mathewhe/aqua_rat huggingface dataset:
Question: In a competitive examination batch A 7% candidates got selected from the total appeared candidates. Batch B also had an equal number of candidates appeared and 10% candidates got selected with 15 more candidates got selected than batch A. what was the number of candidates appeared from each batch?
(A) 100
(B) 360
(C) 500
(D) 240
(E) 120
Rationale: Explanation :
Solution: Let the number of candidates appeared from each batch be x.
then, 10% of x - 7% of x =15.
=>3% of x =15
=>3x/100 =15 => x =15*100/3 = 500
Answer : C
Answer: (C) 500
Question: One hundred gallons of fuel are purchased at $0.70 per gallon. The fuel is consumed at a rate of $0.40 worth of fuel per hour. At this rate, how many hours are required to consume the 100 gallons of fuel?
(A) 150
(B) 175
(C) 200
(D) 225
(E) 250
Rationale: The fuel is consumed at this rate: $0.40/$0.70 = 4/7 gallons per hour.
The time it takes to consume 100 gallons is: 100 / (4/7) = 175 hours.
The answer is B.
Answer: (B) 175
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
(A) 3.5
(B) 3.9
(C) 3.1
(D) 4.5
(E) 4.6
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E
Answer: (E) 4.6
Question: A man rows his boat 80 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 6
(B) 8
(C) 5
(D) 7
(E) 9
Rationale: Speed downstream = d/t = 80/(2 1/2) = 32 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (32 - 18)/2
= 7 kmph
Answer: D
Answer: (D) 7
Question: 20 men went to a restaurant. Ninteen of them paid Rs.70 each and the twentieth man paid Rs.90.25 more than the average of all the 20 men. What is the total bill ?
(A) 1495
(B) 1121
(C) 1298
(D) 1102
(E) 1191
Rationale: Let the average bill paid by twenty members = 'x'
But 19 men paid each = Rs. 70
20th man paid Rs. 90.25 more than the avg bill of 20 = x + 90.25
20x = 19(70) + x + 90.25
19x = 1330 + 90.25
19x = 1420.25
x = 1420.25/19 = Rs. 74.75
But the total bill = 20 x 74.75 = Rs. 1495
Answer: A
Answer: (A) 1495
Question: The average age of a husband and his wife was 23 years at the time of their marriage.After five years they have a one year old child.The average age of the family now is
(A) 19 years
(B) 23 years
(C) 28.5 years
(D) 29.3 years
(E) 19.3 years
Rationale: (h+w)/2 = 23 --> h+w = 46
after five years
H+W + C = 46+10+1 = 57
average age of family = 57/3 = 19
ANSWER:A
Answer: (A) 19 years
Question: A man traveled a total distance of 1800 km. He traveled one-third of the whole trip by plane and the distance traveled by train is one-half of the distance traveled by bus. If he traveled by train, plane and bus, how many kilometers did he travel by bus?
(A) 700
(B) 800
(C) 900
(D) 1000
(E) 1100
Rationale: total distance traveled = 1800 km.
distance traveled by plane = 600 km.
distance traveled by bus = x
distance traveled by train = x/2
x + x/2 + 600 = 1800
3x/2 = 1200
x = 800 km
The answer is B.
Answer: (B) 800
Question: The ages of two friends is in the ratio of 6:5.If the sum of their ages is 66. Then after how many years will the ratio become 7:6?
(A) 5
(B) 6
(C) 8
(D) 9
(E) 10
Rationale: the ratio of ages is 6:5 or we can say 6x and 5x
so , 6x+5x=66 (sum)
x=6
the ages are 6*6=36 and 6*5=30
let the years after which ratio will become 7:6 be y
36+y/30+y=7/6
the value of y will be 6
ANSWER:B
Answer: (B) 6
Question: For integers U and V, when U is divided by V, the remainder is Zero. Which of the following must be true?
