mathewhe/aqua_rat huggingface dataset:
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/455
(B) 3/19
(C) 14/160
(D) 8/79
(E) 2/546
Rationale: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (Â²Câ‚)(â´Câ‚‚)/Â¹âµCâ‚ƒ
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455
Answer: A
Answer: (A) 12/455
Question: A restaurant spends one quarter of its monthly budget for rent and two thrid of the rest for food and beverages. What percentage of the budget does the restaurant spend for food and beverages?
(A) 23.5%
(B) 50%
(C) 35%
(D) 37.5%
(E) 75%
Rationale: Spend on rent = 1/4
Spend on food and beverage= 2/4 of remaining = 2/3*3/4= 1/2
so 1/2= 50.0%
B is the answer
Answer: (B) 50%
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 108 km/hr. What is the length of the platform?
(A) 229
(B) 240
(C) 288
(D) 480
(E) 221
Rationale: Speed = 108 * 5/18 = 30 m/sec.
Length of the train = 30 * 20 = 600 m.
Let the length of the platform be x m . Then,
(x + 600)/36 = 30 => x = 480 m.
Answer: D
Answer: (D) 480
Question: One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
I. 24
II. 20
III. 5
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II and II
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 8 and 5 are the base and height of triangle .
Area = 1/2 * 8 * 5 = 20
There is no lower limit on the area of any triangle whose only 2 sides are known . Area> 0
So we can also have triangle with area = 5
Suppose we want to take 8 as the hypotenuse in the right angled triangle , then one of the other sides(base or height) will be less than 8 .
Hence , product will be lesser than 20 .
Answer D
Answer: (D) II and III only
Question: A man took some money for borrowed, for 3 years the total will be Rs.5000 and 5 years it will be Rs.6000/-. Then how much amount he borrowed?
(A) s.2000/-
(B) s.2500/-
(C) s.2770/-
(D) s.2800/-
(E) s.3500/-
Rationale: 3 years --------> Rs.5000/-
5 years --------> Rs.6000/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.5000/- - Rs.1500/- = Rs.3500/-
P = Rs.3500/-
E
Answer: (E) s.3500/-
Question: In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?
(A) 20
(B) 30
(C) 24
(D) 12
(E) 26
Rationale: Explanation :
Number of matches won by the team in June: 30% of 60 = 18
After a phenomenal winning streak the average is 50%
Let the team played x matches continuously and won all of them to achieve an average winning percentage of 50%.
So total matches played by the team = (60+x)
Total matches won by the team = (18+x)
Total matches won = 50% of Total matches played
=> (18+x) = 50% of (60+x)
=> 18+x = (50/100)*(60+x)
=> 18+x = (1/2)*(60+x)
=> 36+2x = 60+x
=> x = 24
Answer : C
Answer: (C) 24
Question: For any 4 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) None of the above
Rationale: Let the 3 numbers be x, y and z.
Question: Which of the following is equivalent to (x + y + z)/3
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141
II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent
Answer: A
Answer: (A) I only
Question: A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to
pass a man standing at a crossing.
(A) 10 seconds
(B) 12 seconds
(C) 14 seconds
(D) 16 seconds
(E) None of these
Rationale: Explanation:
As we need to get answer in seconds, so never forget to convert speed into meter per second.
Speed = 30 km/hr = 30* 5/18 m/sec
= 25/3 m/sec
Distance = length of train = 100 meter
Required time =
DistanceSpeed=100253=100
∗
325=12sec
Answer: B
Answer: (B) 12 seconds
Question: In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/4 the number that used Kennedy Airport and 3 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?
(A)  18.6
(B)  9.3
(C)  6.2
(D)  3.1
(E)  1.03
Rationale: number of
passengers using Kennedy airport = 37/3 =~12.43
Passengers using Miami airport = 12.43/4=~3.1
passengers using logan airport = 3.1/3 =~1.03
so E
Answer: (E)  1.03
Question: In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket inchours, and the hot-water leak alone would fill the same bucket inhhours, wherec < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it tookthours to fill the bucket, which of the following must be true?
