mathewhe/aqua_rat huggingface dataset:
Question: A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B ?
(A) 1100
(B) 800
(C) 1400
(D) 1200
(E) None of them
Rationale: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 6600 x (2/11))= Rs. 1200.
Answer is D.
Answer: (D) 1200
Question: The average salary of all the employees in a small organization is Rs 8,000. The average salary of 7 technicians is Rs 12,000 and the average salary of the rest is Rs 6,000. The total number of employees in the organisation is?
(A) 21
(B) 20
(C) 26
(D) 22
(E) 25
Rationale: Let total number of employees be X.
Then, 8000 x X = 7 x 12000 + (X - 7) x 6000
X = 26.
Thus, the total number of employees in the organization is 26.
ANSWER:C
Answer: (C) 26
Question: In a stack of boards at a lumber yard, the 24th board counting from the top of the stack is immediately below the 14th board counting from the bottom of the stack. how many boards are in the stack?
(A) 36
(B) 46
(C) 55
(D) 54
(E) 42
Rationale: 1 2 3 ... 14 15 16 ...................
..............24 23 ................. 1
So the number of boards = 24+12 =36
Option: A
Answer: (A) 36
Question: If $100 invested at a certain rate of simple interest amounts to $140 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?
(A) $190
(B) $180
(C) $200
(D) $240
(E) $270
Rationale: 100 amounts to 140 in 3 years.
i.e (principal + interest ) on 120 in 3 years = 140
100 + 100*(r/100)*(3) = 140 => r = 40/3
150 in 6 years = principal + interest
= 150 + 150*(r/100)*(6)
= 270
Answer is E.
Answer: (E) $270
Question: A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 245, then how much amount should C pay as his share of rent?
(A) 35
(B) 45
(C) 25
(D) 63
(E) 55
Rationale: A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=245×9/35=7×9=63
Answer is D
Answer: (D) 63
Question: The average age of A and B is 30 years. If C were to replace A, the average would be 25 and if C were to replace B, the average would be 40. What are the age of A, B and C?
(A) 45,15,35
(B) 35,15,45
(C) 30,25,53
(D) 40,30,25
(E) None of the above
Rationale: Given A + B = 60â€¦(i)
C + B = 50 â€¦ (ii)
A + C = 80â€¦(iii)
(i) + (ii) + (iii) â‡’ A + B + C = 95â€¦(iv)
from (i) and (iv), we get
C = 35years
âˆ´ B = 15 years and A = 45 years
Answer A
Answer: (A) 45,15,35
Question: Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio Q of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job?
(A) 5 to 1
(B) 10 to 7
(C) 1 to 5
(D) 7 to 10
(E) 9 to 10
Rationale: Solutioning this exercise can be facilitated by using a R T W (rate time work) table:
We translate the exercise into the table:
R T W
X t/2 1
Y t 1
Z (t/2*3/2 =3t/4) 1
From this table we find the rates
Rx = 2/t
Ry = 1/t
Rz = 4/3t
The Q is what is the ratio of (Tx + Ty) / (Ty + Tz)
Rx + Ry = 2/t + 4/3t = 6/3t+4/3t = 10/3t
Ry+Rz = 1/t + 4/3t = 3/3t + 4/3t = 7/3t
The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7
Since Time Ratio Q is the inverse of work, the the answer is 7 to 10
CORRECT ANSWER D
Answer: (D) 7 to 10
Question: What is the sum of all the composite numbers up to 22?
(A) 228
(B) 277
(C) 153
(D) 132
(E) 281
Rationale: Explanation:
4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 +21= 153
Answer: C
Answer: (C) 153
Question: 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
(A) 24
(B) 77
(C) 88
(D) 29
(E) 21
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
27 : 36 :: 18 : x
[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
{\color{Blue} x=\frac{36\times 18}{27}}
x = 24
So 24 days will be required to get work done by 27 men.
Answer: A) 24 days
Answer: (A) 24
Question: Vijay lent out an amount Rs. 10000 into two parts, one at 8% p.a. and the remaining at 10% p.a. both on simple interest. At the end of the year he received Rs. 890 as total interest. What was the amount he lent out at 8% pa.a?