(A) U and V share no common factors other than 1
(B) UV is odd.
(C) At least one of U and V is odd
(D) The sum U + V is odd
(E) U is odd
Rationale: At least one of U and V is odd
C
Answer: (C) At least one of U and V is odd
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 5 : 1, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
(A) 1 : 1
(B) 2 : 3
(C) 5 : 2
(D) 4 : 3
(E) 7 : 9
Rationale: Mixture A has a total of 5 + 3 = 8 parts. If in the final mixture this represents 4 parts, then the total number of parts in mixture B should be (8/4)*3 = 6.
So, we should take of mixture B a quantity with 5 and 1 parts, respectively.
This will give us in the final mixture (5 + 5) : (3 + 1), which means 10:4, or 5:2.
Answer C.
Answer: (C) 5 : 2
Question: In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 60 and a standard deviation of 10, which of the following is exactly 1.75 standard deviations more than the mean?
(A) a) 48
(B) b) 60
(C) c) 72
(D) d) 77.5
(E) e) 81
Rationale: Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.
Here, we're told two things about a group of numbers:
1) The average of the group is 60
2) The standard deviation of the group is 10
If you go 1 SDupfrom the average, you hit.....60+10 = 70
If you go 1 SDdownfrom the average, you hit.....60-10 = 50
If you go 2 SDsupfrom the average, you hit.....60+2(10) = 80
If you go 2 SDsdownfrom the average, you hit.....60-2(10) = 40
Etc.
Here, we're asked for the number that is EXACTLY 1.75 SDs above the mean....
1.75 SDsupwould be.....60 + 1.75(10) = 77.5
D
Answer: (D) d) 77.5
Question: The number of female students in a college in the previous year was 450. If in the current year the number of male students in the college doubled over that of the previous year but the proportion of male students halved, then what is the number of female students in the college in the current year?
(A) 1500
(B) 1800
(C) 2100
(D) 2400
(E) 2700
Rationale: Let x be the number of male students last year. The number of male students this year is 2x.
Let y be the number of female students this year.
x/450 = 2(2x/y)
y = 1800
The answer is B.
Answer: (B) 1800
Question: If a man crosses a 500 m long street in 5 minutes. What is his speed?
(A) 6 km/hr
(B) 7.1 km/hr
(C) 7.2 km/hr
(D) 8 km/hr
(E) 8.5 km/hr
Rationale: distance = 500 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=500/300=1.67m/s=1.67×18/5 km/hr=6 km/hr
A
Answer: (A) 6 km/hr
Question: A train is 360 meter long is running at a speed of 60 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 27 seconds
(B) 29 seconds
(C) 40 seconds
(D) 30 seconds
(E) 12 seconds
Rationale: Speed = 60 Km/hr = 60*(5/18) m/sec = 50/3 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (3/50) = 30 seconds
Answer:D
Answer: (D) 30 seconds
Question: How many three digit numbers can be formed in which if one digit is 3 then it must be follwed by 7 and repetetion of digits is not allowed
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: if 7 is to be followed by 3 , then the numbers will be either 37_ or _37.
for 37_ ,we have 370,371,372,374,375,376,378,379.
and for _37,we have 137,237,437,537,637,837,937.
therefore i think the answer is 15
ANSWER:D
Answer: (D) 15
Question: a person travels from his house to office from 11:10 am to 12:10 am and covers a distence of 1km. find the average speed of the person.
(A) 20.1km/h
(B) 20.5km/h
(C) 1km/h
(D) 22.1km/h
(E) 20.9km/h
Rationale: time=12:10-11:10= 1hour
distance= 1km
speed=1*1= 1km/h
ANSWER:C
Answer: (C) 1km/h
Question: A man purchases two watches at 560. He sells one at 15% profit and other at 10% loss. Then he neither gains nor lose. Find the cost price of each watch.
