is (n+r -1)C(r-1).
Answer: (C) 4^6
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age
(A) 14
(B) 15
(C) 20
(D) 22
(E) 23
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 6 = 26 => x = 5
So Deepak age is = 3(5) = 15
Answer: Option B
Answer: (B) 15
Question: A clock is set right at 1 p.m. If it gains one minute in an hour, then what is the true time when the clock indicates 6 p.m. in the same day?
(A) 55 5⁄61 minutes past 5
(B) 5 minutes past 6
(C) 5 minutes to 6
(D) 59 1⁄64 minutes past 5
(E) None of these
Rationale: Time interval indicated by incorrect clock
= 6 p.m – 1 p.m = 5hrs.
Time gained by incorrect clock in one hour
= + 1 min. = +1⁄60 hr.
Using the formula, True time interval /Time interval in incorrect clock
= 1 /1+hour gained in 1 hour by incorrect clock
⇒ Truetimeinterval/5=1/1+1/60
⇒ True time interval = 5×60/61=4 56/61
∴ True time = 1 p.m. + 4 56/61 hrs.
= 5 p.m. + 56⁄61 hrs. = 5 p.m. + 56⁄61 × 60 min.
= 555⁄61 minutes past 5.
Answer A
Answer: (A) 55 5⁄61 minutes past 5
Question: what is the smallest integer that is multiple of 5,7,8
(A) A)70
(B) B)35
(C) C)200
(D) D)280
(E) E)140
Rationale: It is the lcm of 5, 7 and 8 which is 280.
The answer is D.
Answer: (D) D)280
Question: 25% of the total cost of a plot of area 280 sq.ft. is Rs.132370. What is the rate per sq.ft of the plot?
(A) Rs.2091
(B) Rs.1891
(C) Rs.1981
(D) Rs.1991
(E) None of these
Rationale: Explanation:
25% = ¼
:. Cost of total area = Rs.132370x4
Rate per sq.ft = 132370x4/280 = Rs.1891/-
Answer: Option B
Answer: (B) Rs.1891
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Ingrid bake?
(A) 0.125%
(B) 1.25%
(C) 31.7%
(D) 125%
(E) 0.152%
Rationale: 9.18x+5.17x+2.05x = 16.4x = 148 cookies
x= 148/16.4 = 9 (approx)
So, Ingrid baked 9*5.17 cookies or 47 cookies (approx)
% share = 47/148 = 31.7 approx
Hence, answer is C.
Answer: (C) 31.7%
Question: X and Y started a business investing Rs. 50,000 and Rs 40,000 respectively. In what ratio the profit earned after 2 years be divided between X and Y respectively?
(A) 3:2
(B) 9:2
(C) 5 : 4
(D) 1:4
(E) 18:4
Rationale: X:Y = 50000 : 40000 = 5 : 4
ANSWER:C
Answer: (C) 5 : 4
Question: A man whose bowling average is 12.4, takes 8 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
(A) 173
(B) 174
(C) 175
(D) 176
(E) 177
Rationale: 12.4*x+26=(8+x)12
solve equation x=175
ANSWER:C
Answer: (C) 175
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 6 %
(B) 8 %
(C) 5 5/11%
(D) 11 %
(E) 5%
Rationale: Explanation:
Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
Gain % =(300/5500	x 100)%= 5 5/11%
Answer:C
Answer: (C) 5 5/11%
Question: People standing in a straight line are wearing alternating colored shirts. The pattern of shirts begins with red, followed by green, blue, and yellow. This pattern continues (red, green, blue, and yellow) until it ends with a green shirt. If there are more than 4 people in line, which of the following cannot be the number of people in the line?
(A) 18
(B) 22
(C) 42
(D) 41
(E) 74
Rationale: The correct answer should not take the form: 4x + 2. Hence, it is D
Answer: (D) 41
Question: If x/|y| = 1 which of the following must be true?
