mathewhe/aqua_rat huggingface dataset:
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
( example 99 = 9+9 = 18=1+8=9, so #=9)
(A) 4/10
(B) 4/9
(C) 1/2
(D) 6/10
(E) 5/9
Rationale: First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability = 50/90 = 5/9
Correct answer E
Answer: (E) 5/9
Question: Lucy deposited $67600 in an investment fund that provided 16 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in months, did her investment earn a total interest of $5300?
(A) 90.5
(B) 92
(C) 93
(D) 90
(E) 96.1
Rationale: A = P + I = 67600 + 5300 = 72900
72900 = 67600(1 + 8/4*100)^(4t)
(729/676) = (102/100)^(4t)
t =7 1/2 yrs = 90 months
Answer: D
Answer: (D) 90
Question: For any positive x, y and z if x is n% of y and z is m% of y then what percentage Q must x be of z?
(A) (n/m)%
(B) (m × n)%
(C) (100 / [m × n]) %
(D) (100 × m/n)%
(E) (100 × n/m)%
Rationale: x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer Q is 100n/m %.E
Answer: (E) (100 × n/m)%
Question: Simplify: 0.6*0.6+0.6*0.6
(A) 0.52
(B) 0.42
(C) 0.48
(D) 0.64
(E) 0.46
Rationale: Given exp. = 0.6*0.6+(0.6*6) = 0.36+0.1 = 0.46
Answer is E.
Answer: (E) 0.46
Question: The number 95 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers?
(A) 9
(B) 10
(C) 15
(D) 18
(E) 20
Rationale: The only possible sum for 4 different squares of an integer with total sum number is 95 are :
49 + 36 + 9 + 1 = 95 which are the square from numbers : 7, 6, 3, 1 (total sum number is 17)
or
81 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 15)
hence the answer is (C)
Answer: (C) 15
Question: This is an ancient problem dating back to about 310 A.D.
Demochares had lived one-fourth of his life as a boy, one-fifth as a young, one-third as a man. and has spent thirteen years in his dotage. How old is Demochares?
(A) 44
(B) 53
(C) 75
(D) 60
(E) 50
Rationale: D
60
Demochares must be sixty years of age.
Answer: (D) 60
Question: A book is bought for Rs.600/- and sold at a profit of 10% find its selling price?
(A) s.740/-
(B) s.660/-
(C) s.680/-
(D) s.720/-
(E) s.620/-
Rationale: 100 % ------> 600 (100 * 6 = 600)
110 % ------> 660 (110 * 6 = 660)
Selling price = Rs.660/-
Option 'B'
Answer: (B) s.660/-
Question: Rekha took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 588 as interest at the end of the loan period, what was the rate of interest?
(A) 5
(B) 6
(C) 4
(D) 3
(E) 7
Rationale: Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 588
12R2 = 588
R2 = 49 => R = 7.
Answer:E
Answer: (E) 7
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 5.2 hrs
(B) 2.9 hrs
(C) 1.9 hrs
(D) 7.2 hrs
(E) 1.4 hrs
Rationale: Net part filled in 1 hour = (1/4 - 1/9) = 5/36
The cistern will be filled in 36/5 hrs i.e., 7.2 hrs.
Answer:D
Answer: (D) 7.2 hrs
Question: If P(32, 6) = kC (32, 6), then what is the value of k?
(A) 6
(B) 32
(C) 120
(D) 720
(E) None
Rationale: Since 32P6 = k32C6
⇒ 32/ ( 32-6 ) = k(32/ ( 32-6 )
⇒k = 6! = 720
Answer D
Answer: (D) 720
Question: In what time will a train 200 meters long cross an electric pole, if its speed is 128 km/hr
(A) 5 seconds
(B) 5.7 seconds
(C) 3 seconds
(D) 2.5 seconds
(E) None of these
Rationale: Explanation:
First convert speed into m/sec
Speed = 128*(5/18) = 35 m/sec
Time = Distance/speed
= 200/35 = 5.7 seconds
Option B
Answer: (B) 5.7 seconds
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 270
(B) 287
(C) 269
(D) 200
(E) 271
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer: A
Answer: (A) 270
Question: The area of a parallelogram is 243sq m and its altitude is three times the corresponding base. What is the length of the base?