I. (c/2) < t < (h/2)
II. c < t < h
III. 0 < t < h
(A) a) I only
(B) b) II only
(C) c) I and III
(D) d) I and II
(E) e) III only
Rationale: I picked numbers for this problem
C = 2 hours
H = 3 hours
C<H
2 people working together formula is
1/C + 1/H = 1/t
1/2 + 1/3 = 1/t
t = 6/5 = 1.2
Substitute the values of C, H and t in the 3 choices given below
Only 1, 3 are valid.Therefore C is the best answer
Answer: (C) c) I and III
Question: A certain boxer has agreed to pay his opponent a fee of 2.5% of his total purse for every pound over the specified weight limit he weighs in. If the boxer pays his opponent a fee of $26,250 after weighing in eight pounds over the specified limit, what was the boxer's purse?
(A) $65,625
(B) $105,000
(C) $150,000
(D) $131,250
(E) $1,050,000
Rationale: .025*8 = .2
26250/.2 = $131,250
Answer: D
Answer: (D) $131,250
Question: The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
(A) 74
(B) 94
(C) 184
(D) 364
(E) None of these
Rationale: EXPLANATION
L.C.M. of 6, 9, 15 and 18 is 90.
Let required number be 90k + 4, which is multiple of 7.
Least value of k for which (90k + 4) is divisible by 7 is k = 4.
Required number = (90 x 4) + 4 = 364.
Answer D
Answer: (D) 364
Question: A triangle having three sides 10 cm, 17 cm, and 21 cm.A square is formed by one side lying on the longest side of the triangle.What is the maximum possible Area of the square found inside the triangle?
(A) 168/29
(B) 178/29
(C) 188/28
(D) 198/28
(E) 198/29
Rationale: s=1/2(10+17+21)=24
a=84
84=1/2*21*h
h=8
8/21=168/29
ANSWER:A
Answer: (A) 168/29
Question: The difference between two numbers is 2395. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is
(A) 120
(B) 239
(C) 476
(D) 523
(E) 526
Rationale: Let the smaller number be x.
Then, larger number = (2395 + x)
Therefore 2395 + x = (6x + 15)
‹=› 5x = 2380
‹=› x = 476.
ANSWER:C
Answer: (C) 476
Question: Five unbiased coin are tossed. What is the probability of getting atmost
one head?
(A) 31/24
(B) 31/34
(C) 31/32
(D) 31/35
(E) 31/36
Rationale: Here n(S)= 2^5
Let E=event of getting atmost one head =
n(E)= 31
P(E)=n(E)/n(S)=31/32
Answer option C)
Answer: (C) 31/32
Question: if 8^25 divided by 7 then what is reminder
(A) 25
(B) 1
(C) 0
(D) 2
(E) 3
Rationale: 8^25/7
8 can be written as 7*1+1
(7*1+1)^25/7
(ax+1)^n/a always gives the remainder 1
here a=7,x=1,n=25
Hence remainder is 1
ANSWER:B
Answer: (B) 1
Question: An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 4 ?
(A) 1/9
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: n(n+1) to be divisible by 4 either n or n+1 must be a multiples of 4.
In each following group of numbers: {1, 2, 3, 4}, {5, 6, 7, 8}, ..., {97, 98, 99, 100} there are EXACTLY 2 numbers out of 3 satisfying the above condition. For example in {1, 2, 3, 4} n can be: 3, or 4. Thus, the overall probability is 2/4 = 1/2.
Answer: C.
Answer: (C) 1/2
Question: A can do a work in 15 days B in 14 days and C in 16 days . If they work on it together then in how many days required to complete the work?
