RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Of the 19,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?
A. 14.3%
B. 16.67%
C. 33%
D. 28.6%
Answer: C. 33%
Explanation: The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.
If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.
What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 33%.
Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.
The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?
The correct answer is 2nd place.
Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.C
Question: Three friends A, Band C started a business by investing a sum of money in the ratio of 5 : 7 : 6. After 6 months C withdraws half of his capital. If the sum invested by ‘A’ is 40,000, out of a total annual profit of 33,000, C’s share will be
A.9,000
B.12,000
C.11,000
D.10,000
Answer: A.9,000
Explanation: Sum invested by A, B and C is
5 × 12 : 7 × 12 : 6 × 6 + 3 × 6
or, 60 : 84 : 54 or, 10 : 14 : 9
\Share of C = 9⁄33 × 33,000 = 9,000
Answer A
Question: If a particular player is never chosen, in how many ways can 11 cricket players be chosen out of 14 players?
A.45
B.56
C.64
D.78
Answer: D.78
Explanation: A particular players is never chosen, it means that 11 players are selected out of 13 players.
=> Required number of ways = 13C11
= 78
D
Question: The ratio of Laxmi's age to the age of her mother is 3:11. The difference of their ages is 24 years. The ratio of their ages after 3 years will be?
A.1 : 9
B.1 : 3
C.1 : 2
D.1 : 1
Answer: B.1 : 3
Explanation: Suppose age of Laxmi is x years.
The difference of their ages
\inline \therefore Ratio of their ages after 3 years = =
= 12 : 36 = 1 : 3
Answer:B
Question: If the product of two numbers is 82500 and their H.C.F. is 55, find their L.C.M.
A.2574
B.2500
C.1500
D.1574
Answer: C.1500
Explanation: Explanation:
HCF * LCM = 82500, because we know
Product of two numbers = Product of HCF and LCM
LCM = 82500/55 = 1500
Option C
Question: 4, 5, 7, 11, 19, (...)
A.22
B.35
C.27
D.32
Answer: B.35
Explanation: 4
4 × 2 - 3 = 5
5 × 2 - 3 = 7
7 × 2 - 3 = 11
11 × 2 - 3 = 19
19 × 2 - 3 = 35
Answer is B.
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
A.384
B.287
C.279
D.267
Answer: A.384
Explanation: Average mark scored by all the three boys =
[64/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 384
Answer: A
Question: Car A runs at the speed of 52km/hr & reaches its destination in 10hr. Car B runs at the speed of 46 km/h & reaches its destination in 8h. What is the respective ratio of distances covered by Car A & Car B?
A.62:25
B.66:52
C.68:15
D.65:41
Answer: D.65:41
Explanation: Sol. Distance travelled by Car A = 52 × 10 = 520 km
Distance travelled by Car B = 46 × 8 = 368 km
Ratio = 520/368 = 65:41
D
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
A.4/5
B.7/8
C.9/8
D.1/3
Answer: D.1/3
Explanation: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Ans: D
Question: In a garden, 26 trees are planted at equal distances along a yard 300 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
A.10
B.8
C.12
D.14
Answer: C.12
Explanation: 26 trees have 25 gaps between them.
Length of each gap = 300/25 = 12
i.e., distance between two consecutive trees = 12
Answer is C.
Question: It costs $2 for the first 15 minutes to use the bumper cars at a fair ground. After the first 15 minutes it costs $6 per hour. If a certain customer uses the bumper cars for 3 hours and 25 minutes, how much will it cost him?
A.$22
B.$3
C.$15
D.$21
Answer: D.$21
Explanation: 3 hrs 25 min = 205 min
First 15 min ------> $2
Time left is 190 min...
Now, 60 min costs $ 6
1 min costs $ 6/60
190 min costs $ 6/60*190 => $ 19
So, Total cost will be $19 + $2 => $ 21
The answer will be (D) $21
Question: Bella is taking a trip in her car from New York (point A) Chicago, Illinois (point B). She is traveling at an average speed of 50 miles per hour, If the total distance from point A to point B is 790 miles, in approximately how long will Bella reach her destination?
A.10 hours
B.12.50 hours
C.15.80 hours
D.25 hours
Answer: C.15.80 hours
Explanation: Answer is (C). If she is traveling at a speed of 50 miles per hour and her trip is a total of 790 miles, 790 miles divided by 50 miles per hours would equal 15.80 hours, just shy of 16 hours.
Question: The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is?
A.4 months
B.6 months
C.8 months
D.9 months
Answer: A.4 months
Explanation: S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time =(100 x 80/1600 x 15)year
=1/3	year = 4 months.
Answer:A
Question: A 12 lt solution is 33 1/3% acid. How much water must be added to get the solution having 20 % acid.
