mathewhe/aqua_rat huggingface dataset:
Question: What number continues the sequence?
25, 50, 27, 46, 31, 38, 39, ?
(A) 11
(B) 33
(C) 52
(D) 22
(E) 66
Rationale: D
22
There are two alternate sequences, the first increases by 2, 4, 8 etc and the second decreases by 4, 8, 16 etc.
Answer: (D) 22
Question: Victor gets 92 % marks in examinations. If these are 368 marks, find the maximum marks.
(A) 334
(B) 500
(C) 400
(D) 288
(E) 271
Rationale: Let the maximum marks be m
Then 92 % of m = 368
⇒ 92/100 × m = 368
⇒ m = (368 × 100)/92
⇒ m = 36800/92
⇒ m = 400
Therefore, maximum marks in the examinations are 400.
Answer : C
Answer: (C) 400
Question: If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question, but the easiest way is as follows: since we cannot have two correct answers just pick a prime greater than 3, square it and see what would be the remainder upon division of it by 12.
n=5 --> n^2=25 --> remainder upon division 25 by 12 is 1.
Answer: B
Answer: (B) 1
Question: If a quality control check is made inspecting a sample of 2 light bulbs from a box of 10 lighbulbs, how many different samples can be chosen?
(A) 6
(B) 24
(C) 45
(D) 66
(E) 72
Rationale: Try using the formula for combinations:
n!/r!(n-r)!
10!/2!(10-2)!
10!/2!*8!
10*9/2*1
=45
C
Answer: (C) 45
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 27.8 km/hr
(B) 22.9 km/hr
(C) 26.6 km/hr
(D) 79.2 km/hr
(E) 12.9 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer: D
Answer: (D) 79.2 km/hr
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 10 per metre of cloth. What is the cost price of one metre of cloth?
(A) 95
(B) 28
(C) 90
(D) 26
(E) 11
Rationale: Explanation:
SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 10 = Rs. 95.
Answer: A
Answer: (A) 95
Question: A fort had provision of food for 150 men for 45 days. After 20 days, 40 men left the fort. The number of days for which the remaining food will last, is:
(A) 29	1/5
(B) 37	1/4
(C) 42
(D) 34
(E) 45
Rationale: we have food for 150 men for 45 days.
After 20 days food left for 150 men for 25 days.
so
150 : 25
now we have 110 men and x days
110 : 150 :: 25 : x
x = (150*25)/110 = 34 days.
ANSWER:D
Answer: (D) 34
Question: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 7?
(A) A)1
(B) B)2
(C) C)4
(D) D)7
(E) E)16
Rationale: Points to remember -
1. If oneAdd/Subtractthe same amont from every term in a set, SD doesn't change.
2. If oneMultiply/Divideevery term by the same number in a set, SD changes by same number.
Hence the answer to the above question is D
Answer: (D) D)7
Question: A merchant purchased a jacket for $48 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A)  $0
(B)  $3
(C)  $4
(D)  $12
(E)  $16
Rationale: Actual Cost = $48
SP = Actual Cost + Mark up
= Actual Cost + 40% SP
= 48*100/60
on sale SP = 80/100(48*100/60) = 64
Gross profit = $16
Answer is E
Answer: (E)  $16
Question: A certain machine produces 650 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 7 days?
(A) 7,000
(B) 24,000
(C) 40,000
(D) 109,200
(E) 168,000
Rationale: Since 7 days consist of 24*7 hours the total hours of a week is 168 hours.
Since every hour the machine produces 650 units of product P the total product during 168 hours is 650*168= 109,200
Correct Option : D
Answer: (D) 109,200
Question: How many kg of sugar costing Rs. 9/kg must be mixed with 27kg of sugar costing Rs. 7/ kg so that there may be a gain of 10% the mixture at Rs. 9.24 per kg?
(A) 45
(B) 47
(C) 49
(D) 52
(E) 63
Rationale: Selling Price(SP) of 1 kg mixture= Rs. 9.24
Profit = 10%
Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP
=100(100+10)×9.24=100110×9.24=92.411= Rs.8.4
By rule of alligation,
CP of 1 kg sugar of 1st kind CP of 1 kg sugar of 2nd kind
Rs. 9 Rs. 7
Mean Price
Rs.8.4
8.4 - 7 = 1.4 9 - 8.4 = 0.6
i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3
Suppose x
kg of kind1 sugar is mixed with 27 kg of kind2 sugar.
then x : 27 = 7 : 3
⇒3x=27×7⇒x=9×7=63
E
Answer: (E) 63
Question: What is the place value of 5 in the numeral 5259
(A) 2500
(B) 3400
(C) 3500
(D) 5000
(E) 4000
Rationale: Option 'D'
5 * 1000 = 5000
Answer: (D) 5000
Question: If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
(A) 49%
(B) 90%
(C) 60%
(D) 40%
(E) 41%
Rationale: 8 = (1*20*R)/100
R = 40%
Answer:D
Answer: (D) 40%
Question: What is the probability that when a hand of 5 cards is drawn from a well shuffled deck of 52 cards, it contains all the Queens?