(A) 3360/210
(B) 3360/21
(C) 3360/674
(D) 3360/240
(E) 3360/224
Rationale: Person ( A ) ( B ) ( C ) (A+B+C)
Time - (15) ( 14 ) (16)
Rate - (224) (240) (210) (674)
Work - (3360) (3360) (3360) (3360)
therefore A+B+C requires (3360/674) days to complete entire work
= 3360/674
Answer is C
Answer: (C) 3360/674
Question: (0.12)(power 3) - (0.1)(power 3)/ (0.12)(power 2) + 0.012 + (0.1)(power 2) is:
(A) 0.68
(B) 0.086
(C) 0.86
(D) 0.068
(E) None of them
Rationale: Given expression
= (0.12) (power 3) - (0.1)(power 3) / (0.12)(power 2) + (0.12 x 0.1) + (0.1)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.12 - 0.1)
= 0.02
Answer is E.
Answer: (E) None of them
Question: Find the no.of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat?
(A) 7!
(B) 3!
(C) 9!
(D) 10!
(E) 11!
Rationale: Ans.(B)
Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places in 3P3 = 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways
Answer: (B) 3!
Question: 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally ?
(A) 18 litres
(B) 24 litres of wine
(C) 32 litres
(D) 42 litres
(E) None
Rationale: Solution
Let the quantity of the wine in the cask originally be x litres
then, quantity of wine left in cask after 4 operations
= [x(1- 8/x)4] litres.
Therefore x(1- 8/x)4 / x = 16/81 =› (1- 8/x)4 = (2/3)2
=› (x - 8 / x) = 2/3 =› 3x - 24 = 2x =› x = 24.
Answer B
Answer: (B) 24 litres of wine
Question: January 1, 2008 is Tuesday. What day of the week lies on Jan. 1, 2009 ?
(A) Sunday
(B) Monday
(C) Wednesday
(D) Thursday
(E) Friday
Rationale: The year 2008 is a leap year. So, it has 2 odd days.
1st day of the year 2008 is Tuesday (Given)
So, 1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.
answer :D
Answer: (D) Thursday
Question: A woman can row upstream 14 kmph and downstream 26 kmph. Find the rate of the stream and woman rate in still water.
(A) 4,20
(B) 20,20
(C) 8,20
(D) 20,5
(E) 6,20
Rationale: Explanation:
Please remember,
If a is rate downstream and b is rate upstream
Rate of current = 1/2(a-b)
Rate in still water = 1/2(a+b)
=> Rate of current = 1/2(26-14) = 6 kmph
=> Rate in still water = 1/2(26+14) = 20 kmph
Option E
Answer: (E) 6,20
Question: Find the odd man out
2, 4, 8, 16, 24, 32,64
(A) 2
(B) 4
(C) 24
(D) 32
(E) 64
Rationale: 2^1=2
2^2 = 4
2^3 =8
2^4=16
2^5=32
2^6=64
ANSWER:C
Answer: (C) 24
Question: If 148 is multiplied first by 163 and then by 236, Which of the following numbers would come at the unit's place?
(A) 8
(B) 6
(C) 4
(D) 3
(E) None of these
Rationale: Explanation:
148 * 163 * 236 = 8 * 3 * 6 = 4 at the unit's place.
When the numbers are multiplied, the unit digit of the final product is obtained as the product of the unit digits of individual numbers.
ANSWER: C
Answer: (C) 4
Question: A pupil's marks were wrongly entered as 85 instead of 33. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
(A) 30
(B) 104
(C) 20
(D) 25
(E) 26
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (85 - 33)
=> X/2 = 52
=> X = 104.
ANSWER:B
Answer: (B) 104
Question: If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word
"MANGO" would be
(A) 82357
(B) 89343
(C) 84629
(D) 82347
(E) 88347
Rationale: M-8
A-2
N-3
G-4
O-7
so for mango the code is 82347
ANSWER:D
Answer: (D) 82347
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
(A) 9/209
(B) 9/27
(C) 9/20
(D) 9/22
(E) 9/21
Rationale: Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.
Answer: C) 9/20
Answer: (C) 9/20
Question: Amit and Ananthu can do a work in 10 days and 20 days respectively. Amit started the work and left after 2 days. Ananthu took over and completed the work. In how many days was the total work completed?
