RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A company’s four cars running 12 hrs a day consume 1200 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 20% less fuel than the company’s four cars. How many lts of fuel will be consumed in the next 6 days?
A.1200 lt
B.1440 lt
C.1664 lt
D.1728 lt
Answer: B.1440 lt
Explanation: Given that
4 cars running 12 hrs a day consume 1200 lts. of fuel in 10 days.
1 car consumption per hour per day = 1200 /4 *12 *10 = 2.5 litre
Now question say new car consume 20% less fuel than the company’s four cars = 80/100 of 2.5 = 2 ( 20 percent less than 2.5)
Hence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 2 *12 *6*5 =720
similarly = old 4 car consumption for next 6 days for 12 hrs =2.5*6*12*4 = 720
hence total is = 720+720= 1440 lt
Ans is B .
Question: The product of all the prime numbers less than 18 is closest to which of the following powers of 10 ?
A.10^9
B.10^8
C.10^7
D.10^6
Answer: D.10^6
Explanation: Product of Prime numbers less than 18 is 2*3*5*7*11*13*17
2*5=10 .
10*11*3*7*13*17 = 10*10*3*10*10*20 (approximately) ~ Product will be >10^5 <10^7 i.e. 10^6
D is the answer
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days X do they need to finish the same job?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time X= 3 days to finish the task
IMO A
Question: The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?
A.296
B.252
C.344
D.388
Answer: C.344
Explanation: Let the four numbers be x, x + 2, x + 4 and x + 6.
=> x + x + 2 + x + 4 + x + 6 = 36
=> 4x + 12 = 36 => x = 6
The numbers are 6, 8, 10 and 12.
Sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344.
ANSWER:C
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
A.10.18 p.m
B.10.29 p.m
C.10.30 p.m
D.10.38 p.m
Answer: C.10.30 p.m
Explanation: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C
Question: If 10 gallons of grape juice are added to 40 gallons of a mixture, which contains 30 percent grape juice then what percent of the resulting mixture is grape juice?
A.14%
B.25%
C.48%
D.34%
Answer: C.48%
Explanation: OFFICIAL SOLUTION:
If we start with 40 gallons of a mixture that is 10% grape juice, then we have:
40 × 0.30 = 12 gallons of grape juice.
40 × 0.70 = 28 gallons of other components.
If we add 10 gallons of grape juice, we will end up with 24 gallons of grape juice and 36 gallons of other components, and we will have a total of 50 gallons of the mixture.
So 24/50 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 24/50 = 48/100= 48%.
The correct answer is choice (C)
Question: Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 40 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
A.a) x minutes
B.b) x/2 minutes
C.c) 2x/3 minutes
D.d) 3x/2 minutes
Answer: D.d) 3x/2 minutes
Explanation: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.
Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min
now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km.
So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = 3x/2. hence answer should be D.
Question: In a class of 38 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
A.3
B.5
C.8
D.13
Answer: B.5
Explanation: Total # of students = 38
Avg # of books per student = 2
Total # of books = 38*2 = 76
# of student borrowed at least 3 books = 38-2-12-10 = 14
# of books borrowed by above 14 students = 76-(12*1)+(10*2) = 44
Considering that 13 out of above 14 students borrowed only 3 books, # of books borrowed = 13*3 = 39
So maximum # of books borrowed by any single student = 44- 39= 5
Option B
Question: A fruit seller sells mangoes at the rate of Rs.10 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 5%
A.Rs 8.81
B.Rs 9.35
C.Rs 10.35
D.Rs 12.35
Answer: D.Rs 12.35
Explanation: Explanation:
85 : 10 = 105 : x
x= (10×105/85)
= Rs 12.35
Option D
Question: If the cost price is 80% of the selling price, then what is the profit percent?
A.5%
B.11%
C.13%
D.25%
Answer: D.25%
Explanation: Let S.P. = $100
C.P. = $80
Profit = $20
Profit% = 20/80 * 100 = 25/6 = 25%
Answer is D
Question: Anil and Ravi invest Rs.60,000 and Rs.40,000 and they got loss of Rs.5,000 at the end of year. Then what was the loss for Ravi in Percentage?
A.2%
B.3%
C.5%
D.6%
Answer: C.5%
Explanation: ratio of their investment is 3:2
so the lost of ravi is 2000rs
40000*(x/100)=2000
then x=5%
ANSWER:C
Question: How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/53 ?
A.6
B.3
C.2
D.1
Answer: C.2
Explanation: There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.
So, we start with
a=1, we get b as -ve. out
a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)
a=3, we get b as 3. Yes (Now we have 3 possible solutions)
a=4, we get b as fraction. Out
a=5, we get b again as some fraction. Out
a=6 already taken.
We have A,B options left. C,D,E are out.