(A) x = -y
(B) x = y
(C) x = y^2
(D) x^2 = y^2
(E) x^3 = y^3
Rationale: x/|y| = 1
x= 1 |y|
Squaring both sides
x^2= (1 |y|) ^2= y^2
D is the answer
Answer: (D) x^2 = y^2
Question: Two sacks together contained 40 kilograms of sugar. If after 1 kilogram of sugar was taken from the first sack and poured into the second the weight of the sugar in the first sack became 60% the weight of the sugar in the second, what was the original difference in the weights of the sacks?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: Say the weight of the second sack after change is x kilograms, then the weight of the first sack after change would be 0.6x. Since the total weight of sugar in both sacks remained the same then x+0.6x=40, which gives x=25.
Now, if the weight of the second sack after change is 25 kilograms then initially it was 25−1=24 kilograms and the initial weight of the first sack was 40−24=16 kilograms, so the difference was 24−16=8 kilograms.
Answer: C
Answer: (C) 8
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $60,000. 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) $10,000
(B) $26,400
(C) $12,000
(D) $12,800
(E) $13,200
Rationale: 1 machine of type B will cost: 20% down payment of 60,000 = 12,000plusremaining sum (50,000-12,000=48,000) with 40% of finance charges 48,000*1.4=67,200 --> 12,000+67,200=79,200;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 79,200 - 52,800 = 26,400.
Answer: B.
Answer: (B) $26,400
Question: If |5x-30| = 100, then find the sum of the values of x?
(A) 1
(B) -2
(C) 12
(D) -3
(E) 4
Rationale: |5x-30| = 100
5x-30 = 100 or 5x-30 = -100
5x = 130 or 5x = -70
x = 26 or x = -14
sum = 26-14 = 12
Answer is C
Answer: (C) 12
Question: A and B start walking towards each other at 5am at speed of 4kmph and 8kmph. They were initially 36km apart. At what time do they meet?
(A) 8am
(B) 6am
(C) 7am
(D) 10am
(E) 8pm
Rationale: Time of meeting = distance / relative speed = 36/8 + 4 = 36/12 = 3 hrs after 5am = 8am
Answer is A
Answer: (A) 8am
Question: a number divided by 44 leaves remainder 17 what is the remainder when same number divided by 8
(A) 5
(B) 7
(C) 9
(D) 10
(E) 11
Rationale: add 44+17=61
now 61 divided by 8 so we get 5 as reaminder
ANSWER:A
Answer: (A) 5
Question: Health insurance Plan Q requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
(A) $600
(B) $1000
(C) $3800
(D) $5300
(E) $6200
Rationale: 0.5 * 600 = 300 where Q = B
Answer: (B) $1000
Question: A 300 meter long train crosses a plaƞorm in 39 seconds while it crosses a signal pole in 18 seconds.
What is the length of the plaƞorm.
(A) 310 meter
(B) 335 meter
(C) 345 meter
(D) 350 meter
(E) None of these
Rationale: Explanation:
Speed = Distance/Ɵme = 300/18 = 50/3 m/sec
Let the length of the plaƞorm be x meters
then
Distance=Speed
∗
Timex+300=503
∗
39=>3(x+300)=1950=>x=350 meters
Answer: D
Answer: (D) 350 meter
Question: It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
(A) 16^2+1
(B) 12
(C) (2^96+1)
(D) 24
(E) 4^4+6
Rationale: Explanation:
Let 2^32 = x. Then, (2^32 + 1) = (x + 1).
Let (x + 1) be completely divisible by the natural number N. Then,
(296 + 1) = [(2^32)3 + 1] = (x^3 + 1) = (x + 1)(x^2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
C
Answer: (C) (2^96+1)
Question: Evaluate: 50 - 12÷4×2 =
(A) 44
(B) 54
(C) 16
(D) 27
(E) 30
Rationale: According to order of operations, 12÷4×2 (division and multiplication) is done first from left to right
12÷4×2 = 3 × 2 = 6
Hence
50 - 12÷4×2 = 50 - 6 = 44
correct answer A)44
Answer: (A) 44
Question: I sold a book at a profit of 10%. Had I sold it for $120 more, 15% would have been gained. Find the cost price?