A.8
B.9
C.10
D.7
Answer: A.8
Explanation: A 12 lt solution is 33 1/3% acid.
means 4 ltr acid and 8 ltr water.
If x is final solution, then
4 ltr = x* 20/100
x=20 ltr
so water to be added = 20-12= 8 ltr
ANSWER:A
Question: If x > 7, which of the following is equal to (x^2 + 2x + 1)/(x^2 - 1) ?
A.(x + 4)/(4(x - 4))
B.(x - 4)/(x + 4)
C.(x - 2)/(x + 4)
D.(x + 1)/(x - 1)
Answer: D.(x + 1)/(x - 1)
Explanation: (x^2 + 2x + 1)/(x^2 - 1)
= (x + 1)(x + 1) / (x + 1)(x - 1)
=(x + 1)/(x - 1)
D. (x + 1)/(x - 1)
Question: At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 20% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?
A.4/25
B.8/23
C.2/5
D.8/14
Answer: D.8/14
Explanation: let there be 100 books in all
Historic fiction books = 40% of total = 40
Other books = 60
New historic fiction = 40% of 40 = 16
Other new books = 20% of 60 = 12
total new books = 28
fraction = 16/28 = 8/14
Ans: D
Question: What is the decimal equivalent of (1/4)^2?
A.0.0016
B.0.0625
C.0.16
D.0.25
Answer: B.0.0625
Explanation: 1/4= 25/100 => (25/100)^2=625/10000 = 0.0625
ANSWER:B
Question: Find the simple interest on $1000 for 3 years at 10% per annum?
A.$250
B.$300
C.$500
D.$600
Answer: B.$300
Explanation: SI = PTR/100
= 1000*3*10/100 = $300
Answer is B
Question: For how many values of W, is |||W - 5| -10| -5| = 2?
(Those ls are mods)
A. 0
B. 2
C. 4
D. 8
Answer: D. 8
Explanation: I think its 8
|||W-5|-10|-5| =2
let |W-5| = a which makes above
||a-10|-5| =2
let |a-10| = b which makes
|b-5| = 2
now for the above b can take 3, 7
for every b =3 a can have 13, 7
and for b = 7 a can have 17 and 3
so 'a' has four solutions 13, 7, 17 and 3
for a = 13; W has 18 or -8 thus has 2 for every combination hence 4x2 = 8
answer D
Question: what is the remainder of (3682*3684*3686) divided by 19?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: 3686%19 = 0
so ans = 0
ANSWER:A
Question: An artist sells paintings through an on-line store, which take a commission of 11% of the price set by the distributor. The distributor obtains the painting from an artist at the price of $20 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 11% profit on the cost of the item?
A.28.11
B.27.99
C.36.44
D.44.12
Answer: A.28.11
Explanation: Painter price = $20;The distributor wants to maintain a 11% profit on the cost of the item, thus he must get $20*1.11 = $22.20 after the store takes a commission of 11% of the final price --> (final price)*0.79 = $22.20 --> (final price) = $28.11. Answer: A.
Question: If a coin is tossed twice, what is the probability that one of the flips was heads and one of the flips was tails?
A.1/2
B.1/8
C.1/4
D.1/6
Answer: A.1/2
Explanation: The possible cases are =>{Head,Head} {Head,Tail} {Tail,Head} {Tail,Tail}
Possible Cases=4
Favourable cases = 2
P(E) = 2/4 = 1/2
Answer: A
Question: The average age of a board of 8 functional directors in a company is the same as it was 3 years ago, a younger man having been substituted for one of the directors. How much younger was the new man than the director whose place he took.
A.24 years
B.26 years
C.28 years
D.27 years
Answer: A.24 years
Explanation: Let the new man was younger than the director = x years and 3 years ago, the sum of ages of board of directors
= S – 8 × 3 = S – 24
Then, 3 years ago, average age of board of directors
= S−24/8
Now, S−24/8=S−x/8
⇒ x = 24 years
Shortcut Method : If the new young director would have been not substituted, then total age would have increased at present by 8 × 3 = 24 years.
Therefore, the new man is 24 years younger keeping the average at present same as 3 years ago.
Answer A
Question: What is the remainder when 121212.......(300) digits is divided by 99.
A.18
B.36
C.72
D.0
Answer: A.18
Explanation: 12/99=12
1212/99=24
121212/99=36
.
.
.
121212...(300)/99=(12*300)%99=36
if they say 300 digits then (12*150)%99=18
ANSWER:A
Question: 31, 29, 24, 22, 17, ?
A.15
B.23
C.13
D.25
Answer: A.15
Explanation: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer : A.
Question: A man goes to work daily. Everyday his wife picks him from railway station at 6 o'clock. One day, he left office early and reached the station at 5 o'clock. So, he started walking home. On the way, he met his wife, and they returned together in the car. They reached home ten minutes earlier than usual time. How much time did the man walk?