(A) 5529
(B) 5500
(C) 5529
(D) 5502
(E) 5029
Rationale: Let the amount lent out at 8% p.a. be Rs. A
=> (A * 8)/100 + [(10000 - A) * 10]/100 = 890
=> A = Rs. 5500.Answer:B
Answer: (B) 5500
Question: When 999^500 is divided by 5, the remainder is
(A) 0
(B) remainder is 1
(C) 2
(D) 3
(E) 4
Rationale: 999^500 is to be divided by 5
We can reduce the number to 4^500 (as the remainder of 999/5 is 4 and we can get the same remainder for 4^500 and 999^500 regardless of which is divided 5 )
Now, let's notice the pattern of remainders of powers of 4 when divided by 5
R{(4^1)/5} = 4
R{(4^2)/5} = 1
R{(4^3)/5} = 4
R{(4^4)/5} = 1
and so on
So, even powers of 4 give a remainder of 1
Hence, R{(4^500)/5} will be 1
R{(999^500)/5} will also be 1
Correct Option : B
Answer: (B) remainder is 1
Question: A factory has 500 workers, 10 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?
(A)  3
(B)  10
(C)  25
(D)  30
(E)  60
Rationale: Currently the factory has 0.10*500=50 women.
After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 110-50=60 more women.
Answer: E.
Answer: (E)  60
Question: If x, y, and z are positive integers, and 2x = 5y = 8z, then the least possible value of x + y + z is
(A) 15
(B) 28
(C) 33
(D) 42
(E) 60
Rationale: Take LCM of 2,5 and 8 = 40
Now 2x = 40 => x =20
5y = 40 => y = 8
8z = 40 => z =5
20+8+5 = 33.
Option C.
Answer: (C) 33
Question: A secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ?
(A) 25 min
(B) 32 min
(C) 33 min
(D) 34 min
(E) 35 min
Rationale: at start one person will tell to 2 persons, it will take 5 min, now that 1+2 = 3 persons will tell this to next 6 persons, then 1+2+6 = 9 persons will tell to next 18 persons, then 1+2+6+18 = 27 persons to 54 similarly 1+2+6+18+54 = 81 persons will tell this to 162 persons similarly 1+2+6+18+54+162 = 243 persons will tell this to 486 persons, upto this step total persons who have listened this secret = 2+6+18+54+162+486 = 728, and total time taken upto this step = 5*6 = 30 min, now next 5 min will be sufficient to tell this message to next 40 persons so total time taken = 35 min
ANSWER:E
Answer: (E) 35 min
Question: 9, 12, 11, 14, 13, ?, 15
(A) 16
(B) 12
(C) 14
(D) 17
(E) 20
Rationale: A
16
Alternatively, 3 is added and one is subtracted.
Answer: (A) 16
Question: In a game of 70 points, A can give B 5 points and C 25 points. then how many points can B give C in a game of 50?
(A) 9.38
(B) 8.38
(C) 15.38
(D) 13.38
(E) 16.38
Rationale: In a game of 70 points,A give B 5 points and c 25 points means B=65,C=45
In 65 points B give 20 since 65-45=20
In 50 points B gives=50*20/65=15.38
ANSWER:C
Answer: (C) 15.38
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 26%
(B) 20%
(C) 21%
(D) 29%
(E) 22%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: (B) 20%
Question: A fruit seller sells mangoes at the rate of Rs.11 per kg and thereby loses 10%. At what price per kg, he should have sold them to make a profit of 10%?
(A) Rs.13.44
(B) Rs.12
(C) Rs.12.25
(D) Rs.12.31
(E) None
Rationale: Solution
90 : 11 = 110 : x
x= (11Ã—110/90)
= Rs.13.44
Hence, S.p per Kg	= Rs.13.44
Answer A
Answer: (A) Rs.13.44
Question: If 4 spiders make 4 webs in 4 days, then 1 spider will make 1 web in how many days?
(A) 4
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:4
Webs 4:1
1 x 4 x x = 4 x 1 x 4
=> x= 4
Answer is A
Answer: (A) 4
Question: The three sides of an acute angled triangle (all in cms) are 12, 19 and k. How many integer values can k take?
(A) 23
(B) 22
(C) 15
(D) 8
(E) 7
Rationale: In acute angle triangles all angles in the triangle should be less than 90.
The maximum length of k can be when it is the hypotenuse of the triangle.
So, k= sqrt(12^2 + 19^2) = 22.5 (approx)
The maximum length of k can be when side of length 12 is the hypotenuse of the triangle.
So, k = sqrt (19^2 - 12^2) = 14.7 (approx)
So, k>14.7 and k<22.5.
Hence, possible values for k can be 15,16,17,18,19,20,21 and 22. Total 8 values.
Answer D.
Answer: (D) 8
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 100, the runs scored by B are?
A. 15 B. 18
(A) 22
(B) 24
(C) 99
(D) 77
(E) 24
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 100 = 24
Answer: B
Answer: (B) 24
Question: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 60 ounces of this substance?
