RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A certain auto manufacturer sold 4% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.4 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
A.20,00,000
B.21,00,000
C.23,00,000
D.23,90,000
Answer: C.23,00,000
Explanation: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-4/100(X)
If sales in 2006,X= 2.4 million find X-4/100(X)
(2.4 x 10^6)-4/100(2.4 x 10^6)
2400000-96000=23,04,000-----> 23,00,000(approx)
Answer-C
Question: A customer pays 30 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
A.A)$50
B.B)$60
C.C)$70
D.D)$80
Answer: A.A)$50
Explanation: Let x be the original price.
x - 20 = 30
x - 20 + 20 = 30 + 20
x + 0 = 50
x = 50
correct answer is A)$50
Question: In a dairy farm, 20 cows eat 20 bags of husk in 20 days. In how many days one cow will eat one bag of husk?
A.1
B.40
C.20
D.26
Answer: C.20
Explanation: Explanation :
One bag of husk = 20 cows per day
⇒ 20 × 1 × 20 = 1 × 20 × x
For one cow = 20 days
Answer : C
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
A.28 days
B.76 days
C.16 days
D.18 days
Answer: A.28 days
Explanation: 8/12 + 6/x = 1
X = 18 days
Answer:A
Question: Two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer W between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
A.12
B.15
C.17
D.W=18
Answer: D.W=18
Explanation: Since we are concerned with integers W between 1 and 20, write down the primes till 40.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
(you should be very comfortable with the first few primes... )
2, 3, 5, 7, 11,12, 13, 17, 19, 23, 29, 31, 37 - Three pairs (11,13), (7,17), (5, 19)
2, 3, 5, 7, 11, 13,15,17, 19, 23, 29, 31, 37 - Three pairs (13, 17), (11, 19), (7, 23)
2, 3, 5, 7, 11, 13,17, 19, 23, 29, 31, 37 - Three pairs (11, 23), (5, 29), (3, 31)
2, 3, 5, 7, 11, 13, 17,18,19, 23, 29, 31, 37 - Four pairs (17, 19), (13, 23), (7, 29), (5, 31)
2, 3, 5, 7, 11, 13, 17, 19,20,23, 29, 31, 37 - definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore.
Answer (D).
Question: The average of first five prime numbers greater than 20 is?
A.32.2
B.32.98
C.32.3
D.32.8
Answer: A.32.2
Explanation: 23 + 29 + 31 + 37 + 41
= 161/5
= 32.2
Answer: A
Question: An eccentric casino owner decides that his casino should only use chips in $4 and $7 denominations. Which of the following amount cannot be paid out using these chips?
A.$26
B.$29
C.$28
D.$25
Answer: C.$28
Explanation: Yes, the number of 4 or/and 7 dollar chips can be zero, however both being zero mean that the casino is paying out $0, which is not realistic.
Each option but C can be represented as the sum of a multiple of 4 and a multiple of 7:
A. $29 = 7*3 + 4*2
B. $26 = 7*2 + 4*3
C. $25 = 7*3 + 4*1
E. $21 = 7*3
Answer: C.
Question: On a two-dimensional coordinate plane, the line q = x^2 - x^3 touches the x-axis in how many places?
A. 0
B. 1
C. 2
D. 3
Answer: C. 2
Explanation: Apparently it's q = x^2 - x^3 instead of q = x^2 - q^3.
In this case: the x-intercept is the value(s) of x for q = 0.
0 = x^2 - x^3;
0 = x^2(1 - x);
x = 0 or x = 1.
Answer: C.
Question: A train running at the speed of 60 km/hr crosses a pole in 18 sec. What is the length of the train?
A.356
B.278
C.300
D.279
Answer: C.300
Explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 18 = 300 m
Answer: C
Question: There are 5,260 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?