A.50 minutes.
B.55 minutes.
C.54 minutes.
D.52 minutes.
Answer: B.55 minutes.
Explanation: the man leaves office 1 hr means 60 minute early..wife and man save 10 minutes..so if wife does not meat his husband then she has to go (10/2)=5 minutes more..so husband walk for(60-5)=55 minutes.
ANSWER:B
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 222 marks in the second test and failed by 39 marks in that test. Find the pass mark in the first test?
A.768
B.232
C.246
D.625
Answer: B.232
Explanation: Let the maximum mark in each test be M.
The candidate failed by 36 marks in the second test.
pass mark in the second test = 222 + 39 = 252
45/100 M = 261
Pass mark in the first test = 40/100 M = 40/45 * 261 = 232
Answer:B
Question: The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 60 kmph. Find the speed of the boat in still water and the speed of the stream?
A.5 kmph
B.4 kmph
C.9 kmph
D.8 kmph
Answer: A.5 kmph
Explanation: Speed of the boat in still water = (50+60)/2 = 55 kmph. Speed of the stream
= (60-50)/2
= 5 kmph.
Answer:A
Question: Calculate how many days it will take for 5 boys to paint a 65 m long wall if 2 boys can paint a 40 m long wall in 4 days,
A.2.6 days
B.3.6 days
C.5.6 days
D.6 days
Answer: A.2.6 days
Explanation: The length of wall painted by one boy in one day = 40 / 2 * 1/4 = 5 m
No. of days required to paint 50 m cloth by 8 boys = 65/ 5 *1/ 5 = 2.6 days.
A
Question: What is the least value of x, So that 2x5478 is divisible by 9
A.7
B.8
C.9
D.1
Answer: D.1
Explanation: Explanation:
The sum of the digits of the number is divisible by 9.
Then the number is divisible by 9.
2 + x + 5 + 4 + 7 + 8 = 26 + x
Least value of x may be '1',
So that the total 26 + 1 = 27
is divisible by 9.
Answer: Option D
Question: Tom is 12 years older than his sister, Amy. He is also four times her age. How olx is Tom?
A.14 years
B.15 years
C.16 years
D.17 years
Answer: C.16 years
Explanation: Amy's age is x.
Tom is 12 years older than her, so his age is x+12. He is also, however, 4 times his sister's age, so his age is also 4x.
x+12=4x
3x=12
x=4
This means Amy is 4 years old. If Tom is 12 years older, or 4 times her age, this means he is 16 years old.
ANSWER: C
Question: In an exam, students need to answer 120 multiple choice questions. If the question paper is divided into 10 sections, how many questions are there in a section?
A.6
B.12
C.10
D.4
Answer: B.12
Explanation: 120 questions divided into 10 sections means each section containing 120/10=12 questions. Answer B.
Question: Sameer spends 40% of his salary on food articles and 1/3rdof the remaining on transport. If he saves Rs.450 per month which is half of the balance after spending on food items and transport, what is his monthly salary?
A.Rs.1125
B.Rs.2250
C.Rs.2500
D.Rs.4500
Answer: B.Rs.2250
Explanation: Explanation:
Suppose, salary = Rs.100
Expenditure on food = Rs.40
Balance = Rs.60
Expenditure on transport
= 1/3×60=Rs.20
Now balance = Rs.40
Saving = Rs.20
If saving is 20, salary = Rs.100
If saving is 450,
salary = Rs.(100/20×450)=Rs.2250
Correct Option: B
Question: Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 10 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
A.R-4
B.R/(R+4)
C.R/(R-8)
D.8/(R-20)
Answer: C.R/(R-8)
Explanation: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.
In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*10T=R(T-1) --> 20T=RT-R --> T=R/(R-20).
Answer: C.
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
A.1
B.2
C.3
D.5
Answer: B.2
Explanation: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
B
Question: if a2+b2=177and ab=54 then find the value of a+b/a-b?
A.5
B.15
C.6
D.3
Answer: A.5
Explanation: (a+b)2=a2+b2+2ab=117+2*24=225
a+b=15
(a-b)2=a2+b2-2ab=117-2*54
a-b=3
a+b/a-b=15/3=5
ANSWER A 5
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
A.134
B.145
C.166
D.150
Answer: C.166
Explanation: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Question: At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 21 liters of forest green to change it to Verdant green?
A.1/3
B.7
C.1/2
D.1/7
Answer: B.7
Explanation: 21 liter of Forset green have 12 liter of blue and 9 liter of yellow
Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is
Blue/yellow =12/(9+x) = ¾
27+3x=48 => x =7
Answer : B
Question: A certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 6 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 60 mph?
A.15%
B.20%
C.25%
D.30%
Answer: C.25%
Explanation: Total time for travelling 80 miles @ 60 mph = 80/60 = 4/3 hour = 80 minutes.