(A) 27
(B) 36
(C) 25
(D) 64
(E) 147
Rationale: 112 ounces of a substance has a volume of 48 cubic inches
60 ounces of a substance has a volume of (48/112)*60 = 25 cubic inches
Answer A
Alternatively , we can use estimation
112 ounces of a substance has a volume of 48 cubic inches
56 ounces of a substance has a volume of 24 cubic inches
Therefore , 60 will have a volume a little more than 24 ,that is 25
C
Answer: (C) 25
Question: There are 3 red shoes, 2 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
(A) 3/5
(B) 2/9
(C) 5/9
(D) 4/9
(E) 2/3
Rationale: total 5 from take one.
5c1=5
red 3 from one
3c1=3
3/5
ANSWER:A
Answer: (A) 3/5
Question: X does a work in 20 days. Y does the same work in 40 days. In how many days they together will do the same work?
(A) 10
(B) 12
(C) 20
(D) 30
(E) 13.33
Rationale: X's 1day's work= 1/20
Y's 1 day's work=1/40
(X+Y)'s 1day's work= (1/20+1/40)=1/13.33
both together will finish the work in 13.33 days.
correct option is E
Answer: (E) 13.33
Question: If the sum of the two numbers is 22 and the sum of their squares is 404, then the product of the numbers is:
(A) 40
(B) 44
(C) 80
(D) 88
(E) 84
Rationale: Let the numbers be x and y.
Then, (x + y) = 22 and x2 + y2 = 404
Now,
2xy = (x + y)2 - (x2 + y2)
2xy= 222 - 404 = 484 - 404 = 80
xy = 40
ANSWER:A
Answer: (A) 40
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150 meter
(B) 145 meter
(C) 140 meter
(D) 135 meter
(E) 130 meter
Rationale: Explanation:
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train(Distance) = Speed * Time
=50/3âˆ—9=150meter
ANSWER IS A
Answer: (A) 150 meter
Question: What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, 12m 95cm?
(A) 25 cms
(B) 30 cms
(C) 35 cms
(D) 38 cms
(E) 45 cms
Rationale: HCF of 7m, 3m 85cm, 12m 95cm is 35 cms.
ANSWER:C
Answer: (C) 35 cms
Question: Which of the following is equal to 10^-(-2)^4?
(A) 1/(10^14)
(B) 1/(10^16)
(C) 1/(10^12)
(D) 1/(10^8)
(E) 1/(10^6)
Rationale: 10^-(-2)^4 => 10^-(-2^4) => 10^-(16) = 1/(10^16)
Answer : B
Answer: (B) 1/(10^16)
Question: The population of a town is 231400. If it increase at the rate of 3% per annum. What will be its population for 2years hence?
(A) 200000
(B) 245492
(C) 194582
(D) 194481
(E) 215460
Rationale: population after 2years = 231400*(1+ 3/100)^2 = 245492
Answer is B
Answer: (B) 245492
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) 16%
(B) 17%
(C) 18%
(D) 58%
(E) 13%
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: The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?
(A) 6
(B) 7
(C) 8
(D) 4
(E) 1
Rationale: Let the numbers x, x + 2, x + 4, x + 6 and x + 8
Then, [x + (x + 2) + (x + 4) + (x + 6) + (x + 8)]5 = 61
or 5x + 20 = 305 => x = 57
So, required difference = (57 + 8) - 57 = 8.
Answer: C
Answer: (C) 8
Question: The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 18-inch screen would be how many square inches greater than the area of a square 16-inch screen?
(A) 2
(B) 4
(C) 34
(D) 38
(E) 40
Rationale: Pythogoras will help here!
let the sides be x and diagonal be d
Then d ^2 = 2x^2
and
Area = x^2
Now plug in the given diagonal values to find x values
and then subtract the areas
Ans will be 18^2/2 - 16^2 /2 = 68 /2 = 34
Ans C.
Answer: (C) 34
Question: Find the area of a parallelogram with base 14 cm and height 24 cm.
(A) 336
(B) 384
(C) 345
(D) 244
(E) 242
Rationale: Area of a parallelogram = base * height = 14 * 24 = 336 cm2
Answer: Option A
Answer: (A) 336
Question: How many positive integers less than 300 can be formed using the numbers 1, 2, 3 a for the digits?
(A)  30
(B)  52
(C)  66
(D)  68
(E)  84
Rationale: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
Number of possibilities = 3*3*3 = 27.
Then, just add up the number of 1 digits numbers = 3, so total is 27+3 = 30.