A.5,280 - 12
B.5,280/12
C.12(5,260)
D.12^2(5,280)
Answer: C.12(5,260)
Explanation: 1 feet = 12 inches
1 mile = 5260 feet
1 mile = 5260*12 inches
Ans: C
Question: The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 12.5 percent, what was the annual interest rate last year?
A.1%
B.1.1%
C.9.1%
D.11.36%
Answer: D.11.36%
Explanation: 12.5=1.1*x
X=11.36%
Answer D)
Question: Find the nest term in series ?
25 16 9 4 1 0 ?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: the series is in the form of perferct square series
5,4,3,2,1,0, then comes 1
the answer is 1
ANSWER:B
Question: The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is
A.15 cm
B.25 cm
C.35 cm
D.42 cm
Answer: C.35 cm
Explanation: Solution
Required length	= H.C.F of 700 cm, 385 cm and 1295 cm
‹=› 35 cm.
Answer C
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
A.40%
B.33 1/3%
C.60%
D.66 2/3%
Answer: C.60%
Explanation: Given ratio = 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage = 3x/5x * 100 = 60%.
ANSWER:C
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
A.17 days
B.19 days
C.10 days
D.16 days
Answer: C.10 days
Explanation: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
Answer: C
Question: In a recent election, Ms. Robbins received 7,200 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
A.0.06N + 3,200
B.0.1N + 7,200
C.0.06N + 7,200
D.0.1N + 8,000
Answer: C.0.06N + 7,200
Explanation: total vote = N
vote cast by independent voters = 0.4 N
vote cast by registered voters = 0.6 N
vote received by Ms. Robbins = 7200 + 10% of vote be registered voters = 7200 + 0.06 N
Answer choice C
Question: Look at this series: 53, 53, 48, 48, 43, 43, ... What number should come next?
A.A)12
B.B)14
C.C)38
D.D)53
Answer: C.C)38
Explanation: In this series, each number is repeated, then 5 is subtracted to arrive at the next number.
Answer: C
Question: A worker is paid x rupees for painting every 20 metres of a wall and y rupees for painting every extra metre. During one week, he painted 20 metres on Monday, 22 metres on Tuesday, 24 metres on Wednesday, 26 metres on Thursday and 28 metres on Friday. What is his average daily earning rupees for the five day week?
A.x + (8/5)y
B.(5x + 9y)/5
C.x+4y
D.None of these
Answer: C.x+4y
Explanation: Explanation :
On Monday, the payment = Rs x
On Tuesday, the payment = Rs (x + 2y)
On Wednesday, the payment = Rs (x + 4y)
On Thursday, the payment = Rs (x + 6y)
On Friday, the payment = Rs (x + 8y)
Average daily earning during the five-day week = (5x +20y)/5
= x + 4y
Answer : C
Question: In a hostel there were 100 students. To accommodate 25 more students the average is decreased by some rupees. But total expenditure increased by Rs.500. If the total expenditure of the hostel now 8500, find decrease of average budget?
A.20
B.15
C.12
D.18
Answer: C.12
Explanation: Let average is x
100x + 500=8500
x = 80
let decrease = y
125(80– y)= 8500
y = 12
Answer:C
Question: If a man lost 10% by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 32%?
A.13.25
B.14.36
C.15.85
D.12.27
Answer: D.12.27
Explanation: 90% ---- 18
132% ---- ?
90/132 * 18 = 12.27
Answer: D
Question: The owner of a local jewelry store hired four watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/5 of the diamonds he had then, and 4 more besides. He escaped with three diamonds. How many did he steal originally?
A.4095
B.4995
C.2595
D.None of these
Answer: B.4995
Explanation: Explanation :
Since, thief escaped with 1 diamond,
Before 4th watchman, he had ( 3 + 4 ) x 5 = 35 diamonds.
Before 3rd watchman, he had ( 35 + 4 ) x 5 = 195 diamonds.
Before 2nd watchman, he had ( 195+ 4 ) x 5 = 995 diamonds.
