mathewhe/aqua_rat huggingface dataset:
Question: 15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days .How many days will 10 men and 10 boys together take to complete the same work
(A) 10 days
(B) 11 days
(C) 12 days
(D) 13 days
(E) None of these
Rationale: Solution:
Work done by one man in one day=1/(15*10)
Work done by one boy in one day=1/(20*15)
Work done by 10 men and 10 boys in one day=10[ 1/(15*10) + 1/(20*15)]
Days taken=1/Work done by 10 men and 10 boys in one day
=10 days
Answer A
Answer: (A) 10 days
Question: A code is to be made by arranging 8 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B, two of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
(A) 42
(B) 210
(C) 420
(D) 840
(E) 6,720
Rationale: we have 8 letters out of which 3 are of one kind, 1 are of another kind..
so total ways = 8!/3!1!=6720
ans E
Answer: (E) 6,720
Question: If pq represents a positive two digit number, where p and q are single digit integers, which of the following cannot be true?
(A) p+q =9
(B) (p)(q)=9
(C) p-q = 9
(D) q-p= 9
(E) p/q = 9
Rationale: (A) pq = 45 or 63 or 27
(B) pq = 33 or 19
(C) 90
(D) impossible
(E) pq = 91
(D) is impossible because 09 is not a valid two digit number --- if there's a zero in the ten's place, that's just 9, a single digit number. Therefore, no valid two digit number would satisfy (D).
ans D
Answer: (D) q-p= 9
Question: Two pipes can fill a tank in 18 minutes and 20 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 1/15
(B) 1/16
(C) 1/11
(D) 1/10
(E) 1/12
Rationale: Part of the filled by all the three pipes in one minute
= 1/18 + 1/21 - 1/45 = 1/12
So, the tank becomes full in 12 minutes.
Answer:E
Answer: (E) 1/12
Question: Roy was suffering from severe headaches. He went to see his doctor and the doctor gave him five tablets asking him to take one tablet every 15 minutes.
How much time will it take Roy to consume all the five tablets?
(A) 60 minutes
(B) 65 minutes
(C) 50 minutes
(D) 45 minutes
(E) 55 minutes
Rationale: A
60 minutes
Roy will be able to consume all the five tablets in an hour.
Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.
Answer: (A) 60 minutes
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.9
(B) 31.1
(C) 31.6
(D) 31.2
(E) 31.5
Rationale: :
100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer: C
Answer: (C) 31.6
Question: Eight mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?
(A) 20160
(B) 2400
(C) 12000
(D) 36002
(E) 7200
Rationale: Arrangement of 8=8!. In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them). So, the needed arrangement is 8!/2=20160.
Answer: A
Answer: (A) 20160
Question: Line Q has the equation 5y – 3x = 90. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.)
(A) 58
(B) 61
(C) 64
(D) 67
(E) 70
Rationale: 5y - 3x = 90 and so y = 3x/5 + 18
When x = 0, then y = 18.
When y = 0, then x = -30
The slope is 3/5, so the slope of line S is -5/3.
Through the point (-30, 0), 0 = -5(-30)/3 + c
The y-intercept is c = -50.
Thus the perpendicular line S can have y-intercepts from -49 up to 17.
The number of possible lines is 49 + 17 + 1 = 67
The answer is D.
Answer: (D) 67
Question: If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 5 children have two children of the same sex and one of the opposite sex?
(A) 1/3
(B) 2/3
(C) 1/4
(D) 5/16
(E) 3/5
Rationale: No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 5 = 5C2
Total possible outcomes - 2^5 (each child can be either a girl or a boy)
Probability=2C1*5C2/2^5= 2*5/2*2*2*2*2=10/32=5/16
Ans=D
Answer: (D) 5/16
Question: If r and y are different prime numbers less than ten, what must be true about the sum of r and y?