(A) 224, 300
(B) 200, 300
(C) 224, 336
(D) 200, 336
(E) None of these
Rationale: Here, in whole transaction, there is neither gains nor loss, therefore,
Amount of gain in one watch = Amount of loss in other watch
⇒ 0.15 × CP1 = 0.10 × CP2
⇒ CP1/CP2=0.10/0.15=23
Also CP1 + CP2 = 560
∴ CP1 = 2/2+3×560=224
and CP2 = 560 – 224 = 336
Answer C
Answer: (C) 224, 336
Question: What is the slope of a line perpendicular to 2y = -6x - 10?
(A) 3
(B) -3
(C) -1
(D) 1/3
(E) -1/3
Rationale: For lines to be perpendicular ,
slope of line 1 * slope of line 2 = -1
(-6/3) * (x) = -1
x = (1/3)
where x is slope of line 2
Ans - D
Answer: (D) 1/3
Question: A certain sum of money at simple interest amounted Rs.1023 in 12 years at 4% per annum, find the sum?
(A) 338
(B) 689
(C) 691
(D) 646
(E) 261
Rationale: 1023 = P [1 + (12*4)/100]
P = 691
Answer:C
Answer: (C) 691
Question: Raja spends 35% of his monthly income on household items, 20% of his monthly income on buying cloths, 5% of his monthly income on medicines and saves the remaining amount which is Rs. 15000. Find his monthly income.
(A) Rs. 40000
(B) Rs. 36000
(C) Rs. 37500
(D) Rs. 45000
(E) None of these
Rationale: Savings 40% - 15000
Expenditure 60 % - 22500
Total - 37500
Answer : C
Answer: (C) Rs. 37500
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
(A) 16 cm
(B) 18 cm
(C) 20 cm
(D) 22 cm
(E) 24 cm
Rationale: 2(l + b)	=	5
b	1
2l + 2b = 5b
3b = 2l
b =	2	l
3
Then, Area = 216 cm2
l x b = 216
l x	2	l	= 216
3
l2 = 324
l = 18 cm.
B
Answer: (B) 18 cm
Question: A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
(A) 150 m
(B) 180 m
(C) 200 m
(D) 240 m
(E) 250 m
Rationale: Speed =40 km/hr =40×(5/18)=(100/9) m/s Length of the train = (Speed x Time)
=(100/9*18) m
=200 m
Answer: C
Answer: (C) 200 m
Question: Antonio works in a bakery. He made cookies that cost $1.50 and made $255. How many customer did he have?
(A) 200 customers
(B) 85 customers
(C) 250 customers
(D) 100customers
(E) 170 customers
Rationale: A cookie costs $1.50 adding another one is $3. 255 divided by 3 is 85.85 x 2 is 170. He had 170 customers. The correct answer is E.
Answer: (E) 170 customers
Question: What approximate value should come in place of the question mark (?) in the following equation?40.75 Ã— 10.77 â€“ 18.75 Ã— 11.15 = (47 + ?) Ã— 4
(A) 10.454
(B) 11.454
(C) 12.454
(D) 14.454
(E) 18.454
Rationale: Solve using approximation
Answer A
Answer: (A) 10.454
Question: If any amount is distributed among A ,B and C so that the part of A is doubled that of the part of B and part of b is 2 time the part of C .Find the ratio among their parts.
(A) 1:2:4
(B) 4:2:1
(C) 8:4:1
(D) 2:4:1
(E) 4:3:2
Rationale: By the assumptions as mentioned we have A=2B and B=2C. So A=2(2C) and we get A=4C. We have, therefore, A:B:C = 4C:2C:C. By cancelling the ratio with C we have 8:4:1. The answer is, therefore, B.
Answer: (B) 4:2:1
Question: Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 748.