Before 1st watchman, he had ( 995 + 4 ) x 5 = 4995 diamonds.
Answer : B
Question: An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 21 as commission, the cloth sold through him on that day is worth
A.333
B.500
C.840
D.299
Answer: C.840
Explanation: Explanation:
Let the total sale be Rs. x.
Then, 2.5%. of x = 21 <=> (25/10 * 1/100 * x) = 21 <=> x = 840.
Answer: C
Question: A greengrocer was selling apple at a penny each, chickoos at 2 for a penny and peanuts at 3
for a penny. A father spent 7p and got the same amount of each type of fruit for each of his three
children. What did each child get?
A.1 2 1
B.1 2 2
C.1 2 3
D.1 2 4
Answer: A.1 2 1
Explanation: A father spent 7p
Each child gets 1 apple=Father spent 3p on 3 apples.
Remaining 4p.
Suppose each child gets 2 chickoos=Father spent 3p on 6 chickoos
Remaining 1p
Now if each child gets 1 peanut=Father spent 1p on 3 peanuts
Ans: 1 2 1
ANSWER:A
Question: 8, 12, 18, 27, 40.5, (...)
A.60.75
B.30.27
C.60.9
D.30.79
Answer: A.60.75
Explanation: 8
(8×3)÷ 2 = 12
(12×3)÷ 2 = 18
(18×3)÷ 2 = 27
(27×3)÷ 2 = 40.5
(40.5×3)÷ 2 = 60.75
Answer is A
Question: In a series of six consecutive odd numbers, the sum of the third and fifth numbers is 50. What are the third and fifth number respectively?
A.27,31
B.31,35
C.21,25
D.23,27
Answer: D.23,27
Explanation: Let the numbers be x, x + 1, x + 3, x + 5 and x + 7.
Given (x + 3) + (x + 7) = 50
=> 2x + 10 = 50 => x = 20
The third number = x + 3 = 20 + 3 = 23.
The fifth number = x + 7 = 20 + 7 = 27.
Answer: D
Question: The speed of a boat in still water in 20 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 24 minutes is:
A.9.2
B.10.2
C.9.8
D.9.6
Answer: D.9.6
Explanation: Speed downstream = (20 + 4) = 24 kmph
Time = 24 minutes =24/60 hour = 2/5 hour
Distance travelled = Time × speed =2/5×24 = 9.6 km
Answer is D.
Question: 14 men can complete a piece of work in 32 days. In how many days can 16 men complete that piece of work?
A.23
B.27 3/4
C.20 1/2
D.27 1/2
Answer: D.27 1/2
Explanation: 14 * 32 = 16 * x => x = 27 1/2 days
Answer:D
Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk ?
A.34 days
B.40 days
C.46 days
D.50 days
Answer: B.40 days
Explanation: Explanation:
Less Cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
[Cows1 40
Bags 40 1]::40:x
=>x∗40∗1=40∗1∗40
=>x=40
Option B
Question: I have 20 rupees. I bought 1, 2, 5 rupee stamps. They are different in numbers by the reason of no change, the shop keeper gives 3 one rupee stamps. So how many stamp(s) I have.
A.9
B.10
C.11
D.12
Answer: B.10
Explanation: 5x+2y = 17
where, x and y are integer.
x = 3, y= 1 (possible)
y= 6, x = 1 (possible)
=> as they are different in number so, x is not equal to 3
one rupee coin = 3
2 two coin = 6
5 rupee coin = 1
Total = 10.
ANSWER:B
Question: A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 50 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?
A.79
B.89
C.95
D.77.27
Answer: D.77.27
Explanation: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6
A1+A2+A3+A4+A5+A6 = 100*6 = 600
The year before , the 5 courses be B1, B2 , B3 , B4 , B5
B1+B2+B3+B4+B5 = 50*5 = 250
Student's average = (600+250)/11 = 77.27
Answer D
Question: If a 10 lit. mixture contains milk and water in the ratio 2:1 then, how much more mixture should be added to change the ratio to 1:2 ?