(A) the sum is even
(B) the sum is odd
(C) the sum is less than ten
(D) the sum is greater than ten
(E) the sum is less than 13
Rationale: This has to be solved by checking for each option:
Prime numbers less that 10 = 2, 3, 5, 7
A. the sum is even
May or may not be true. r = 3, y, = 5 -> True.
r = 2, y = 3 - True
B. the sum is odd
May or may not be true. r = 3, y, = 5 -> False.
r = 2, y = 3 - True
C. the sum is less than ten
May or may not be true r= 5, y = 7, Sum = 12
r = 2, y = 3. Sum = 5
D. the sum is greater than ten
May or may not be true r= 5, y = 7, Sum = 12
r = 2, y = 3. Sum = 5
E. the sum is less than 13
This will always be true.
Maximum sum = 7 + 5 = 12.
This is always less than 13.
Correct Option: E
Answer: (E) the sum is less than 13
Question: The total circumference of two circles is 25. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
(A) 5.7
(B) 6.0
(C) 4.0
(D) 9.7
(E) 18.0
Rationale: Let r= Radius of smaller circle. Let R = Radius of larger circle
Therefore:
2πr + 2πR = 25
where 2r = R
Thus:
2πr + 4πr = 25
6πr = 25
r = approx 1.33
πR + 2Rπ = 25
3πR = 25
R = approx 2.65
r + R = approx 3.98 = 4.0
Answer : C
Answer: (C) 4.0
Question: The salary of a person was reduced by 14%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
(A) 10%
(B) 16.3%
(C) 13.7%
(D) 15.1%
(E) 12.3%
Rationale: Let the original salary be $100
New salary = $86
Increase on 86=14
Increase on 100 = 14/86* 100 = 16.3%
Answer is B
Answer: (B) 16.3%
Question: A and B can complete a work in 30days and 15day. They started doing the work together but after 5days B had to leave and A alone completed the remaining work. The whole work was completed in?
(A) 10days
(B) 12days
(C) 20days
(D) 18days
(E) 25days
Rationale: A+B 1day work = 1/30 + 1/15 = 1/10
Work done by A and B in 10days = 1/10 * 5 = 1/2
Remaining work = 1-1/2 = 1/2
Now 1/30 work is done by A in 1day
1/2 work will be done by A in 30*1/2 = 15days
Total time taken = 15+5 = 20days
Answer is C
Answer: (C) 20days
Question: Let a1, a2, . . . , ar be r not necessarily distinct positive integers such that
(x + a1)(x + a2) · · · (x + ar) = xr + 230xr−1 + · · · + 2007,
where each missing term on the right has degree between 1 and r − 2
inclusive. What is the value of r ?
(A) 4
(B) 12
(C) 63
(D) 669
(E) 2007
Rationale: The conditions imply a1 + a2 + · · · + ar = 230 and a1a2 · · · ar = 2007. One checks that
2007 = 32 · 223, where 223 is prime. We deduce that some aj is 223, two aj’s are 3, and the
remaining aj’s are 1. Since their sum is 230 = 223 + 3 + 3 + 1, we obtain r = 4.
correct answer A
Answer: (A) 4
Question: In a school with 652 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is
(A) 150
(B) 200
(C) 250
(D) 163
(E) None
Rationale: Sol.
Let the number of grils be x.
Then, number of boys = (652 - x).
Then, (11 3/4 × 652)
⇔ 11x + 12(652 - x) ⇔ x = 7824 - 7661 ⇔ 163.
Answer D
Answer: (D) 163
Question: Find the annual income derived by investing $ 6800 in 30% stock at 136.
(A) 550
(B) 1500
(C) 250
(D) 1300
(E) 400
Rationale: By investing $ 136, income obtained = $ 30.
By investing $ 6800, income obtained = $ [(30/136)*6800] = $ 1500.
Answer B.
Answer: (B) 1500
Question: A sum of money at simple interest amounts to $ 680 in 3 years and to $710 in 4 years. The sum is:
(A) $153
(B) $698
(C) $590
(D) $549
(E) $675
Rationale: C
$590
S.I. for 1 year = $(710- 680) = $30.