Answer: A
Answer: (A)  30
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 17 ways
(B) 19 ways
(C) 30 ways
(D) 16 ways
(E) 11 ways
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer:C
Answer: (C) 30 ways
Question: A bus travels first one-fourth of the distance with a speed of 9 km/hr, next one fourth of the distance with 15 km/hr, third one-fourth distance with a speed of 20 km/hr and last one fourth with 30 km/hr. The average speed of the car for the whole journey is:
(A) 19.09 km/hr
(B) 29.09 km/hr
(C) 39.09 km/hr
(D) 49.09 km/hr
(E) None of these
Rationale: Explanation :
Let whole distance traveled be x
and average speed of the car be y
=> (x/4)/10+(x/4)/20+(x/4)/30+(x/4)/40=x/y
=> 1/10+1/20+1/30+x/40=4/y
=> (24+12+4+3)/240=4/y
=> 33/240=4/y
=> y=29.09
Answer : B
Answer: (B) 29.09 km/hr
Question: The sum of the square of the three consecutive even natural numbers is 1460. Find the numbers?
(A) 18, 20, 22
(B) 20, 22, 24
(C) 22, 24, 26
(D) 24, 26, 28
(E) None of these
Rationale: Three consecutive even natural numbers be 2x - 2, 2x and 2x + 2.
(2x - 2)2 + (2x)2 + (2x + 2)2 = 1460
4x2 - 8x + 4 + 4x2 + 8x + 4 = 1460
12x2 = 1452 => x2 = 121 => x = ± 11
As the numbers are positive, 2x > 0. Hence x > 0. Hence x = 11.
Required numbers are 20, 22, 24.
ANSWER:B
Answer: (B) 20, 22, 24
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
(A) 2 hrs 15 min
(B) 4 hrs 24 min
(C) 5 hrs
(D) 3 hrs
(E) 2 hrs
Rationale: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
ANSWER:D
Answer: (D) 3 hrs
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
(A) 3:5
(B) 3:4
(C) 3:9
(D) 3:1
(E) 3:2
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4,Answer: B
Answer: (B) 3:4
Question: The present population of a town is 4320. Population increase rate is 20% p.a. Find the population of town before 2 years?
(A) 2500
(B) 2100
(C) 3500
(D) 3000
(E) 2050
Rationale: P = 4320
R = 20%
Required population of town = P/(1 + R/100)^T
= 4320/(1 + 20/100)^2
= 4320/(6/5)^2
= 3000(approximately)
Answer is D
Answer: (D) 3000
Question: An even number, total of whose digits is 27, is always divisible by
(A) 14
(B) 9
(C) 7
(D) 6
(E) None of these
Rationale: Explanation:
An even number is always divisible by 2.
Further, any number sum of whose digits is 27 ie,
(2 + 7 = 9) is always divisible by 9.
.: The number is divisible by both 2 and 9.
.: The number is divisible by 2 x 9 = 18
Answer: Option E
Answer: (E) None of these
Question: If q and y are both odd prime numbers and q < y, how many distinct positive integer factors does 2qy have?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Since 2qy prime factors are q^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.D
Answer: (D) 8
Question: Find the term next in series..
1,1/2,3/2,2,5,1/3,16/3,15,12,1/4,25/4,?
(A) 48
(B) 58
(C) 40
(D) 43
(E) 44
Rationale: [1,1/2,3/2,2],[5,1/3/16/3,15],[12,1/4,25/4,x]
1+1/2=3/2......1/1/2=2
5+1/3=16/3.....5/1/3=15
12+1/4=25/4....12/1/4=48
ANSWER:A
Answer: (A) 48
Question: If a man lost 4% by selling oranges at the rate of 24 a rupee at how many a rupee must he sell them to gain 44%?
(A) 16
(B) 8
(C) 9
(D) 4
(E) 3
Rationale: 96% ---- 24
144% ---- ?
96/144 * 24 = 16
Answer: A
Answer: (A) 16
Question: A 270 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
(A) 210m
(B) 220m
(C) 230m
(D) 240m
(E) 250m
Rationale: Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+270/9=500/9
x=230
Ans is 230m
ANSWER:C
Answer: (C) 230m
Question: January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?
(A) Saturday
(B) Wednesday
(C) Thursday
(D) Saturday
(E) None of these
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 Tuesday
Hence January 1, 2009 = (Tuesday + 2 odd days) = Thursday
Answer : Option C
Answer: (C) Thursday
Question: If Robert got marks in 6 subjects= {50, 62, 66,74, 80, 82}, what is the total mean and median of the marks ?
(A) 160
(B) 139
(C) 100
(D) 121
(E) 150
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (50+ 62+ 66+74+ 80+ 82)/6 = 69
Median = (50 + 80)/2 = 70
Total = 139
Option B
Answer: (B) 139
Question: There are 450 birds at a small zoo. The number of birds is 5 times the number of all the other animals combined. How many more birds are there than non bird animals at the zoo?