(A) 4
(B) 9
(C) 10
(D) 4
(E) 12
Rationale: 3x * x = 243 => x
= 9
Answer: B
Answer: (B) 9
Question: There are 8 disks in a container that are numbered 23, 24, 25, 26, 28, 29, 30 and 31. 4 disks are randomly removed from the container, one after the other, without replacement. Then a list of 5 numbers containing the 4 numbers on the disks selected, together with the number 27 will be made. What is the probability that 27 is the median of the list of 5 numbers?
(A) 2/5
(B) 17/35
(C) 1/2
(D) 18/35
(E) 5/9
Rationale: we must consider that there are two ways to choose from A or B, and then two ways to choose each number from their respective groups:
Group A (23,24,25,26) and Group B (28,39,30,31). Then we saw that in order to have a median of 27 we need to have 2 from group and and 2 from group B.
The probability of that is 4/8 x 3/7 x 4/6 x 3/5 x (1/2) x (1/2) = 18/35.
Answer: D.
Answer: (D) 18/35
Question: Which of the following is closest to 1/6+1/66+1/666
(A) 1/4.5
(B) 1/7
(C) 1/5.67
(D) 1/9
(E) 1/8
Rationale: 1/6+1/66+1/666=0.16+0.015+0.0015=0.1765=1/5.665
Answer C
Answer: (C) 1/5.67
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 35 more. What was his original selling price?
(A)  $770
(B)  $550
(C)  $700
(D)  $1100
(E)  $840
Rationale: Let the original purchase price be X
So original selling price at 10% profit = 1.1X
If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)
He would have received $35 more in second scenario => 1.3(0.9X) - 1.1X = 35
=> 0.07X = 35
=> X = $500
Original purchase price = $500
Hence, original selling price (at 10% of profit) = 1.1(500) = $550
Option B
Answer: (B)  $550
Question: Craig sells major appliances. For each appliance he sells, Craig receives a commission of $50 plus 10 percent of the selling price. During one particular week Craig sold 6 appliances for selling prices totaling $3,620. What was the total of Craig's commissions for that week?
(A) $412
(B) $526
(C) $585
(D) $605
(E) $662
Rationale: Craig receives a commission of $50 on each appliance plus a 10% commission on total sales, thus his commission was 6*50 + 0.1*3,620 = 662.
Answer: E.
Answer: (E) $662
Question: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is?
(A) 127
(B) 688
(C) 200
(D) 121
(E) 123
Rationale: Let C.P. be Rs. x.
Then, 5% of x = 350 - 340 = 10
x/20 = 10 => x = 200
Answer: C
Answer: (C) 200
Question: The side of a square is increased by 15% then how much % does its area increases?
(A) 30.75 %
(B) 35.85 %
(C) 37.55 %
(D) 35.65 %
(E) 32.25 %
Rationale: a = 100 a2 = 10000
a = 115 a2 = 13225
----------------
10000 --------- 3225
100 -------? => 32.25 %
Answer:E
Answer: (E) 32.25 %
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
(A) 8 days
(B) 10 days
(C) 20/3 days
(D) 14 days
(E) 16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 Ã— 20/30 = 20/3 days
C)
Answer: (C) 20/3 days
Question: Three cannons are firing at a target. If their individual probabilities to hit the target are 0.4, 0.2, and 0.3 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94
(A) 0.06
(B) 0.336
(C) 0.21
(D) 0.29
(E) 0.94
Rationale: The probability that eachdoesn'thit is: 0.4, 0.2, and 0.3. When we have multiple independent events, we multiply the probabilities:
.6*.8*.7 = 0.336.
Option: B
Answer: (B) 0.336
Question: The average weight of three boys P, Q and R is 54 kg, while the average weight of three boys Q, S and T is 60 kg. What is the average weight of P, Q, R, S and T?