A.10 liters of water
B.15 liters of water
C.10 liters of milk
D.20 liters of water
Answer: A.10 liters of water
Explanation: If you add the same mixture again,the ratio will still remain the same.
The question should be how much water to be added
In 10 litres, let quantity of milk = 2x and quantity of water = x
=> 2x + x = 10
=> x = 10/3 , 2x = 20/3
Let y litres of water be added to make the ratio 1:2
=> (20/3) / (10/3 + y) = 1 / 2
=> 40/3 = 10/3 + y
=> y = 10 liters
Therefore,10 liters of water to be added.
ANSWER:A
Question: How many four letter combinations can be formed using the letters of the word TRIPS?
A.12
B.24
C.120
D.240
Answer: C.120
Explanation: The number of letters in the given word is five.
The number of four letter combinations that can be formed using these five letters is
= 5 * 4 * 3 * 2 = 120.
Answer: C
Question: At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $65,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
A.$10,000
B.$33,000
C.$12,000
D.$12,800
Answer: B.$33,000
Explanation: 1 machine of type B will cost: 20% down payment of 65,000 = 13,000plusremaining sum (65,000-13,000=52,000) with 40% of finance charges 52,000*1.4=72,800 --> 13,000+72,800=85,800;
2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000plusremaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;
Difference = 85,800 - 52,800 = 33,000.
Answer: B.
Question: Andy has 20 pairs of matched gloves. If he loses 14 individual gloves, which of the following is NOT a possible number of matched pairs he has left?
A.9
B.11
C.13
D.14
Answer: D.14
Explanation: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched of pairs
Case1: If 14 gloves are gone the maximum probability of losing maximum gloves is 14 pairs of gloves out of 20. This means i m having 6 pairs of gloves. [Minimum number of gloves i can have is 6 pairs]
Case2: If 14 gloves are gone the maximum probability of losing minimum gloves is 14/2 = 7 means i can lose 7 glove. in this scenario i will be having 13 gloves.
Hence10 < Available Glove Pair < 14
any given time I cant possess 14 glove pair for the above mentioned scenario. And thats the answer. D.
Question: Out of a total of 1,000 employees at a certain corporation, 52 percent are female and 40 percent of these females work in research. If 45 percent of the total number of employees work in research, how many male employees do NOT work in research?
A. 238
B. 480
C. 392
D. 208
Answer: A. 238
Explanation: total number of female employees =52% =520
female employees working in research =(2/5)*520=208
Total no of employees working in research =45% =450
Total male employees =48%=480
male employees working in research =450-208=242
male employees not working in research =480-242=238
Answer A
Question: Ten percent of Ram's monthly salary is equal to eight percent of Shyam's monthly salary. Shyam's monthly salary is twice Abhinav's monthly salary. If Abhinav's annual salary is Rs. 1.92 lakhs, find Ram's monthly salary?
A.Rs. 18000
B.Rs. 20000
C.Rs. 25600
D.Rs. 32000
Answer: C.Rs. 25600
Explanation: Let the monthly salaries of Ram and Shyam be Rs. r and Rs. s respectively.
10/100 r = 8/100 s
r = 4/5 s
Monthly salary of Abhinav = (1.92 lakhs)/12 = Rs. 0.16 lakhs
s = 2(0.16 lakhs) = 0.32 lakhs
r = 4/5(0.32 lakhs) = Rs. 25600
ANSWER:C
Question: A box contains five bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
A.256/625
B.1/6
C.369/625
D.1/5
Answer: C.369/625
Explanation: Required probability
= 1 - 256/625
= 369/625
Answer: C
Question: In a rectangular coordinate system, what is the area of a triangle whose vertices have the coordinates (-1, 0), (7, 4), and (7, -4)?
A.29
B.30
C.31
D.32
Answer: D.32
Explanation: The triangle is symmetric about the x-axis.