S.I. for 3 years = $(30 x 3) = $90.
Principal = $(680 - 90) = $590.
Answer: (C) $590
Question: Which number can we add to 987654 to get a number exactly divisible by 456?
(A) 18
(B) 24
(C) 30
(D) 36
(E) 42
Rationale: 987654 / 456 = 2165 with a remainder of 414.
We need to add 456 - 414 = 42
The answer is E.
Answer: (E) 42
Question: A car covers a distance of 984 km in 6 ½ hours. Find its speed?
(A) 104 kmph
(B) 187 kmph
(C) 164 kmph
(D) 175 kmph
(E) 106 kmph
Rationale: 984/6
= 164 kmph
Answer: C
Answer: (C) 164 kmph
Question: A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 9. What are the coordinates of P?
(A) (57/10, 57/10)
(B) (3/10, 3/10)
(C) (63/10, 63/10)
(D) (27/10, 27/10)
(E) (9/10, 9/10)
Rationale: The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
x = 3 + (6-3)*(9/10) = 3 + 27/10 = 57/10 = y
The answer is A.
Answer: (A) (57/10, 57/10)
Question: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 48 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 45 cents?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let number of Apples = A
number of oranges = B
A+B=10 --- 1
.48 =(.4A + .6 B)/10
=> 48 = 4A + 6B ----2
Solving 1 and 2, we get
A= 6
B= 4
Let the number of oranges put back = C
45*(10-c) = 40*6 + 60(4-C)
=> C= 2
Answer B
Answer: (B) 2
Question: If the average (arithmetic mean) of five consecutive negative integers is 10k – 1, what is the difference between the greatest and least of the five integers?
(A) 4K
(B) 4k^2 -4k
(C) 4-4k
(D) 4
(E) 4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 10k - 1
=> n = 50k - 5
Greatest = n + 2 = 50k - 5 + 2 = 50k - 3
Least = n - 2 = 50k - 5 - 2
=> Difference = 50k - 3 - (50k - 7)
= 4
Answer - D
Answer: (D) 4
Question: In some code, letters, a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. However, we don’t know which letter represent which number.
Consider the following relationships:
i. a + c = e
ii. b – d = d
iii. e + a = b
(A) b = 4, d = 2
(B) a = 4, e = 6
(C) b = 6, e = 2
(D) a = 4, c = 6
(E) None
Rationale: Explanation :
From the given equations, we see that , b=10 and d=5.
Now 'a' and 'c' must be 4 and 2 respectively.
So, e = 6.
Answer : B
Answer: (B) a = 4, e = 6
Question: The cost price of a radio is Rs.2400 and it was sold for Rs.2100, find the loss %?
(A) 12.5%
(B) 11%
(C) 13%
(D) 15%
(E) 12.8%
Rationale: 2400 ---- 300
100 ---- ? => 12.5%
Answer:A
Answer: (A) 12.5%
Question: 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.
(A) 4 days
(B) 6 days
(C) 2 days
(D) 8 days
(E) 10 days
Rationale: Explanation :
Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = Â½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days
Answer IS A
Answer: (A) 4 days
Question: A fruit shop on its opening in a day, had 400 mangoes and 600 oranges. If 57 percent of the mangoes and 42 percent of the oranges got sold during the day, what percent of the total number of planted fruits were sold ?
(A)  45.5%
(B)  46.5%
(C)  48.0%
(D)  49.5%
(E)  51.0%
Rationale: 57% of 400 mangoes sold, hence 0.47*200 = 228 sold.
42% of 600 oranges sold, hence 0.42*600 = 252 sold.
Thus (germinated)/(total) = (228 + 252)/(400 + 600) = 480/1000 = 48% fruits sold.
Answer: C.
Answer: (C)  48.0%
Question: Walking 7/6 of his usual rate, a boy reaches his school 6 min early. Find his usual time to reach the school?