(A) 191/379015
(B) 171/379015
(C) 181/379015
(D) 379015/192
(E) 192/379015
Rationale: nCr = n!/(n-r)!r!
Total number of possible hands = 52C5
52C5 = 2274090
Number of hands with 4 Queens = 4C4 × 48C1
4C4 = 24
48C1 = 48
(other 1 card must be chosen from the rest 48 cards)
Hence P (a hand will have 4 Queens) = (4C4 × 48C1)/52C5 = 192/379015
E
Answer: (E) 192/379015
Question: A cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm. Find the total area of the wet surface.
(A) 42 m sqaure
(B) 49 m sqaure
(C) 52 m sqaure
(D) 64 m sqaure
(E) None of these
Rationale: Explanation:
Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(4*1.25+6*1.25)]+6*4 = 49 m square
Option B
Answer: (B) 49 m sqaure
Question: When positive integer p is divided by positive integer x, the remainder is 5 and when positive integer q is divided by positive integer y, the remainder is 8. Which of the following is a possible value for x + y?
I.16
II. 15
III. 14
(A) I and II only
(B) II only
(C) III only
(D) II and III only
(E) None
Rationale: p/x -- remainder is 5 => x is anything greater than 5. Minimum value of x could be 6.
q/y -- remainder is 8 => y is anything greater than 8. Minimum value of y could be 9.
Hence, the minimum value of x+y = 15. So, I and II are correct.
ANSWER:A
Answer: (A) I and II only
Question: The average age of a group of 16 students was 20. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
(A) 22 years
(B) 30 years
(C) 38 years
(D) 32 years
(E) None of these
Rationale: Answer
The average age of a group of 16 students is 20.
Therefore, the sum of the ages of all 16 of them = 16 * 20 = 320
When two new students join the group, the average age increases by 2. New average = 22.
Now, there are 18 students.
Therefore, the sum of the ages of all 18 of them = 18 * 22 = 396
Therefore, the sum of the ages of the two new students who joined = 396 - 320 = 76
And the average age of each of the two new students = 76/2 = 38 years.
Answer C
Answer: (C) 38 years
Question: Which of the following is NOT prime?
(A) 1,556,551
(B) 2,442,113
(C) 3,893,257
(D) 3,999,991
(E) 9,999,991
Rationale: 3,999,991 = 4,000,000 - 9 = (2000)^2 - 3^2
So this number is a product of two numbers other than 1 and itself. This means it is not prime. This must be the answer.
Let's take a look at (E) too.
9,999,991 = 10,000,000 - 9
Here the difference is that 10,000,000 is not a perfect square. It has odd number of 0s. So this would be a prime number.
Answer (D)
Answer: (D) 3,999,991
Question: A, B and C can do a work in 4 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
(A) 2 2/3
(B) 2 2/8
(C) 2 2/0
(D) 2 2/2
(E) 2 2/11
Rationale: Work done by all three of them in one day = 1/4 + 1/8 + 1/12 = 11/24
The number of days required = 24/11 = 2 2/11 days.
Answer:E
Answer: (E) 2 2/11
Question: There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is
(A) 1/5
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5
A
Answer: (A) 1/5
Question: There are some chickens and some chicken field. If we sell 75 chickens Then the feed will last 20 days longer.If we buy 100 chickens more, then the feed will get over before 15 days.What is the present number of chickens?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: let x=number of chicken,y=no of days,z= each day chicken's feed....so total feed=xyz then eqn 1 will be xyz=(x-75)(y+20)z.....
and eqn 2 will be xyz=(x+100)(y-15)z if we solve this two eqn we get x=300
ANSWER:C
Answer: (C) 300
Question: Insert the missing number.
2, 6, 12, 20, 30, 42, 56,72 (....)
(A) 22
(B) 38
(C) 72
(D) 66
(E) 90
Rationale: Explanation:
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7, 7 x 8, 8 x 9
So, the next number is 9 x 10 = 90.