(A) 18 days
(B) 20 days
(C) 23 days
(D) 25 days
(E) 27 days
Rationale: Amit’s one day’s work= 1/10
Amit’s 2 day’s work = 1/10 *2 = 1/5
Work left= 1-1/5 = 4/5
Ananthu’s one day’s work= 1/20
Ananthu can do work in = 4/5 *20 = 16 days
So total days = 16+2 = 18 days
ANSWER:A
Answer: (A) 18 days
Question: Ms. Williams sold two properties, X and Y, for $20,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
(A) $1600.67
(B) $1500.67
(C) $1450.67
(D) $1706.67
(E) $1666.67
Rationale: There is a property to solve such questions withCommon Selling PriceandCommon %gain and loss. such cases always result in a loss and...
Total %Loss = (Common Gain% or Loss%/10)^2
Hence Here Loss% = (20/10)^2 = 4%
which means he recovered only 96% of his investment which amount to a total revenue = 20000 + 20000 = 40000
i.e. 96% of cost = 40000
therefore, 4% of cost (Loss) = $1666.67
Answer: E
Answer: (E) $1666.67
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 10/21
(B) 11/21
(C) 2/7
(D) 5/7
(E) 6/7
Rationale: Explanation:
Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S)	= Number of ways of drawing 2 balls out of 7
= 7C2 `
=	(7 x 6)/ (2 x 1)
= 21.
Let E = Event of drawing 2 balls, none of which is blue.
n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.
= 5C2
=	(5 x 4) / (2 x 1)
= 10.
P(E) =	n(E)	/ n(S) = 10/21.
ANSWER IS A
Answer: (A) 10/21
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
(A) 120 sec
(B) 198 sec
(C) 178 sec
(D) 665 sec
(E) 276 sec
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer:A
Answer: (A) 120 sec
Question: In how many ways can a cricket eleven be chosen out of a batch of
15 players ?
(A) 1635
(B) 1365
(C) 1536
(D) 3651
(E) 1366
Rationale: Required number of ways = 15c11 = 15c(15-11) = 11c4
= 15x14x13x12/4x3x2x1 = 1365.
Answer B.
Answer: (B) 1365
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 17%
(B) 19%
(C) 18%
(D) 14%
(E) 16%
Rationale: Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer: C
Answer: (C) 18%
Question: hree unbiased coins are tossed. What is the probability of getting at least 2 tails?
(A) 0.5
(B) 0.8
(C) 0.2
(D) 0.9
(E) 0.1
Rationale: Explanation:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
E = {HTT, THT, TTH, TTT}
n(S) = 8
n(E) = 4
P(E) =n(E) / n(S) = 4/8 = 0.5
ANSWER: A
Answer: (A) 0.5
Question: In a weight-lifting competition, the total weight of Joe's two lifts was 1800 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?
(A) 225
(B) 275
(C) 325
(D) 350
(E) 700
Rationale: This problem is a general word translation. We first define variables and then set up equations.
We can define the following variables:
F = the weight of the first lift
S = the weight of the second lift
We are given that the total weight of Joe's two lifts was 1800 pounds. We sum the two variables to obtain:
F + S = 1800
We are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift. We express this as:
2F = 300 + S
2F – 300 = S
We can now plug in (2F – 300) for S into the first equation, so we have:
F + 2F – 300 = 1800
3F = 2100
F = 700
Answer is E.
Answer: (E) 700
Question: Ashwin rented a power tool from a rental shop. The rent for the tool was $25 for the first hour and $10 for each additional hour. If Ashwin paid a total of $125, excluding sales tax, to rent the tool, for how many hours did she rent it?
(A) 11
(B) 12
(C) 15
(D) 18
(E) 16
Rationale: 25 + 10n = 125
n = 10
Total time = n+1 hrs = 10+1 hrs = 11 hrs
Answer : A
Answer: (A) 11
Question: A thief is noticed by a policeman from a distance of 220 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 120
(B) 277
(C) 2987
(D) 278
(E) 271
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 220 - 100 = 120 m.
Answer: A
Answer: (A) 120
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
(A) 7
(B) 6
(C) 5
(D) 2
(E) 4
Rationale: A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
Answer: C
Answer: (C) 5
Question: The sum of money at compound interest amounts to thrice itself in 4 years. In how many years will it be 15 times itself?