(A) 22
(B) 28
(C) 99
(D) 42
(E) 66
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
6 --------- ?
=42 m
Answer:D
Answer: (D) 42
Question: Which of the following statements is definitely true , if A is the brother of B and C. Q is B's son and R is A's father.
(A) A is B's son
(B) A is C's son
(C) A is B's nephew
(D) A is B's niece
(E) A is Q's uncle
Rationale: Explanation:
A, B, C are brothers, so since Q is B's son, A is his uncle
Answer E
Answer: (E) A is Q's uncle
Question: A shopkeeper sold an article for Rs 2524.36. Approximately what was his profit percent if the cost price of the article was Rs 2400
(A) 4%
(B) 5%
(C) 6%
(D) 7%
(E) 8%
Rationale: Explanation:
Gain % = (125.36*100/2400) = 5.2 % = 5% approx
Option B
Answer: (B) 5%
Question: Sheela deposits Rs. 3800 in bank savings account. If this is 32% of her monthly income. What is her monthly income in?
(A) 22000
(B) 20000
(C) 11875
(D) 12340
(E) None of these
Rationale: Explanation :
32% of income = Rs. 3800
100% of income = 3800 X 100/32 = Rs. 11875
Answer : C
Answer: (C) 11875
Question: How many prime numbers between 1 and 100 are factors of 210?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: factor of 210= 2*3*5*7--- 4 prime numbers
B
Answer: (B) 4
Question: Line m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 8) and (8,-2). What is the slope of line m?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: The midpoint of (2,8) and (8,-2) is (5,3).
The slope of a line through (0,-2) and (5,3) is (3-(-2))/(5-0) = 5/5 = 1
The answer is D.
Answer: (D) 1
Question: If n is a 36-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 3
II. n is divisible by 9
III. n is divisible by 36
(A) I only
(B) I and II only
(C) I ,II and III only
(D) II and III only
(E) III
Rationale: Rule for divisibility by 3: The sum of the digits of the number should be multiple of 3
Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.
Rules for divisibility by 36: The sum of the digits should a multiple of 36
Consider no 11111111...36 times = The sum 36*1=36----> divisbible by 3,9 and 36
consider number to be 222....36 times, then sum of the no. 36*2=72 divisibly by 3,9 and 36
So why so because when you sum the numbers either you can add the digits 36 times or multiply the digit *36..
Note that since 36 is divisble by 36,9 and 3 and thus the sum of the nos will be divisible by all the nos.
Ans is C
Answer: (C) I ,II and III only
Question: The second largest prime number is?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The second largest prime number is 3.
C)
Answer: (C) 3
Question: If there are 4 peanuts in a box and Mary puts 2 more peanuts inside, how many peanuts are in the box?
(A) 8
(B) 9
(C) 6
(D) 11
(E) 12
Rationale: 2+4=6
correct answer is C)6
Answer: (C) 6
Question: Two-third of a positive number and 16/216 of its reciprocal are equal. The number is:
(A) 5/12
(B) 12/5
(C) 1/3
(D) 144/25
(E) 146/25
Rationale: Let the number be x. Then,
2/3 x = 16/216 * 1/x
x2 = 16/216 * 3/2 = 16/144 = 1/9
x = 1/3
ANSWER:C
Answer: (C) 1/3
Question: A certain car increased its average speed by 5 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 26 miles per hour, how many miles did the car travel in the third 5-minute interval?
(A) 1.0
(B) 1.5
(C) 2.0
(D) 2.5
(E) 3.0
Rationale: In the third time interval the average speed of the car was 22+5+5=36 miles per hour;
In 5 minutes (1/12 hour) at that speed car would travel 36*1/12=3 miles.
Answer: E.
Answer: (E) 3.0
Question: A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.50 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?