(A) 338
(B) 279
(C) 279
(D) 342
(E) 211
Rationale: Explanation:
Total weight of (P + Q + R) = {54*3} kg = 162 kg
Total weight of(Q + S + T) = (60 *3) kg = 180 kg
Adding both, we get : P + 2Q + S + R + T = (162 + 180) kg = 342 kg
So, to find the average weight of P, Q, R, S & T, we ought to know Q's weight, which is not given.
The data is inadequate.
ANSWER:D
Answer: (D) 342
Question: The length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencingthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 50 m
(B) 60 m
(C) 65 m
(D) 75 m
(E) 80 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: (B) 60 m
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 5^a and y = 7^b, which of the following is a possible units digit of xy?
(A) 1
(B) 4
(C) 5
(D) 7
(E) 8
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=5
a=2; X=25
a=3; X=125........ Units digit repeat in a cycle of 5......
Similarly, Finding all values ofYfor positive values ofb
When,
b=1; Y=7
b=2; Y= 49
b=3; Y= 343
b=4; Y=2041
b=5; Y=16807....... Units digit repeat in cycle of 7,9,3,1,7,9,3....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=5 and Y=7: Units digit of XY = 35
When X=5 and Y=9: Units digit of XY = 45
When X=5 and Y=3: Units digit of XY = 15
When X=5 and Y=1: Units digit of XY = 5
Only one possibilities for Units digit of XY i.e. 5
therefore answer is C
Answer: (C) 5
Question: Using all the letters of the word "FRIDAY", how many different words can be formed?
(A) A)7
(B) B)8!
(C) C)8
(D) D)7!
(E) E)5!
Rationale: Explanation:
Total number of letters = 5
Using these letters the number of 5 letters words formed is 5!.
Answer: Option E
Answer: (E) E)5!
Question: When 52416 is divided by 312, the quotient is 168. what will be the quotient when 522.416 is divided by 0.0168?
(A) 5
(B) 6
(C) 4
(D) 3
(E) 7
Rationale: for the 1st no. there are 3 digits after decimal
for the 2nd no. there are 5 digits after decimal
total no. of decimals = 8
req. no. of digits=(n-1)=(8-1)=7
ANSWER :E
Answer: (E) 7
Question: The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.850 find the number of laborers?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: 2450 850
\ /
1250
/ \
400 1200
1:3
1-->6
3-->?
18
ANSWER:E
Answer: (E) 18
Question: There is a road beside a river.Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first ?
(A) 5.4 km /hr
(B) 7.2 km /hr
(C) 8.4 km/hr
(D) 9.6 km /hr
(E) 4.6 km /hr
Rationale: speed of cycle both side on road will be same
average speed of cycle = 12 kmhr
downstream , boat speed =10+4= 14kmhr
upstream = 10- 4 = 6kmhr
averge of boat speeds =( 2* 14* 6)/14+6=8.4 kmhr
ANSWER:C
Answer: (C) 8.4 km/hr
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 187 m
(B) 278 m
(C) 279 m
(D) 270 m
(E) 872 m
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: (D) 270 m
Question: Find the odd man out. 1050, 510, 242, 106, 46, 16, 3
(A) 46
(B) 106
(C) 510
(D) 1050
(E) 16
Rationale: Explanation :
1050
(1050 - 30)/2 = 510
(510 - 26)/2 = 242
(242 - 22)/2 = 110
(110 - 18)/2 = 46
(46- 14)/2 = 16
(16- 10)/2 = 3
Hence, 110 should have come in place of 106
Answer : Option B
Answer: (B) 106
Question: If the area of circle is 616 sq cm then its circumference?
(A) 11
(B) 88
(C) 99
(D) 266
(E) 12
Rationale: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88 Answer: B
Answer: (B) 88
Question: ((1^(m+1))/(5^(m+1)))((1^18)/(4^18)) = 1/(2(10)^35)
What is m?