The part above the x-axis forms a triangle with a base of 8 and a height of 4.
The area of this part is (1/2)(8)(4).
We can double this to find the area of the whole triangle.
The total area is (2)(1/2)(8)(4) = 32.
The answer is D.
Question: The "factor count" of an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest?
A.60
B.61
C.62
D.63
Answer: A.60
Explanation: (A)	60 = 2^2*3*5 --> factor count = 3;
(B)	61 = prime --> factor count = 1;
(C)	62 = 2*31 --> factor count = 2;
(D)	63 = 3^2*7 --> factor count = 2;
(E)	64 = 2^6 --> factor count = 1.
Answer: A.
Question: A bag contains 80 black balls and 10 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A.2/5
B.5/7
C.1/9
D.1/4
Answer: C.1/9
Explanation: Total number of balls = 80+10 = 90
no. of white balls = 10
probability of drawing a white ball = 10/90 = 1/9
Answer is C
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 45 years, was replaced by a new person. Find the age of the new person?
A.18
B.56
C.12
D.15
Answer: D.15
Explanation: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 45 + Q
=> Q = 15
Answer:D
Question: Find out the wrong term in the series 2, 5, 10, 50, 500, 5000
A.5000
B.3877
C.6777
D.2892
Answer: A.5000
Explanation: Explanation:
Each term of the series is the product of the preceding two terms
So, 5000 is wrong and it must be replaced by (500*50) = 25000
Answer: A) 5000
Question: How many positive integers less than 248 are multiple of 4 but NOT multiples of 6?
A.20
B.41
C.42
D.53
Answer: B.41
Explanation: 244/4=61
Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0
240/12=20
61-20=41
Answer: B
Question: How many two-digit numbers yield a remainder of 3 when divided by both 4 and 14?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: Easier to start with numbers that are of the form 14p+3 ---> 17,31,45,59,73,87.
Out of these 3 (31,59,87) are also of the form 4q+3. Thus 3 is the answer. D is the correct answer.
Question: If 25 toys cost Rs, 234, what do 35 toys cost?
A.327.6
B.564.6
C.546.6
D.654.6
Answer: A.327.6
Explanation: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
x=(35 X 234)/25 =327.60
Answer is A
Question: The average age of a husband, wife and their child 2 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
A.19.2 years
B.28.5 years
C.16.4 years
D.15.6 years
Answer: B.28.5 years
Explanation: Sum of the present ages of husband, wife and child
= (23 * 2 + 5 * 2) = 57 years.
Required average
= 57/2
= 28.5 years.
Answer:B
Question: In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that atleast 1 women is included in the committee?
A.38
B.40
C.42
D.46
Answer: D.46
Explanation: 1W 2M 2W 1M 3W
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
Atleast one women = total - with out women
Atleast one women = 56 - 10 = 46
D)
Question: Which of the following fractions is smaller than 17/50?
A.2/5
B.11/34
C.43/99
D.8/21
Answer: B.11/34
Explanation: Answer B
17/50=0.34
11/34=0.323529 which is 0.01647 smaller than 0.34
Question: If x is a positive integer, and two sides of a certain triangle have lengths 30 and 45 respectively, which of the following could be the length of the third side of the triangle?
I. 45
II. 75
III. 145
A.I only
B.II only
C.I and II only
D.II and III only
Answer: A.I only
Explanation: Following the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides:
Difference of other 2 sides < any side < sum of other two sides. Let the third side of triangle be AB.
So, 45 - 30 < AB < 45+30,
and 15 < AB < 75
Check if any of the answers are between 15 and 75.
I: 45 ; could be a possible value.
II: 75 ; could not be a possible value.
III: 145; could not be a possible value.
Answer :A
Question: If 3x - 3x-1 = 18, then the value of xx is
A.3
B.8
C.27
D.36
Answer: C.27
Explanation: Sol.