(A) 0.40x
(B) 1.20x
(C) 1.40x
(D) 1.60x
(E) 3.20x
Rationale: because we have a total of 4X
Also from Mar- Oct the rakes will be deducted by 1/8 X
so
In Apr they pay for the storage 0.5 * 4X * 7/8
In May they pay for the storage 0.5 * 4X * 6/8
In Jun they pay for the storage 0.5 * 4X * 5/8
In Jul they pay for the storage 0.5 * 4X * 4/8
In Aug they pay for the storage 0.5 * 4X * 3/8
In Sep they pay for the storage 0.5 * 4X * 2/8
In Oct they pay for the storage 0.5 * 4X * 1/8
total = 0.5 * 4X * 1/8 * [ 1+2+3+4+5+6+7]
= 0.5 * X/2 * (28)
= 7.0X
D
Answer: (D) 1.60x
Question: There are 27 bicycles and 10 tricycles in the storage area at Stanley's flat building. Each bicycle has 2 wheels and each tricycle has 3 wheels. How many wheels are there in all?
(A) 84
(B) 67
(C) 39
(D) 21
(E) 11
Rationale: Step 1: Find the number of bicycle wheels.
2 × 27 = 54
Step 2: Find the number of tricycle wheels.
3 × 10 = 30
Step 3: Find the total number of wheels.
54 + 30 = 84
There are 84 wheels in all.
Answer is A.
Answer: (A) 84
Question: A grocer has a sale of Rs. 5400, Rs. 9000, Rs. 6300, Rs. 7200 and Rs.4500 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5600?
(A) s. 1200
(B) s. 5400
(C) s. 5400
(D) s. 4999
(E) s. 5000
Rationale: Total sale for 5 months = Rs. (5400 + 9000 + 6300+ 7200 + 4500) = Rs. 32400.
Required sale = Rs. [ (5600 x 6) - 32400 ]
= Rs. (33600 - 32400)
= Rs.1200.
Option A
Answer: (A) s. 1200
Question: A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 20% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
(A) 1:20
(B) 1:10
(C) 1:8
(D) 1:4
(E) 1:2
Rationale: He needs to make a profit of 20%, which means he needs to sell the milk +water combination for 39.6 (20% of 33 +33)
Now, he plans to sell 1 liter of this solution of milk and water for 36. which means he needs to sell 1.1 liters of this solution to earn 39.6. (36 for 1 liter and so 39.6 for 1.1 liters)
Hence the water added would be .1 liter.
Therefore the ratio of water to milk is .1/1 = 1/10
ANSWER:B
Answer: (B) 1:10
Question: The length of a room is 7 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
(A) 25650
(B) 25750
(C) 26550
(D) 26750
(E) 29925
Rationale: Area = 7 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 7 × 4.75 × 900
= 7 × 4275 = Rs. 29925
Answer is E
Answer: (E) 29925
Question: V is the volume of a cylinder; the radius of the cylinder is 4.5. The height of the cylinder is 550% more than the radius. Which of the following is true?
(A) 100 < V < 300
(B) 300 < V < 500
(C) 500 < V < 700
(D) 700 < V < 900
(E) 900 < V < 1900
Rationale: As we see the answers are in form of range we can use approximation
Volume of cylinder is πr^2h
Given π= 22/7 and r = 4.5 so r^2 ~ 20 and h = 6.5 * 4.5 ~ 29
So 22/7 * 20 * 29 ~ 1823
so answer should be
E. 900 < V < 1900
Answer : E
Answer: (E) 900 < V < 1900
Question: (212 + 222 + 232 + ... + 302) = ?
(A) 385
(B) 2485
(C) 2570
(D) 3255
(E) none
Rationale: Solution
(212 + 222 + 232 + ... + 302) = a+(n-1)d=last number .....so 212+(n-1)10=302.....so n=10. so sum= n/2(2a+(n-1)d) = 10/2(2*212+9*10) = 2570.
Answer C
Answer: (C) 2570
Question: If k is a positive integer, which of the following must be divisible by 22?