Given, the car uses 1 gallon for every 40 minutes of driving @ 60 mph. Thus in 80 minutes it will use = 2 gallons. Thus, full tank = 2+6 = 8 gallons ---> 2/8 = 25% of the fuel used. C is the correct answer.
Question: Sourav walks 20 meters towards North. He then turns left and walks 40 meters. He again turns left and walks 20 meters. Further, he moves 20 meters after turning to
right. How far is he from his original position?
A.87
B.66
C.60
D.27
Answer: C.60
Explanation: Explanation:
No explanation is available for this question!
ANSWER: C
Question: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
A.9
B.8
C.5
D.5
Answer: A.9
Explanation: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9
Answer:A
Question: Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?
A.m/(m + n)
B.n/(m + n)
C.mn/(m + n)
D.mn/(m – n)
Answer: D.mn/(m – n)
Explanation: “Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars? ”
Since the number “1500 jars” appears over and over, let’s arbitrarily say 1500 jars = 1 lot, and we’ll use units of lots per hour to simplify our calculations.
P’s individual rate is (1 lot)/(m hours) = 1/m. The combined rate of P & Q is (1 lot)/(n hours) = 1/n. We know
(P’s rate alone) + (Q’s rate alone) = (P and Q’s combined rate)
(Q’s rate alone) = (P and Q’s combined rate) – (P’s rate alone)
(Q’s rate alone) = 1/n – 1/m = m/ (nm) – n/ (nm) = (m – n)/(nm)
We now know Q’s rate, and we want the amount of 1 lot, so we use the “art” equation.
1 = [(m – n)/ (nm)]*T
T = (mn)/(m – n)
Answer = D
Question: If 2x/|y| = -16 which of the following must be true?
A.x = -y
B.x = y
C.x^2 =64 * y^2
D.x^2 = y^2
Answer: C.x^2 =64 * y^2
Explanation: 2x/|y| = -16
2x= -16 |y|
Squaring both sides
4*x^2= (-16 |y|) ^2=256* y^2
x^2 = 64 * y^2
C is the answer
Question: The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field?
A.32999
B.37500
C.37199
D.37512
Answer: B.37500
Explanation: Let length = x meters, then breadth = 0.6x
Given that perimeter = 800 meters
=> 2[ x + 0.6x] = 800
=> x = 250 m
Length = 250m and breadth = 0.6 * 250 = 150m
Area = 250 * 150 = 37500
Answer: B
Question: Find the fourth proportion to 6,12,18
A.24
B.12
C.36
D.8
Answer: C.36
Explanation: Explanation:
6:12 :: 18:x
=> 6/12= 18/x
=> x = 18*12/6
=> x = 24
Answer:C
Question: A car takes 6 hours to cover a distance of 360 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.60
B.50
C.40
D.70
Answer: C.40
Explanation: Time = 6
Distance = 360
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 360/9 = 40 Kmph
Answer C.
Question: Two trains start simultaneously from opposite ends of a 160-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 160-km trip in 5 hours. Train Y, travelling at a constant rate, completes the 160-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y?
A.56
B.58
C.60
D.62
Answer: C.60
Explanation: If the two trains cover a total distance D, then Train X travels (3/8)*D while Train Y travels (5/8)*D. If the trains travel 160 km to the meeting point, then Train X travels (3/8)*160 = 60 km. The answer is C.
Question: Set S consists of integers {1,2,3,4}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 6?
A.1/3
B.1/6
C.2/3
D.2/5
Answer: B.1/6
Explanation: Number of ways you can choose 2 from 4 = 4C2 = 6
E = event of getting the 2 numbers is more than 6 = (3,4) = 1
probability = 1/6
Answer is B
Question: The greatest possible length which can be used to measure exactly the length 3m ,6m 85cm, 8m 95 cm is?
A.25cm
B.101cm
C.5cm
D.42cm
Answer: C.5cm
Explanation: Required length = H.C.F of 300cm, 685cm, 895cm = 5cm
Answer is C
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 3 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
A.179:2
B.178:3
C.179:1
D.179:54
Answer: D.179:54
Explanation: Quantity of alcohol in vessel P = 62.5/100 * 3 = 15/8 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 15/8 + 7/2 = 43/8 = 5.375 litres
As 7 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 5.375 : 1.625 = 179 : 54.
Answer:D
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
A.46
B.99
C.8826
D.266
Answer: A.46
Explanation: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.Answer: A
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
A.120
B.882
C.662
D.4112
Answer: A.120
Explanation: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2
Answer: A
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many W ways can the assembly line be arranged?
A.120
B.240
C.360
D.480
Answer: C.360
Explanation: C) 360
short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want W=6C!/2 -> 720/2 = 360