(A) 400
(B) 360
(C) 270
(D) 180
(E) 90
Rationale: Total birds = 450 = 5 * Other Animals (X)
or X = 90.
So, Difference in Birds and X = 450-90 = 360.
Answer is B.
Answer: (B) 360
Question: Given a set of n rays in a plane, we define a reversal as the operation of reversing precisely one ray and obtaining a new set of n rays.
Q1: if n = 2001 and if k reversals are performed such that all the rays are reversed, then a possible value of k is
a. 4000 b. 4002 c. 2011 d. 1999
(A) 2336
(B) 2011
(C) 1366
(D) 288
(E) 1232
Rationale: there are n rays. If we reverse all of them, we would have a complete reversed set after n reversals. After that any reversal that we perform has to be undone with another reversal to obtain complete reversal. We can have a complete reversal after k reversals if k = n + 2m (m ∈ N). i.e., k could be some number greater than (or equal to) n and of the same type (even/odd)
So n = 2001 then k = 2001 + 2m
So k = 2011
Answer.B
Answer: (B) 2011
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5
(B) 2.9
(C) 2.6
(D) 2.1
(E) 2.2
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer:A
Answer: (A) 2.5
Question: What is 10-8+6-4+...+(-10)?
(A)  0
(B)  5
(C)  2
(D)  14
(E)  16
Rationale: The expression considers all even numbers between 10 and -10 with alternate addition and subtraction of the numbers.
The numbers to be used are: 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, and -10
Now, the first term is positive and the next term is subtracted. So, the required expression becomes,
10 - 8 + 6 - 4 + 2 - 0 + (-2) - (-4) + (-6) - (-8) + (-10)
= 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10
= 30 - 30
= 0
Hence the correct answer choice is A.
Answer: (A)  0
Question: Increasing the original price of a certain item by 25 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent?
(A) 31.25
(B) 37.5
(C) 50.0
(D) 52.5
(E) 62.5
Rationale: We're told that the original price of an item is increased by 25% and then THAT price is increased by 30%....
IF....
Starting value = $100
+ 25% = 100 + .25(100) = 125
+ 30% = 125 + .30(125) = 125 + 37.5 = 162.5
The question asks how the final price relates to the original price. This is essentially about Percentage Change, which means we should use the Percentage Change Formula:
Percentage Change = (New - Old)/Old = Difference/Original
Doing either calculation will yield the same result:
62.5/100 = 62.50%
Final Answer:
E
Answer: (E) 62.5
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
(A) 31/32
(B) 31/39
(C) 31/36
(D) 31/33
(E) 31/31
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer: OA
Answer: (A) 31/32
Question: Walking at 3/4 of his usual place, a man reaches his office 20 minute late. Find his usual time?
(A) 2 hr
(B) 1 hr
(C) 3 hr
(D) 1.5 hr
(E) 2.5 hr
Rationale: Let the original speed be S and time be T
If new speed=SÃ—3/4, then new time would be TÃ—4/3(D = ST = Constant).
Given,
3T/4âˆ’T=20T/3
â‡’ T=60 minutes
= 1 hour
Answer :A
Answer: (A) 2 hr
Question: The probability that A can shoot a target two out of two times is 0.25. What is the probability that the target will be missed by A immediately after such two shots?
(A) 0.25
(B) 0.5
(C) 0.7
(D) 0.4
(E) 0.75
Rationale: Suppose there are total 'x' shots.
A shoots 2 out of 2 times. means out of x shots (x>2) A shots 2 out of 2 ----> A shots at least 2 out of x.
therefore, 2/x = 0.25 (given)
the target will be missed by A immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.
thus, the probabilty of missing just after 2 shots is (x-2)/x.
(x-2)/x = 1 - 2/x
= 1 - 0.25
= 0.75
Answer : E
Answer: (E) 0.75
Question: Ramesh, xyz and Rajeev put a partnership. profit is 36000, if Ramesh and xyz ratio is 5 : 4 and xyz and Rajeev 8:9. Find Rajeev's share.
(A) 14000
(B) 15000
(C) 16000
(D) 12000
(E) 17000
Rationale: ramesh:xyz=5:4
xyz:rajeev=8:9
then
ramesh:xyz/rajeev:xyz=5:4/9:8
ramesh/rajeev=10/9
therefore
ramesh:xyz:rajeev=10:8:9
then
rajeev share=(9/27)*36000=12000
ANSWER:D
Answer: (D) 12000