(A) 121 ,123 , 125 ,127
(B) 120 ,122 , 125 ,128
(C) 120 ,121 , 122 ,123
(D) 123 ,125 , 127 ,129
(E) None of these
Rationale: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two
x + (x + 2)
twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 748 is written as
x + (x + 2) + 4 x + 20 = 748
Solve for x and find all four numbers
x = 121 , x + 2 = 123 , x + 4 = 125 , x + 6 = 127
Answer A
Answer: (A) 121 ,123 , 125 ,127
Question: For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 6*/4* ?
(A) 5
(B) 5/4
(C) 4/5
(D) 1/4
(E) 1/5
Rationale: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.
Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.
Based on this definition....
IF....
K = 2
K* = (1/1)(1/2) = 1/2
IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6
We're asked to find the value of 5*/4*
Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....
5* = (1/1)(1/2)(1/3)(1/4)(1/5)
Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'
4* = (1/1)(1/2)(1/3)(1/4)
We're looking for the value of:
(1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)
Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:
1/4
D
Answer: (D) 1/4
Question: A man swims downstream 40 km and upstream 56 km taking 8 hours each time, what is the speed of the man in still water?
(A) 6
(B) 24
(C) 8
(D) 12
(E) 44
Rationale: 40 --- 8 DS = 5
? ---- 1
56 ---- 8 US = 7
? ---- 1 M = ?
M = (5 + 7)/2 = 6
Answer: A
Answer: (A) 6
Question: 35+15x1.5=?
(A) 75
(B) 51.5
(C) 57.5
(D) 5.25
(E) None of them
Rationale: =35+15 x 3/2
=35+45/2
=35+22.5
=57.5
Answer is C
Answer: (C) 57.5
Question: A man buys Rs. 52 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
(A) s. 12
(B) s. 15
(C) s. 18
(D) s. 21
(E) s. 39
Rationale: Dividend on Rs. 52 = Rs.	9/100	x 52 =Rs.	4.68	.
Rs. 12 is an income on Rs. 100.
Rs.	4.68	is an income on Rs.100/12 x 4.68	= Rs. 39.
Answer: Option E
Answer: (E) s. 39
Question: A 240 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 320 m
(E) 330 m
Rationale: Relative speed = (120 + 80) km/hr
=	(200 x(5/18))m/sec
=	(500/9)m/sec.
Let the length of the other train be x metres.
Then,	(x + 240)/9 = 500/9
x + 240 = 500
x = 260.
C
Answer: (C) 260 m
Question: What will come in place of the x in the following Number series? 73205, 6655, 605, 55, x
(A) 64789
(B) 73205
(C) 97654
(D) 45678
(E) 85567
Rationale: (B)
5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205
Answer: (B) 73205
Question: The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
(A) 69
(B) 78
(C) 96
(D) Either (a) or (c)
(E) none of these
Rationale: Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x - y = 3 or y - x = 3.
Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6.
Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9.
So, the number is either 96 or 69.
ANSWER : D
Answer: (D) Either (a) or (c)
Question: 1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member
(A) A.10%
(B) B.39%
(C) C.25%
(D) D.60%
(E) E.50%
Rationale: A,C is too low so I eliminated those answers, E, D was too high of a number, so I chose B as my final answer.B
Answer: (B) B.39%
Question: In a board game, a stack of 42 cards, 5 of which have pictures of fruit, are shuffled and then placed face down. If the first 2 cards selected do not have pictures of fruit, what is the probability that the third card selected will have a picture of fruit?
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/8
Rationale: After 2 cards have been selected, there are 40 cards remaining.
P(third card has a picture of fruit) = 5/40 = 1/8
The answer is E.
Answer: (E) 1/8
Question: The sum of three consecutive even numbers is 24. Find the middle number of the three?
(A) 14
(B) 16
(C) 18
(D) 24
(E) 34
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 24
6P = 24 => P = 4.
The middle number is: 4P = 16.
ANSWER:B
Answer: (B) 16
Question: When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.15
II.18.19
III. 17.16
(A)  I only
(B)  II only
(C)  III only
(D)  I and II only
(E)  I and III only
Rationale: Problem statement was difficult to parse. but some how I managed to understand what we can do.