A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.
When a=b, we have only 1 solution = 3. So, one more solution, where a=b is not possible.
So, answer will be C.
Question: Jhaveri invested in Upendra&Upendra,Celco and Winger shares at Rs. 300,Rs.200 and Rs.5 per share respectively. He bought 100 shares for Rs.1000.The number of Upendra&Upendra and Celco shares he bought are respectively
A.23,17
B.17,23
C.17,60
D.15,25
Answer: D.15,25
Explanation: 300a + 200 b + 5c = 10000
a + b + c = 100
295 a + 195 b = 9500
59 a + 39 b = 1900
using options a = 17 b = 23 we can solve it
ANSWER:D
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.1/2
B.2/5
C.8/15
D.9/20
Answer: D.9/20
Explanation: 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 IS D
Question: Which is the odd number?
1, 8, 27, 64, 125, 196, 216, 343
A.196
B.237
C.2087
D.277
Answer: A.196
Explanation: Explanation:
The pattern in the given question is 13, 23,,33...
In the series, 196 is not a perfect cube and therefore the odd number.
ANSWER: A
Question: A speaks english in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to speak english?
A.25%
B.26%
C.35%
D.45%
Answer: C.35%
Explanation: Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5
P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5
Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%
C
Question: Ram-Leela has $100 in her piggy bank. How much will she have in her bank 52 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?
A.1478
B.1578
C.1678
D.1778
Answer: A.1478
Explanation: The dollar deposits are in an A.P.
1,2,3,4...52 with common difference 1
Sum of the terms is n(n+1) / 2
i.e 52* (52+1) /2
= 52* 53/2 = 1378
Total deposit therefore with Chiu-Lihas is 100 + 1378= 1478$
Question: The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is:
A.7
B.29
C.41
D.67
Answer: C.41
Explanation: x+(x+36)+y=100 => 2x+y=64
Therefore y must be even prime, which is 2.
Therefore 2x+2=64 => x=31
Third prime number= (x+36)= (31+36)= 67.
ANSWER:C
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
A.1000
B.2777
C.2889
D.27670
Answer: A.1000
Explanation: 1120 = P [1 + (5*12/5)/100]
P= 1000.Answer:A
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 30% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
A.80
B.95
C.105
D.120
Answer: D.120
Explanation: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.
Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.
Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.
Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.
If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.
Cavg = (70*1 + 40*2)/3 = 50% are men
Total = 120*100/50 = 240
No. of women = 240 - 120 = 120
D
Question: In a kilometer race, A can give B a 100 m start and C a 150 m start. How many meters start can B give to C?
A.50
B.50/9
C.8500/9
D.500/9
Answer: D.500/9
Explanation: A can give B a 100 m start and C a 150m. Start means when A runs 1000m, B runs 900m and C runs 850m. When B runs 1000m, C will run 1000 x (850/900) m (i.e. 8500/9 m) Thus, B can give C a start of - 1000 - (8500/9), i.e. 500/9 m.
Answer: D
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
A.1/2
B.1/3
C.2/5
D.2/7
Answer: C.2/5
Explanation: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Question: three men invested sum. and their ratio is 5:7:6. profit is 7200.then b's share
A.2000
B.2100
C.2800
D.2300
Answer: C.2800
Explanation: b's share =7/18*7200=2800
ANSWER:C
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
A.22
B.28
C.77
D.12
Answer: B.28
Explanation: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.Answer: B
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and stream is
A.3:1
B.1:3
C.2:4
D.4:2
Answer: A.3:1
Explanation: Explanation:
Let speed downstream = x kmph
Then Speed upstream = 2x kmph
So ratio will be,
(2x+x)/2 : (2x-x)/2
=> 3x/2 : x/2 => 3:1
ANSWER IS A
Question: Oil cans x and y are right circular cylinders and the height and radius of y are each thrice those of x. If the oil in can x filled to capacity sells for $4, how much does the oil in y sell for if y is only 1/3rd filled?
A.$30
B.$25
C.$36
D.$40
Answer: C.$36
Explanation: formula for vol of a cyl is PI*r^2*h
so Vy = 27*Vy
y when 1/3rd filled will cost 9 times x so ans is C
Question: A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 15 miles in the city and then 50 miles on the highway?
A.28
B.30
C.35
D.36
Answer: C.35
Explanation: Answer C
No of Miles per Gallon = Total no of miles/Total no of Gallons
=15+50/(15/25+50/40) ~ 35.13
Question: P and Q be centers of two circle having radius 200cms. These circle intersect each other at some point A and B. Length of PQ is 250 cms. What will the angle AQP be?