3x - 3x-1 = 18
⇔ 3x-1 (3 - 1) = 18
⇔ 3x-1 = 9
⇔ 32
⇔ x-1 = 2
⇔ x = 3.
∴ xx = 33 = 27.
Answer C
Question: On day one, a store sold 96 pens. On each of the next d days, the company sold 44 pens. If the average daily sales of pens over this time period (including day one) is 48 pens, what is the value of d?
A.9
B.10
C.11
D.12
Answer: D.12
Explanation: 96 + 44d = 48(d+1).
4d = 48.
d = 12.
The answer is D.
Question: 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8.
What is half of that number?
A.305
B.315
C.345
D.325
Answer: B.315
Explanation: Let the number be x. then 4/15 of 5/7 of x-4/9 of 2/5 of x=84/21x-8/45x=8
(4/21-8/45)x=8(60-56)/315x=84/315x=8
x=(8*315)/4=6301/2x=315
Hence required number = 315
Answer is B.
Question: A man can row upstream at 25 kmph and downstream at 39 kmph, and then find the speed of the man in still water?
A.22
B.37
C.32
D.27
Answer: C.32
Explanation: US = 25
DS = 39
M = (39 + 25)/2 = 32
Answer:C
Question: Tom, Mary and Sue each wrote an essay for their English class. Together, the three of them wrote a total of 650 pages. Mary and Sue wrote a total of 450 pages together, and Mary and Tom wrote a total of 350 pages together. How many pages did Mary write by herself?
A.200
B.250
C.150
D.300
Answer: C.150
Explanation: Tom + Mary + Sue = 650 pages
Mary + Sue = 450 pages << Plug this into the original formula to get Tom's total
Mary + Tom = 350 pages << Plug this into the original formula to get Sue's total
(Mary + Sue) + Tom = 650 pages >> 450 + Tom = 650 >> Subtract 450 from each side >> Tom = 200
(Tom + Mary) + Sue = 650 pages >> 350 + Sue = 650 >> Subtract 350 from each side >> Sue = 300
Now plug in Tom & Sue into the original formula.
200 + Mary + 300 = 650 <<Subtract 200 and 300 from each side
Mary = 150 pages
Answer: C
Question: The perimeter of a triangle is 42 cm and the inradius of the triangle is 5.0 cm. What is the area of the triangle?
A.128 cm2
B.36.0 cm2
C.105 cm2
D.25 cm2
Answer: C.105 cm2
Explanation: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 5.0 * 42/2
= 105 cm2
Answer: C
Question: How many three digit numbers are there which are equal to 3434 times the sum of their digits?
A.4
B.5
C.6
D.7
Answer: A.4
Explanation: If the product is written abcabc in decimal, then we have
100a+10b+c=34(a+b+c)
100a+10b+c=34(a+b+c)
(a,b,c<10,a≠0a,b,c<10,a≠0). Thus
66a−33c=24b
66a−33c=24b
and, since 1111 divides the left-hand side, 11|b11|b. Since b<10b<10, b=0b=0. We're left with two requirements: 2a=c2a=c and 34|a0c1034|a0c10. Testing the possibilities afforded by 2a=c2a=c, we see 102102 is divisible by 3434, so all its multiples are answers also, and the answer is 4.
Answer is A
Question: The perimeter of a square is 36 m. Find the area of the square.
A.81 mÂ².
B.84 mÂ².
C.86 mÂ².
D.169 mÂ².
Answer: A.81 mÂ².
Explanation: Perimeter of square = 36 m
But perimeter of square = 4 Ã— side
Therefore, 4 Ã— side = 36 m
Therefore, side= 36/4 m = 9m
Now, the area of the square = (side Ã— side)
Therefore, area of the square = 9 Ã— 9 mÂ² = 81 mÂ².
ANSWER : OPTION A
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction?
A.1/12
B.1/18
C.1/19
D.1/16
Answer: A.1/12
Explanation: X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
Answer: A