Answer: E) 90
Answer: (E) 90
Question: The ratio of efficiency of A is to C is 5:3.The ratio of no.of days taken by B is to C is 2:3.A takes 6 days less than C,when A and C completes the work individually.B and C left the work after 2 days.the no of days taken by A to finish the remaining work?
(A) 4.5
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: A : B : C
Efficiency 10 : 9 : 6
No of days 9x : 10x : 15x
given=> 15x-9x = 6
hence, x = 1
Number of days taken by A = 9 and daily work done=10
Number of days taken by B= 10 and daily work done=9 (total work =90)
Number of days taken by C = 15 and daily work done=6
work done by B and C in initial 2 days =30
rest work =60
Number of days required by A to finish = 60/10=6 days
ANSWER:C
Answer: (C) 6
Question: When tossing two coins once, what is the probability of heads on both the coins?
(A) 3/4
(B) 2/4
(C) 1/3
(D) 1/4
(E) 1/2
Rationale: Since two coins are tossed, sample space = 4
Getting heads on both the coins=1
p(E) = 1/4 = 1/4
ANSWER:D
Answer: (D) 1/4
Question: The number of years of service of the eight employees in a production department are 15, 10, 9, 17, 6, 5, 14 and 16. What is the range in the number of years of service of the eight employees?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: = 17-5
= 12
Answer C
Answer: (C) 12
Question: L.C.M of two numbers is 192 and there H.C.F is 16. If one of them is 48. Find the other
(A) 32
(B) 64
(C) 48
(D) 68
(E) 78
Rationale: Explanation:
Product of two numbers = product of their L.C.M and H.C.F
48 x a = 192 x 16
a = (192 x 16)/48 = 64
Answer: Option B
Answer: (B) 64
Question: A Cistern is filled by pipe A in 8 hrs and the full Cistern can be leaked out by an exhaust pipe B in 12 hrs. If both the pipes are opened in what time the Cistern is full?
(A) 12 hrs
(B) 24 hrs
(C) 16 hrs
(D) 32 hrs
(E) None of these
Rationale: Explanation :
Pipe A can fill 1⁄8 of the cistern in 1 hour.
Pipe B can empty 1⁄12 of the cistern in 1 hour
Both Pipe A and B together can effectively fill 1⁄8-1⁄12= 1⁄24 of the cistern in 1 hour
i.e, the cistern will be full in 24 hrs. Answer : Option B
Answer: (B) 24 hrs
Question: Among the employees of a certain company, 52 percent of the employees are male and 48 percent are female. In this company 60 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?
(A)  0.4
(B)  0.3
(C)  0.5
(D)  0.6
(E)  0.7
Rationale: Much faster: draw 4 quadrants
______________Male (52%)_____Female (48%)
Married :__________60%____________40%
Not Married:_______30%____________50%
Therefore: the probability of picking one random person Not Married (he or she) is: 0,52 x 0,30 + 0,50 x 0,50 = 0,15 + 0,25 (approx.)
Solution: approx. 0,4 (answer A)
Answer: (A)  0.4
Question: There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 15 have taken a course in finance and 14 have taken a marketing course. Nine of the employees have taken exactly two of the courses and 3 employee has taken all three of the courses. How many of the 50 employees have taken none of the courses?
(A) 9
(B) 8
(C) 14
(D) 10
(E) 11
Rationale: 50 Employees. Counting every different attendand to the courses we have:
Accounting: 22
Finance: 15
Marketing: 14
Which would add up to 51 different attendands, which is not possible.
Now 9 have taken exactly 2 courses, which means that there are 9 less different attendands. Say that 9 of the Finance attentands also attended Accounting.
51-9= 42
3 Person has taken all three courses. As above, we subtract him from the number of different attendands. Since this time the person took all three courses, we have to substract him two times.
42-6= 36.
Answer : C
Answer: (C) 14
Question: Define r* by the equation r* = π-r. Then ((−π)*)* =
(A)  −2π
(B)  -1
(C)  −π
(D)  2π
(E)  4π
Rationale: for r* f(f(−π)) = f(π − (−π)) = f(π + π) = f(2π) = π − 2π = −π=C
Answer: (C)  −π
Question: In how many ways the word "DARKEST" can be arranged?
(A) 5040
(B) 4506
(C) 3450
(D) 8900
(E) Cannot be determined
Rationale: Explanation :
The required number of ways = 7!