(A) 17
(B) 18
(C) 34
(D) 35
(E) 36
Rationale: ((1^(m+1))/(5^(m+1)))((1^18)/(4^18)) = 1/(2(10)^35)
((1/5)^(m+1) ) * ((1/2)^36) = 1/ (2 * (2*5)^35))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^(m+1)= (1/5)^35
((1/5)^(m+1) ) * ((1/2)^36) = 1/[(2^36)*(5^35)]
So, m=34
Answer C
Answer: (C) 34
Question: Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age
of all
(A) 15.5
(B) 15
(C) 16
(D) Cant be computed
(E) None of these
Rationale: Explanation:
As number of girls and boys is not given so result cant be computed
Answer: Option D
Answer: (D) Cant be computed
Question: Find the simple interest on Rs.567 for 7 months at 9 paisa per month?
(A) s.357.21
(B) s.322.12
(C) s.400
(D) s.278.9
(E) s.300
Rationale: Explanation:
I = (567*7*9)/100 = 357.21
Answer: Option A
Answer: (A) s.357.21
Question: Look at this series: 97, 97, 93, 93, 89, 89, 85, 85, ... What number should come next?
(A) 75
(B) 76
(C) 78
(D) 81
(E) 80
Rationale: Explanation:
In this series, each number is repeated, then 4 is subtracted to arrive at the next number.
Answer: Option D
Answer: (D) 81
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/3 of the remaining paint. How many gallons of paint has Joe used?
(A) 18
(B) 180
(C) 175
(D) 216
(E) 250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/3)*270 = 90 gallons
Total paint used = 180 gallons.
Option B
Answer: (B) 180
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: C99, F102, __, L108, O111, ... What number should fill the blank?
(A) I105
(B) J106
(C) K107
(D) L109
(E) M110
Rationale: A
I105
In this series, the letters progress by 3, and the numbers increase by 3.
Answer: (A) I105
Question: Which of the following numbers is between 1⁄3 and 2⁄5?
(A) .45
(B) .35
(C) .29
(D) .22
(E) .20
Rationale: 1/3 = .333...
2/5 = .4
The only number between these two is 0.35.
The answer is B.
Answer: (B) .35
Question: The average of 10 numbers is calculated as 18. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) A)16
(B) B)18
(C) C)19
(D) D)22
(E) E)24
Rationale: Explanation:
10 * 18 + 36 – 26 = 190=>190/10 = 19
C)
Answer: (C) C)19
Question: A coin is weighted so that the probability of heads on any flip is 0.2, while the probability of tails is 0.8. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?
(A) (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2
(B) (0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2
(C) (0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2
(D) (0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2
(E) (0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2
Rationale: Probability of Head, P(H) = 0.2
Probability of Tail, P(T) = 0.8
Tail will appear NO more than twice
i.e. favourable cases
2 Tails and 3 Heads, Probability = 5C2*(0.2)^3*(0.8)^2
1 Tail and 4 Heads, Probability = 5C1*(0.2)^4*(0.8)^2
0 Tail and 5 Heads, Probability = (0.2)^5
Required Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2
Answer: option A
Answer: (A) (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2
Question: If circles x and y have the same area and circle x has a circumference of 14π, half of the radius of circle y is:
(A) 16
(B) 8
(C) 4
(D) 3.5
(E) 1
Rationale: x be radius of circle x
y be radius of circle y
given:
pi*x^2 = pi*y^2
also,
2*pi*x = 14*pi
x =7
thus y =7
y/2 = 3.5
Ans: D
Answer: (D) 3.5
Question: If n is an integer number, and m=115n, then m must be divisible by which of the following?
(A) 11
(B) 15
(C) 23
(D) 25
(E) 230
Rationale: m=115n
m=5∗23n
So, m must be divisible by 5 & 23 both...
Among the given options only (C) satisfies.
Answer: (C) 23
Question: Ram draws a card randomly among card 1-23 and keep it back. Then Sam draws a card among those. What is the probability that Sam has drawn a card greater than ram.
(A) 11/27
(B) 11/24
(C) 11/23
(D) 11/21
(E) 11/22
Rationale: If Ram draws 1, then Sam can draw anything from 2 to 23 = 22 ways
If Ram draws 2, then Sam can draw anything from 3 to 23 = 21 ways
. . . .
. . . .
If Ram draws 23, Sam has no option = 0 ways.