A.between 0 to 45
B.between 0 to 30
C.between 0 to 60
D.between 0 to 75
Answer: C.between 0 to 60
Explanation: raw the diagram, in triangle AQP, AP = 200 , AQ = 200 and PQ = 250
cos(AQP)= (200^2+250^2-200^2)/(2*200*250)= 5/8 = .625 [using cal, cos(AQP)= 51]
or,
as cos45=.7 & cos60=.5 so, cos(AQP)=.625 lies betn angles 45 & 60
between 0 to 60
ANSWER:C
Question: 306 Ã· ? Ã— 15 + 270 = 405
A.24
B.25
C.34
D.39
Answer: C.34
Explanation: Explanation:
306 Ã· ? Ã— 15 = 405 - 270 = 135
(306 Ã— 15)/? = 135
? = (306Ã— 15)/135 = 34
Answer: Option C
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
A.6
B.7
C.9
D.8
Answer: C.9
Explanation: 9 a.m.
Answer: C
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
A.67 seconds
B.32 seconds
C.40 seconds
D.87 seconds
Answer: C.40 seconds
Explanation: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
A.7:8
B.7:9
C.3:8
D.5:8
Answer: A.7:8
Explanation: Explanation:
Let P age and Q age is 6x years and 7x years.
Then 7x - 6x = 4 <=> x = 4
So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8
Option A
Question: In a class of 250 students, 150 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?
A.80%
B.40%
C.30%
D.20%
Answer: B.40%
Explanation: No of students study french= 250- No of students study spanish = 250-150=100
% of the students study french but not spanish = (100/250)*100 % = 40 %
Answer:B
Question: A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 4 percent and 8 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
A. 3/8
B. 4/5
C. 1/2
D. 3/5
Answer: B. 4/5
Explanation: x * 4/100 * 1 + (20000 - x) * 8/100 * 1 = 1440
4x - 8x = 144000 - 160000
=> -4x = -16000
=> x = 4000/4
So 16000/20000 = 4/5
Answer - B
Question: Kelly rows her canoe 2 miles downstream in 15 minutes. It takes her 60 minutes to row it back upstream the same 2 miles. What was the speed of the water current in mph?
A.3 mph
B.4 mph
C.5 mph
D.6 mph
Answer: A.3 mph
Explanation: Explanation:
Speed of boat Downstream: (2/15) X 60 = 8 mph
Speed of boat Upstream: (2/60) X 60 = 2 mph
Speed of current: 1/2 (8-2) = 6/2 = 3 mph
Answer: Option A
Question: If an average hard drive had a capacity of 0.6 TB in 2000, and average hard drive capacities double every 5 years, what will be the average hard drive capacity in 2050?
A.256
B.512
C.768
D.6144
Answer: D.6144
Explanation: 0.6*2^10=0.6*1024=614.4
The answer is D.
Question: In a sequence, each term starting with the third onward is defined by the following formula an=an−1−an−2an=an−1−an−2, where n is an integer greater than 2. If the first term of that sequence is 3 and the second term is 4, what is the value of the 70th of that sequence?
A.−4
B.−3
C.−1
D.3
Answer: B.−3
Explanation: Given an=an−1−an−2an=an−1−an−2
a3 = a2 - a1 => 4-3 = 1.
a4 = -3
a5 = -4
a6 = -1
a7 = 3
a8 = 4
a9 = 1
a10 = -3
So pattern is 3,4 ,1,-3,-4,-1,3,4,1 and -3 - first term terms...
70th term is -3.
Answer :option B
Question: Choose the missing terms out of the given alternatives.
AZ, BY, CX, ?
A.EF
B.GH
C.ED
D.DW
Answer: D.DW
Explanation: D
DW
The first letter moves one step forward. The second letter moves one step backward.
Question: Adding 30% of x to x is equivalent to multiplying x by which of the following?
A.12.5
B.1.05
C.1.15
D.1.3
Answer: D.1.3
Explanation: 130x/100= 1.3*x
ANSWER:D
Question: 1/2 + [(2/3 * 3/8)/6] - 9/16 =
A. 29/16
B. 19/16
C. 15/16
D. 7/16
Answer: D. 7/16
Explanation: We need to simplify the expression using PEMDAS.
Parentheses
Exponents
Multiplication andDivision
Addition andSubtraction
The calculation of an equation or expression must be carried out in the following order:
1) Operations within parentheses (or absolute value bars or radicals)
2) Exponents
3) Multiplication and division from left to right
4) Addition and subtraction from left to right
The answer is D.
Question: A waitress's income consists of her salary and tips.During one week ,her tips were 9/4 of her salary.What fraction of her income for the week came from tips?
A.9/13
B.1/6
C.1/3
D.4/9
Answer: A.9/13
Explanation: Her tips were 9/4 of her salary.