= 5040
Answer : A
Answer: (A) 5040
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph Answer: A
Answer: (A) 1
Question: A chartered bank offers a five-year Escalator Guaranteed Investment Certificate.In successive years it pays annual interest rates of 4%, 4.5%, 5%, 5.5%, and 6%, respectively, compounded at the end of each year. The bank also offers regular five-year GICs paying a fixed rate of 5% compounded annually. Calculate and compare the maturity values of $1000 invested in each type of GIC. (Note that 5% is the average of the five successive one-year rates paid on the Escalator GIC.)
(A) 1276.28
(B) 1276.22
(C) 1276.29
(D) 1276.21
(E) 1276.23
Rationale: Explanation:
FV = $1000(1.04)(1.045)(1.05)(1.055)(1.06) = $1276.14
the maturity value of the regular GIC is
FV = $= $1276.28
Answer: A) 1276.28
Answer: (A) 1276.28
Question: Each side of a certain parallelogram has length 5. If the area of the parallelogram is 20. Which of the following is the measure of one of its angles?
(A) 30
(B) 45
(C) 53.13
(D) 90
(E) 120
Rationale: area of a parallelogram = b*h
b*h=20
h=20/5=4
sin theta =opp/hyp= 4/5
theta = sin inv of 4/5=53.13 deg
C
Answer: (C) 53.13
Question: January 1, 2008 is Wednesday. What day of the week lies on Jan 1, 2009?
(A) Saturday
(B) Wednesday
(C) Thursday
(D) Tuesday
(E) Friday
Rationale: Explanation:
Number of odd days in 2008 = 2 (since it is a leap year)
(we have taken the complete year 2008 because we need to find out the odd days from 01-Jan-2008 to 31-Dec-2008, that is the whole year 2008)
Given that January 1, 2008 is Wednesday.
Hence January 1, 2009 = (Wednesday + 2 odd days) = Friday
Answer: Option E
Answer: (E) Friday
Question: Find the Value of X :log(x+1) + (log(x-1) = log8
(A) 5
(B) 3
(C) 6
(D) 9
(E) 8
Rationale: Explanation:
log(x+1)(x-1) = log8
log(x^2-1) = log8
x^2-1 = 8
x^2 = 9
x = {-3, 3}
Testing for extraneous solutions eliminates -3 leaving you with:
x = 3
Answer B
Answer: (B) 3
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child ?
(A) 4 years
(B) 8 years
(C) 10 years
(D) 12 years
(E) None
Rationale: Solution
Let the ages of the children be x,(x+3),(x+6),(x+9) and (x+12) years.
Then,	x+(x+3)+(x+6)+(x+9)+(x+12)=50
5x=20
x=4.
Age of the youngest child	=4 years.
Answer A
Answer: (A) 4 years
Question: A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 23 mph, what is the speed of the plain in still air?
(A) 196
(B) 210
(C) 216
(D) 235
(E) 253
Rationale: The speed of the plane in still air = x miles/hour
The speed of the wind is 23 mph
Speed with the wind = (x + 23) mph
Speed against the wind = (x – 23) mph
Time = Distance/ Speed
According to the problem,
420/(x + 23) = 350/(x – 23)
420(x – 23) = 350(x + 23)
420x – 9660 = 350x + 805
420x – 350x = 8050 + 9660
70x = 17710
x = 17710/70
x = 253 ANSWER : E
Answer: (E) 253
Question: If the time is currently 1:30 pm, what time will it be in exactly 643 hours?
(A) 5:30 am
(B) 6:30 am
(C) 7:30 am
(D) 8:30 am
(E) 9:30 am
Rationale: 643 = 26(24) + 19/24
The time will be 19 hours later than 1:30 pm which is 8:30 am.
The answer is D.
Answer: (D) 8:30 am
Question: The ratio of the cost price and selling price is 2:3. The profit percent is?
(A) 20%
(B) 25%
(C) 50%
(D) 75%
(E) 100%
Rationale: Let the C.P. = $2x
Then S.P. = $3x
Then, Gain = 3x-2x = $x
Gain% = x/2x *100 = 50%
Answer is C
Answer: (C) 50%
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
(A) 12
(B) 15
(C) 18
(D) 24
(E) 26
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: (D) 24
Question: A boy traveled from the village to the post-office at the rate of 12.5 kmph and walked back at the rate of 2 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village.
(A) 5 km
(B) 7 km
(C) 9 km
(D) 10 km
(E) 12 km
Rationale: Explanation :
Solution: Average speed = 2xy/(x+y) km/hr
= (2*12.5*2)/(12.5+2) km/hr
= 50/14.5 km/hr.
Total distance = (50/14.5 * 29/5) km.
= 20 km.
Required distance = 20/2 = 10 km.