1) x/y = 15 + 0.15
2) x/y = 18 + 0.19
3) x/y = 17 + 0.16
w.k.t x = yn (i.e Q) + yk=60 (i.e remainder)
therefore :
1) y*0.15=60 -- we can get y an integer.
2) y*0.19=60 -- we can't get y an integer.
3) y*0.16=60 -- we can get y an integer.
Therefore 1 and 3 are possible answers.
Ans E.
Answer: (E)  I and III only
Question: When the integer k is divided by 7, the remainder is 6. Which of the following expressions below when divided by 7, will have a remainder of 5?
I. 4k + 2
II. 6k + 4
III. 8k + 3
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: k = 7j + 6
4k + 2 = 28j + 24 + 2 = 28j + 21 + 5
6k + 4 = 42j + 36 + 4 = 42j + 35 + 5
8k + 3 = 56j + 48 + 3 = 56j + 49 + 2
The answer is D.
Answer: (D) I and II only
Question: A certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 50% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow
(A) a) 2
(B) b) 4.5
(C) c) 1.38
(D) d) 5.5
(E) e) 3
Rationale: If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).
Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.
Therefore 6k = 0.5 (11 + 4k)
=> k = 1.38
Therefore the plant grows by 1.38 feet every day.
Option (C)
Answer: (C) c) 1.38
Question: In how many ways can the letters {U, U, U, R, R,R} be arranged?
(A) 20
(B) 30
(C) 120
(D) 720
(E) 840
Rationale: My answer : A
There is 6! ways to arrange those letters in total, however letter U repeats 3! times and letter R repeats 3! times
=> the way to arrange without repeating = 6!/ [3!x3!] = 20
Answer: (A) 20
Question: Two trains 180 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.7
(B) 10.9
(C) 10.24
(D) 12.24
(E) 18.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 180 + 160 = 340 m.
Required time = 340 * 9/250
= 12.24 sec.
Answer:D
Answer: (D) 12.24
Question: What is the sum of natural numbers between 30 and 100
(A) 4615
(B) 4860
(C) 5000
(D) 5500
(E) 5550
Rationale: a = first number
l = last number
Sn = n/2[a + l]
between 30 and 100 numbers = 71 => 100 - 30 = 70 + 1 = 71
Sn = 71/2 Ã— 130 = 71 Ã— 65 = 4615
Answer : A
Answer: (A) 4615
Question: In how many different number of ways 5 boys and 5 girls can sit on a shopa which can accommodate 5 persons?
(A) 30240
(B) 2000
(C) 3024
(D) 3000
(E) None
Rationale: Option 'A'
10 p5 = 10x9x8x7x6= 30240
Answer: (A) 30240
Question: An bus covers a certain distance at a speed of 260 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 600 km/hr
(B) 720 km/hr
(C) 730 km/hr
(D) 750 km/hr
(E) 780 km/hr
Rationale: Distance = (260 x 5) = 1300 km.
Speed = Distance/Time
Speed = 1300/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1300 x 3 km/hr = 780 km/hr.
E
Answer: (E) 780 km/hr
Question: A sum of Rs. 12500 amounts to Rs. 17000 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 9%
(B) 5%
(C) 6%
(D) 8%
(E) 14%
Rationale: S.I. = (17000 - 12500) = Rs. 4500/-
Rate = (100 * 4500) / (12500 * 4) = 9%
ANSWER:A
Answer: (A) 9%
Question: In how many ways can a team of 11 be chosen out of a batch of 15 players?
(A) 1000
(B) 1245
(C) 1325
(D) 1415
(E) 1365
Rationale: required number of ways = 15C11 = 15C4 = 1365
Answer is E
Answer: (E) 1365
Question: An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 20%. How much will an air-conditioning unit cost in November?