(A)  (k – 4)(k)(k + 3)(k + 7)
(B)  (k – 4)(k – 2)(k + 3)(k + 5)
(C)  (k – 2)(k + 3)(k + 5)(k + 6)
(D)  (k + 1)(k + 3)(k + 5)(k + 7)
(E)  (k – 3)(k + 1)(k + 4)(k + 6)
Rationale: 22=11*2.
Note that the product of two consecutive even integers is always divisible by 8 (since one of them is divisible by 4 and another by 2). Only option B offers two consecutive even numbers for any integer value of k: k-4 and k-2, if k=even or k+3 and k+5 if k=odd.
Also from the following 3 consecutive integers:(k-4), (k-3),(k-2)one must be divisible by 3, if it's not k-4 or k-2 then it must be k-3 (if it's k-4 or k-2 option B is divisible by 3 right away). But if it's k-3 then (k-3)+6=k+3must also be divisible by 3.
So, option B: (k – 4)(k – 2)(k + 3)(k + 5) is divisible by 8 and 3 in any case.
Answer: D.
Answer: (D)  (k + 1)(k + 3)(k + 5)(k + 7)
Question: 98 students represent x percent of the boys at a school. If the boys at the school make up 50% of the total school population of x students, what is x?
(A) 110
(B) 140
(C) 220
(D) 250
(E) 500
Rationale: Let B be the number of boys in the school.
98 = xB/100
B = 0.5x
9800=0.5x^2
x^2 = 19600
x = 140
The answer is B.
Answer: (B) 140
Question: What is the sum of the greatest common factor and the lowest common multiple of 72 and 36?
(A) 192
(B) 220
(C) 224
(D) 108
(E) 284
Rationale: Prime factorization of 36 = 2 x 2 x 3 x 3
Prime factorization of 72 =2 x 2 x 2 x 3 x 3
GCF = 36
LCM = 72
Sum = 108.
Answer D.
Answer: (D) 108
Question: A shopkeeper sold 30articles at the cost price of 25 articles. Then find the profit% or lost%
(A) 15%
(B) 18%
(C) 20% loss
(D) 25%
(E) 30%
Rationale: here 30 articles selling price = 25 articles cost price
so the difference = 25-30 =-5
% of loss = 5*100/25 =20%
correct option is C
Answer: (C) 20% loss
Question: The average marks of a class of 30 students is 30 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 52.5
(B) 52.9
(C) 52.1
(D) 48.75
(E) 42.5
Rationale: Sum of the marks for the class of 30 students = 30 * 30 = 900
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
900 + 3000 = 3900
Average marks of all the students = 3900/80
= 48.75
Answer:D
Answer: (D) 48.75
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
(A) Rs.9000
(B) Rs.9700
(C) Rs.9800
(D) Rs.9900
(E) Rs.10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs.10000
E
Answer: (E) Rs.10000
Question: Eggs are sold in packages of six or eleven only. If Doris bought 62 eggs exactly, what could be the number of large packs Doris bought?
(A) 6.
(B) 2.
(C) 3.
(D) 5.
(E) 4.
Rationale: No strategy involved. Simple question demanding fast calculation.
11x4 = 44 => 62-44=18 => 18/6 is an integer
Ans E. 4.
Good luck
Answer: (E) 4.
Question: A number is said to be prime saturated if the product of all the different positive prime factors of w is less than the square root of w. What is the greatest two digit prime saturated integer ?
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95
Rationale: w 96 = 3 * 32 = 3 * 2^5
Answer is D.
Answer: (D) 96
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 24 seconds, what is the ratio of their speeds?
(A) 1:3
(B) 3:1
(C) 7:3
(D) 3:2
(E) 3:4
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 24 s
= (27x + 17 y)/(x+y) = 24
= (27x + 17 y)/ = 24(x+y)
= 3x = 7y
=x/y = 7/3
Answer :C
Answer: (C) 7:3