Answer : D
Answer: (D) 10 km
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 40%?
I will see what is the quickest way to solve it then I will provide the explanation
(A) 6
(B) 2
(C) 9
(D) 10
(E) 11
Rationale: The following approach might be the easiest one and less error prone.
We need on-time departure rate to be higher than 4/10, so it should be at least 5/11, which means that 5 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 5-3=2 subsequent flights need to depart on-time.
Answer: B.
Answer: (B) 2
Question: There are 5 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
(A) 19
(B) 20
(C) 30
(D) 32
(E) 25
Rationale: First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 5
and for second = 4
so total methods = 5*4 = 20
ANSWER:B
Answer: (B) 20
Question: Due to construction, the speed limit along an 4-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 3.12
(B) B) 8
(C) C) 2.49
(D) D) 15
(E) E) 24
Rationale: Old time in minutes to cross 4 miles stretch = 4*60/55 = 4*12/11 = 4.36
New time in minutes to cross 4 miles stretch = 4*60/35 = 4*12/7 = 6.85
Time difference = 2.49
Ans:C
Answer: (C) C) 2.49
Question: What least number must be subtracted from 427398 so that remaining no.is divisible by 10
(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
On dividing 427398 by 10 we get the remainder 8, so 8 should be subtracted
Answer: Option E
Answer: (E) 8
Question: A batsman in his 20th innings makes a score of 90, and thereby increases his average by 2. What is his average after the 20th innings? He had never been ’not out’.
(A) 52
(B) 37
(C) 39
(D) 43
(E) 42
Rationale: Average score before 20th innings
= 90 - 2 × 20= 50
Average score after 20th innings
=> 50 + 2 = 52
ANSWER:A
Answer: (A) 52
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 6m
(B) 5m
(C) 2m
(D) 8m
(E) 3m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6
= 2m.
Answer:D
Answer: (D) 8m
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 2880, find the total rent of the field.
(A) 3750
(B) 3550
(C) 4250
(D) 2250
(E) 13000
Rationale: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325
(72x)/325=2880 = x=(2880 x 325)/72 = 13000
Hence, total rent of the field is Rs. 13000.
Answer is E.
Answer: (E) 13000
Question: What is the remainder when 3^30 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1}
30 has the form 4k+2, so the units digit of 3^30 is 9.
The remainder when dividing by 5 is 4.
The answer is E.
Answer: (E) 4
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?
(A) 8.09%
(B) 6.07%
(C) 1.09%
(D) 6.09%
(E) 2.09%
Rationale: Explanation:
Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09%
Answer: D
Answer: (D) 6.09%
Question: The perimeter of an isosceles right triangle is 8 + 8 sq rt 2. What is the length of the hypotenuse of the triangle?
(A) 4
(B) 5.656
(C) 5
(D) 6
(E) 7
Rationale: side of triangle is a then perimeter = a+ a +a.sqrt2 ( right angle and pythagorus) =2a +a .sqrt 2 = 8 + 8 Sqrt2 or,
a. ( 2+ sqrt2) = 8(1 + sqrt2), a= 8*(1+sqrt2)/2+sqrt2 =8*2.414/3.414 =0.707*8 then hypotenuse = 5.656
B
Answer: (B) 5.656
Question: Shekar scored 76, 65, 82, 67 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?
(A) 65
(B) 69
(C) 75
(D) 85
(E) 90
Rationale: Explanation :
Average= (76+65+82+67+85)/5 = 375/5 =75
Hence average=75
Answer : C
Answer: (C) 75
Question: If cost of 15 eggs be 75 rupees, then find out the cost of 5 dozen eggs.
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: Cost of 15 eggs = 75 rupees
Cost of 1 egg = 75/15 = 5 rupees,
Cost of 5 dozens, i.e. 5 x 12 = 60 x 5 = 300
Answer : A
Answer: (A) 300
Question: If 5 < x < 9 and y = x + 3, what is the greatest possible integer value of x + y?
(A) 19
(B) 20
(C) 21
(D) 22
(E) 23
Rationale: x+y = x+x+3 = 2x+3
We need to maximize this value and it needs to be an integer.
2x is an integer when the decimal of x is .0 or .5
The largest such value is 8.5
Then x+y = 8.5 + 11.5 = 20.
The answer is B.
Answer: (B) 20
Question: A student was asked 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 should be the remainder in the place of x?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: We have (3+11+7+9+15+13+8+19+17+21+14+x) / 12 = 12
137+x = 144
x = 7
Answer is C
Answer: (C) 7