(A) $458
(B) $470
(C) $474
(D) $484
(E) $491
Rationale: if its previous November (before discount) then price is $470.
but if its November of next year then
16% discount on $470=470(1-16/100)=$394.8
again a corrected raised price of 20% over $394.8=394.8(1+20/100)=473.76~$474
Ans C
Answer: (C) $474
Question: If by selling an article for Rs.60, a person loses 1/7 of money, what would he have gained or lost % by selling it for Rs.77?
(A) 6%
(B) 10%
(C) 14%
(D) 15%
(E) 20%
Rationale: Sol. CP - = EC7 = 70 1-7 6 77-70 % Profit = 100 = 10%
B
Answer: (B) 10%
Question: If two numbers are in the ratio 4:5. If 10 is added to both of the numbers then the ratio becomes 5:6 then find the smallest number?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Explanation:
4:5
4x + 10 : 5x + 10 = 5 : 6
6[4x + 10] = 5[5x + 10]
24x + 60 = 25x + 50
25x - 24x = 60 - 50
x = 10
Then smallest number is =4
4x = 40
Answer: Option D
Answer: (D) 40
Question: Fom the integer n, if n*n*n is odd, then what is true from below options?
(A) n is odd
(B) n is even
(C) n*n is even
(D) n*n is odd
(E) n is odd and n*n is even
Rationale: n is odd and n*n is even
Option E
Answer: (E) n is odd and n*n is even
Question: Baby Isabel plays with blocks. Each block is 2.4 inches tall. She has a collection of 30 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be?
(A) 67"
(B) 90"
(C) 72"
(D) 120"
(E) 151.7"
Rationale: 2.4"*30=72". Answer is C.
Answer: (C) 72"
Question: A does a work in 30 days and B does the same work in 10 days. In how many days they together will do the same work ?
(A) 5.5 days
(B) 6.5 days
(C) 7.5 days
(D) 8.5 days
(E) None of these
Rationale: Explanation:
Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/30
B's 1 day work = 1/10
(A+B)'s 1 day work =
(1/30+1/10)=2/15
So together they can complete work in 7.5 days.
Answer: C
Answer: (C) 7.5 days
Question: A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.
(A) 10 m * 5 m
(B) 15 m * 5 m
(C) 20 m * 5 m
(D) 25 m * 5 m
(E) None of these
Rationale: Explanation:
From the question, 2b+l = 30
=> l = 30-2b
Area=100m2=>l×b=100=>b(30−2b)=100b2−15b+50=0=>(b−10)(b−5)=0
Area=100m2
=>l×b=100
=>b(30−2b)=100
b2−15b+50=0
=>(b−10)(b−5)=0
b = 10 or b = 5
when b = 10 then l = 10
when b = 5 then l = 20
Since the garden is rectangular so we will take value of breadth 5.
So its dimensions are 20 m * 5 m
Option C
Answer: (C) 20 m * 5 m
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 mat-weavers in 16 days?
(A) 25
(B) 19
(C) 39
(D) 61
(E) 64
Rationale: Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers	4	:	16 :: 4 : x
Days	4:16
4 * 4 * x = 16 * 16 * 4
x =	(16 * 16 * 4)/(4 x 4)
x = 64.
Answer is E.
Answer: (E) 64
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 210, how many coins of each type are there?
(A) 20 coins
(B) 50 coins
(C) 100 coins
(D) 120 coins
(E) None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 210
⇒ 1.75x = 210 ⇒ x = 120 coins
Answer D
Answer: (D) 120 coins
Question: Given two fair dice, what is the probability G that the sum of their numbers is 4 if exactly one die shows a 3?
(A) a) 2/11
(B) b) 1/18
(C) c) 3/11
(D) d) 2/39
(E) e) 1/5
Rationale: If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.
G=2/11 would be the answer if 'at least one of the die shows a 3'.A
Answer: (A) a) 2/11