(A) 8 years
(B) 16 years
(C) 2 years
(D) 6 years
(E) 3 years
Rationale: 100 ---- 300 --- 4
900 --- 4
1200----4
1500---4
16 years
Answer: B
Answer: (B) 16 years
Question: A bag contains 3 red, 3 green and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
(A) 5/7
(B) 11/14
(C) 16/21
(D) 19/28
(E) 23/35
Rationale: P(no red balls) = 6/9*5/8*4/7 = 5/21
P(at least one red ball) = 1 - 5/21 = 16/21
The answer is C.
Answer: (C) 16/21
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
(A) 7500
(B) 3600
(C) 8900
(D) 9000
(E) 5000
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
ANSWER A
Answer: (A) 7500
Question: John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 12 minutes earlier. How far is the office from his house?
(A) 3 2/5 Km
(B) 3 1/5 Km
(C) 4 Km
(D) 5 1/5 Km
(E) None
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 20/6
= 24/2 * 20/60
= 20/5 = 4 Km
C
Answer: (C) 4 Km
Question: Ten years ago, Q was half of R's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Let present age of P and Q be x and 2x respectively.
Ten years ago, Q was half of R's age
⇒(x−10)=2(2x−10)
⇒x−10=4x−20
⇒3x=10
⇒x=10/3
Total of their present ages=x+2x
=>10/3 + 20/3
=>30/3
=>10
ANSWER:B
Answer: (B) 10
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 227
(B) 240
(C) 987
(D) 178
(E) 171
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer:B
Answer: (B) 240
Question: Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?
(A) Rs.160/-
(B) Rs.170/-
(C) Rs.180/-
(D) Rs.190/-
(E) Rs.200/-
Rationale: A:B:C = 3:4:5
Total parts = 12
A's share is = 3 parts
12 -----> Rs.600/-
3 -----> Rs.150/-
A's total = 150 + 10 = Rs.160/-
A)
Answer: (A) Rs.160/-
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) 227
(B) 1668
(C) 5400
(D) 1688
(E) 1671
Rationale: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
Answer:C
Answer: (C) 5400
Question: If q>0.9, which of the following options can be the value of q?
(A) 0.9^2
(B) √(0.9)
(C) 0.09
(D) 0.9
(E) 0.9^3
Rationale: Lets take a few examples
When .2 is squared it gives .04
when .5 is squared it gives .25
When .9 is squared it gives .81
So raising a fraction to its power of 2 or 3 only reduces the value of the fraction
This is because
.2 = 2/10
.2^2= 4/100
.2^3=8/1000
Since the denominator gets an extra 0 each time u increase the power , it is going to drag the value down
But if you just think about the opposite case :
Then we can see , if squaring a fraction diminish its value, then taking the square root of it will again increase its value
that is √(0.04) will give you back 0.2
so √(0.04) > 0.04
so obviously diminishing the power will appreciate the value
So q √(0.9) > 0.9
Hence Correct Answer is (B)
Answer: (B) √(0.9)
Question: After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
(A) 20 days
(B) 19 days
(C) 10 days
(D) 12 days
(E) 15 days
Rationale: 1/3 ---- 6
1 -------? A = 18
R = 1/18 * 60/100 = 1/30
1 ----- 1/30--- 2/3 ---- 20 days
ANSWER A
Answer: (A) 20 days
Question: After deducting a commission of 5% a T.V. set costs Rs. 9595. Its gross value is ?
(A) Rs. 10000
(B) Rs. 10074.75
(C) Rs. 10100
(D) None of these
(E) Cannot be determined
Rationale: Answer
∵ 95% of gross value = 9595
∴ gross value = (9595 x 100)/95 = 10100
Correct Option: C
Answer: (C) Rs. 10100
Question: During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 105 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?
(A) 280
(B) 320
(C) 360
(D) 420
(E) 480
Rationale: Easy 280 is the answer.
3/4 ( x/2) = 105
x = 105 * 8 /3 = 280.
Answer A
Answer: (A) 280