Total required ways = 22 + 21 + 20 + . . . . + 0 = 22×23222×232 = 253
Total ways of drawing two cards = 23×23
Required probability = 253/529=11/23
Answer:C
Answer: (C) 11/23
Question: 3.5 can be expressed in terms of percentage as?
(A) 0.35%
(B) 3.5%
(C) 35%
(D) 350%
(E) NONE
Rationale: 3.5 = 35/10 = (35/10 * 100) = 350%
ANSWER:D
Answer: (D) 350%
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
(A) 1/121
(B) 1/213
(C) 1/216
(D) 2/211
(E) 3/213
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 2878
(B) 277
(C) 245
(D) 299
(E) 271
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer: C
Answer: (C) 245
Question: Tom can hit a target 3 times in 6 shots, Marry can hit the target 2 times in 6 shots & mike can hit 4 times in 4 shots. What is the probability that atleast 2shots hit the target ?
(A) 3/4
(B) 4/5
(C) 2/3
(D) 5/7
(E) 6/8
Rationale: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Answer: (C) 2/3
Question: A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is?
(A) 33
(B) 60
(C) 88
(D) 27
(E) 26
Rationale: Explanation:
length of the diagonal = 52*(15/60) =13m
sum of length and breadth = 68*(15/60) = 17m
\inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 }
area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169]
=1/2*120 = 60 sq meter
Answer: B) 60
Answer: (B) 60
Question: 3,14,39,_?
(A) 81
(B) 82
(C) 83
(D) 84
(E) 85
Rationale: n^3 + n^2 + n
Soln : 1^3+1^2+1 = 3
2^3+2^2+2 = 8+4+2 = 14
3^3+3^2+3 = 27+9+3 = 39
4^3+4^2+4 = 64+16+4 = 84
ANSWER:D
Answer: (D) 84
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 81. What is the difference between the two digits of that number?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Sol.
Let the ten’s digit be x and unit’s digit be y,
Then, (10x + y) - (10y + x) = 81 ⇔ 9 (x - y) = 81
⇔ x - y = 9
Answer E
Answer: (E) 9
Question: In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/6 . If the probability that a number 12 or larger is drawn is 1/2 , what is the probability that a number less than or equal to 20 is drawn?
(A)  1/18
(B)  1/6
(C)  2/3
(D)  1/2
(E)  5/6
Rationale: You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 12 or larger
Set 2: Number 20 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both)
1/2 + P(Set 2) - 1/6 = 2/3
P(Set 2) = 2/3
Answer (C)
Answer: (C)  2/3
Question: In how many ways can the word DAILY arranged?
(A) 720
(B) 100
(C) 620
(D) 120
(E) 150
Rationale: DAILY-there are 5 letters.
so we have 5 possible arrangements.
5!=5*4*3*2*1=120 was
Answer is option D
Answer: (D) 120
Question: The value of x + x(xx) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
(A) 10
(B) 2
(C) 8
(D) 6
(E) 4
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer is A.
Answer: (A) 10
Question: A cylinder of height h is 6/7 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
(A) 25%
(B) 50%
(C) 60%
(D) 70%
(E) 100%
Rationale: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 6/7
New cylinder 3/5
So 3/5/6/7 = 3/5*7/6= 0.70 or 70%.
Answer D
Answer: (D) 70%
Question: There is a 55 cm line marked at each centimeter and an insect is placed at every centimeter. 9 frogs are trained to jump a constant distance. The first one jumps 2 cm in every leap, the second one jumps 3 cm and so on until the 9th one jumps 10 cm in every leap and they eat any insect that is available at that spot. If all of them start from start line and finish the entire 55 cm, how many insects were still left after the race was over?
(A) 0
(B) 3
(C) 6
(D) 9
(E) 12
Rationale: Only the prime numbers greater than 10 and less than 55 were left.
That is 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, and 53.
The total is 12.
The answer is E.
Answer: (E) 12
Question: A certain sum of money at simple interest amounted Rs.1240 in 6 years at 4% per annum, find the sum?
(A) 998
(B) 1000
(C) 890
(D) 646
(E) 789
Rationale: 1240 = P [1 + (6*4)/100]
P = 1000
Answer: B
Answer: (B) 1000