(A) $2000
(B) $2500
(C) $2400
(D) $3120
(E) $1540
Rationale: 115% of cost - 110% of cost = $120
5% of cost = $120
cost = 120*100/5 = $2400
Answer is C
Answer: (C) $2400
Question: In how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together?
(A) 6!/2!
(B) 3!*3!
(C) 4!/2!
(D) 4! *(3!/2!)
(E) 3!*3!/2
Rationale: In the word ABROAD , there are 3 vowels - 2 A's and O
Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together
= (4! * 3! )/2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .
The entire vowel group is considered as a single group .
Answer D
Answer: (D) 4! *(3!/2!)
Question: If n is a positive integer and the product of all integers from 1 to n, inclusive, is a multiple of 690, what is the least possible value of n?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 23
Rationale: 690 = 2 * 3 * 5 * 23
so the least value forNcan be 23.
E
Answer: (E) 23
Question: Mohit sold an article for Rs. 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) 15000
(B) 15002
(C) 15029
(D) 15329
(E) 15012
Rationale: Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x = Rs. 1.08x = 18000 - 10/100(18000) = 18000 - 1800 = Rs. 16200
=> 1.08x = 16200
=> x = 15000
Answer: A
Answer: (A) 15000
Question: In how many ways letters of the word RSCUPERATE be arranged?
(A) 357898
(B) 654326
(C) 865453
(D) 545778
(E) 302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: (E) 302400
Question: A cistern is filled by pipe A in 10 hours and the full cistern can be leaked out by an exhaust pipe B in 15 hours. If both the pipes are opened, in what time the cistern is full?
(A) 50hrs
(B) 30hrs
(C) 70hrs
(D) 80hrs
(E) 90hrs
Rationale: time taken to full the cistern=(1/10-1/15)hrs
=1/30
=30hrs
ANSWER:B
Answer: (B) 30hrs
Question: For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x
II. y/7 is an integer
III. The cube root of x is an integer
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: Given 91*x=8*y
It can be equal when x = 8 or -8
and y = 91 or -91
So Statement (I) y < x if we take x = -8 and y =-91
but y > x if we take x = 8 and y = -91, so (I) is not true always
Statement (2) in any case
91/7 or -91/7 is an integer that is 13 or -13. So it is true
Statement (3) cube root of 8 or -8 is 2 and -2 respectively. So it is true always.
answer is E
Answer: (E) II and III
Question: The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle?
(A) 432
(B) 376
(C) 299
(D) 276
(E) 396
Rationale: 2(3x + x) = 88
l = 36 b = 11
lb = 36 * 11
= 396
E
Answer: (E) 396
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 25 days
(B) 24 days
(C) 22 days
(D) 27 days
(E) 21 days
Rationale: B
24 days
B = 1/8 – 1/2 = 1/24 => 24 days
Answer: (B) 24 days
Question: A man invests Rs. 8,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
(A) Rs. 1200
(B) Rs. 1300
(C) Rs. 1500
(D) Rs. 4000
(E) None of these
Rationale: Explanation :
Interest on Rs.8000 at 5% per annum = ( 8000 × 5 × 1) / 100 = Rs. 400
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (8000 + x) × 6 × 1/100.
=> 400 + 2x/25 = (8000 + x) × 6 × 1/100.
=> 40000 + 8x = (8000 + x) × 6.
=> 40000 + 8x = 48000 + 6x.
=> 2x=8000.
=> x=4000.
Answer : D
Answer: (D) Rs. 4000
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, 8 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)  0.25
(E)  0.6
Rationale: Index for females = (20-8)/20 = 3/5 = 0.6
Index for males = (20-12/20 = 2/5 = 0.4
Index for females exceeds males by 0.6 - 0.4 = 0.2
Answer: C
Answer: (C)  0.2