Let's say her salary =$4
This mean her tips = (9/4)($4) =$9
So, her TOTAL INCOME =$4+$9=$13
What fraction of her income for the week came from tips
$9$13=9/13
=A
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
A.232
B.287
C.269
D.500
Answer: D.500
Explanation: P - 340 = (P*4*8)/100
P = 500
Answer: D
Question: If y is 80 percent greater than x, then x is what percent less than y ?
A.20
B.25
C.33 1/3
D.44 4/9
Answer: D.44 4/9
Explanation: y is 80 percent greater than x
Therefore,
y= (180/100) x
Let x be z percent of y.
So, x = (z/100) y
x = (z/100)(180/100) x
Solving, z = 55.55%
Therefore, x is (100 - 55.55 = 44.45) %
ANSWER:D
Question: Two numbers are in the ratio 3 : 4. If their L.C.M. is 60. what is sum of the numbers?
A.35
B.56
C.76
D.84
Answer: A.35
Explanation: Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 60
=> 12x = 60
=> x = 60/12 = 5
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 5 = 35
Answer: Option A
Question: In how many different ways can the letters of the word 'RETAIL' be arranged such that the vowels must occupy only the even positions?
A.None of these
B.64
C.120
D.36
Answer: D.36
Explanation: OEOEOE
3 vowels EAI can be arranged on even places in 3!=6 ways. Similarly 3 consonants can be arranged on odd places in 3!=6 ways.
Total = 6*6 = 36.
Answer: D.
Question: What is the present worth of Rs. 66 due in 2 years at 5% simple interest per annum?
A.60
B.277
C.120
D.888
Answer: A.60
Explanation: Let the present worth be Rs. x. Then,
S.I. = (66 - x)
(x * 5 * 2) / 100 = (66 - x)
10x = 6600 - 100x
110x = 6600 => x = 60.
Answer: A
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
A.80, 49
B.80, 40
C.80, 48
D.80, 46
Answer: B.80, 40
Explanation: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph Answer: B
Question: If John takes 4 minutes to eat x raisins, how many seconds will it take him to eat z raisins, assuming he continues to eat at the same rate?
A.240z/x
B.4xz
C.240x/z
D.240xz
Answer: A.240z/x
Explanation: It will take (z/x)(4) minutes which is (z/x)(4)(60) seconds = 240z/x seconds.
The answer is A.
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.5/20
D.9/20
Answer: A.10/21
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*6)/(2*1)
=42/2
=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*4)/(2*1)
=20/2
=10
P(E)=n(E)/n(s)
=10/21
The answer should be A
Question: On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 155 is how many times an intensity corresponding to a magnitude of 125?
A.40
B.100
C.400
D.1000
Answer: D.1000
Explanation: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:
If intensity for 125 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 165 it'll be 10*10*10*10*x=10^3*x.
Answer: D.
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.8500
C.6500
D.5500
Answer: A.7500
Explanation: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
ANSWER:A
Question: A meeting has to be conducted with 5 managers. Find the number of ways in which the managers may be selected from among 7 managers, if there are 2 managers who refuse to attend the meeting together.
A.6
B.8
C.10
D.11
Answer: D.11
Explanation: The total number of ways to choose 5 managers is 7C5 = 21
We need to subtract the number of groups which include the two managers, which is 5C3 = 10.
21 - 10 = 11
The answer is D.
Question: A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
A.5
B.6
C.9
D.24
Answer: A.5
Explanation: Lets give some identification to the persons
A,B,C,D,E,F
They are arrang in decreasing order of their height
A being tallest and F being smallest
To satisfy both the conditions
A should be in the right most position of the second row (A is the tallest in order to satisfy the condition increasing height from left to right A should be the right most and the back person should be taller then the front so A should be in the second row)
similarly F should be in the left most positon of first row
lets see the combinations
CBA--------second row
FED---------First row
DCA
FEB
DBA
FEC
ECA
FDB
EBA
FDC
these are the combinations which satisfy both the conditions
so the answer is 5 A
Question: In a bag of small balls 1/4 are green, 1/8 are blue, 1/12 are yellow and the remaining 26 white. How many balls are blue?
A.6 balls
B.7 balls
C.8 balls
D.9 balls
Answer: A.6 balls
Explanation: Let us first find the fraction of green, blue and yellow balls
1/4 + 1/8 + 1/12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator
= 11 / 24 , add numerators
The fraction of white balls is given by
24 / 24 - 11 / 24 = 13 / 24
So the fraction 13 / 24 corresponds to 26 balls. If x is the total number of balls then
(13 / 24) of x = 26 balls
or (13 / 24) × x = 26
x = 26 × (24 / 13) = 48 , total number of balls
The fraction of blue balls is 1 / 8 of x. The number of blue balls is given by (1 / 8) of 48 = 6 balls.
ANSWER IS A