mathewhe/aqua_rat huggingface dataset:
Question: A completes a work in 10 days and B complete the same work in 12 days. If both of them work together, then the number of days required to complete the work will be
(A) 6.8 days
(B) 9 days
(C) 10 days
(D) 12 days
(E) 13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 10 × 12/ 22 = 6.8 days.
A
Answer: (A) 6.8 days
Question: If 0.75 : x :: 5 : 8, then x is equal to:
(A) 1.2
(B) 3.45
(C) 8.6
(D) 5.14
(E) 7.2
Rationale: Explanation:
(x x 5) = (0.75 x 8) x =(6/5)=1.20
Answer:A
Answer: (A) 1.2
Question: A bag holds 3 red marbles and 3 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be green?
(A) 1/10
(B) 1/6
(C) 3/10
(D) 1/5
(E) 1/2
Rationale: Given: 3R and 3 G marbles
Required: Probability that 2 marbles removed without replacement are both red
Initially we have to pick one red from a total of 3 red and 3 green marbles
After one green has been picked, we need to pick 1 green from a total of 2 greenand 3 red marbles.
P(Both green) = (3/6)*(2/5) = 1/5
Option D
Answer: (D) 1/5
Question: If x is 30 percent greater than 88, then x =
(A) 68
(B) 70.4
(C) 86
(D) 114.4
(E) 108
Rationale: x=88*1.3=114.4
So the answer is D.
Answer: (D) 114.4
Question: The smallest prime number is:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The smallest prime number is 2.
Answer:B
Answer: (B) 2
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18
(B) 99
(C) 77
(D) 66
(E) 41
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer:A
Answer: (A) 18
Question: Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, 45 what is the minimum possible range in scores of the three test-takers?
(A) a 17
(B) b) 28
(C) c) 35
(D) d) 45
(E) e) 80
Rationale: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
C- 0 and 35
D- 0 and 45
therefore the minimum range is 45, it cant be any lower however you play with the numbers.
D
Answer: (D) d) 45
Question: The G.C.D. of 1.08, 0.31 and 0.9 is:
(A) 0.01
(B) 0.9
(C) 0.18
(D) 0.108
(E) None
Rationale: EXPLANATION
Given numbers are 1.08, 0.31 and 0.90. H.C.F. of 108, 31 and 90 is 1,
H.C.F. of given numbers = 0.01.
Answer A
Answer: (A) 0.01
Question: During a two-week period, the price of an ounce of silver increased by 20 percent by the end of the first week and then decreased by 10 percent of this new price by the end of the second week. If the price of silver was x dollars per ounce at the beginning of the two-week period, what was the price, in dollars per ounce, by the end of the period?
(A) 1.02x
(B) 1.04x
(C) 1.06x
(D) 1.08x
(E) 1.1x
Rationale: The price at the end is 0.9(1.2x)=1.08x
The answer is D.
Answer: (D) 1.08x
Question: The sector of a circle has radius of 28 cm and central angle 135o. Find its perimeter?
(A) 91.5
(B) 91.4
(C) 91.7
(D) 91.3
(E) 122
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 28) + 2(28)
= 66 + 56 = 122 cm
Answer:E
Answer: (E) 122
Question: Which of the following has the most number of divisors?
(A) 99
(B) 101
(C) 176
(D) 182
(E) 179
Rationale: Explanation:
99 = 1 x 3 x 3 x 11
101 = 1 x 101
176 = 1 x 2 x 2 x 2 x 2 x 11
182 = 1 x 2 x 7 x 13
So, divisors of 99 are 1, 3, 9, 11, 33, .99
Divisors of 101 are 1 and 101
Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176
Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.
Hence, 176 has the most number of divisors. Answer: C
Answer: (C) 176
Question: Adam spent 1/6 of his lifetime in adolescence. His facial hair started growing after 1/12 more of his life. He successfully married his girlfriend Diana after 1/7 more of his life. Their son was born after 5 years from then. The son lived just 1/2 of what Adam lived. Adam dies four years after his son died.
(A) 84
(B) 90
(C) 81
(D) 75
(E) 66
Rationale: A
Let us assume that Adam lived for p years.
p/6 + p/12 + p/7 + 5 + p/2 + 4 = x
=> p = 84.
Therefore, Adam lived for 84 years.
Answer: (A) 84
Question: How much 80% of 40 is greater than 10% of 15?
(A) 18
(B) 99
(C) 19
(D) 18
(E) 17
Rationale: (80/100) * 40 – (10/100) * 15
32 - 15 = 17
Answer: E
Answer: (E) 17
Question: The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 186,000. What was the percent increase in the cost of the home?
(A) 60%
(B) 50%
(C) 55%
(D) 40%
(E) 33.3%
Rationale: Increase = 186000-120000 = 66000
% increase = 66000*100/120000 = 55%
Answer: option C
Answer: (C) 55%
Question: If two pipes function simultaneously the reservoir will be filled in 12 hours, one pipe fills the reservoir 10 hours faster than the other. How many hours it takes the second pipe to fill the reservoir?
(A) 15 hours
(B) 18 hours
(C) 30 hours
(D) 20 hours
(E) 22 hours
Rationale: C
30 hours
Answer: (C) 30 hours
Question: The ratio between the length and the breadth of a rectangular park is 1 : 4. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 124545 m
(B) 134561 m
(C) 156787 m
(D) 15450 m
(E) 102400 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 1x metres and breadth = 4x metres.
Then, 2(1x + 4x) = 1600 or x =160.
Length = 160 m and Breadth = 640 m.
Area = (160 x 640) m2 = 102400 m
E
Answer: (E) 102400 m
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
(A) 228
(B) 640
(C) 888
(D) 276
(E) 981
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer:B
Answer: (B) 640
Question: Sanjay deposited Rs. 5000 in the bank. The bank offered simple interest at the rate of 12 per cent per year. After 5 years the total amount received by him will be:
(A) 7,000
(B) 7,500
(C) 7,700
(D) 7,900
(E) 8,000
Rationale: Explanation:
P = Rs. 5000, R = 12% p. a and T = 5 years
S.I = PRT / 100
= 5000 X 12 X 5 X 1/1000
=3000
Amount = P+S. I = Rs. 5000+Rs. 3000 = Rs. 8000
Answer:C
Answer: (C) 7,700
Question: log root(8)/log 8 is equal to
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: => log(8)^1/2/log 8 = 1/2 log 8/log 8 = 1/2
ANSWER A
Answer: (A) 1/2
Question: Baby Isabel plays with blocks. Each block is 1.5 inches tall. She has a collection of 20 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be?
(A) 67"
(B) 30"
(C) 106"
(D) 120"
(E) 151.7"
Rationale: 1.5"*20=30". Answer is B.
Answer: (B) 30"
Question: A military commander has to choose 2 soldiers out of a company of 9 for guarding the headquarters. How many different group combinations of 2 does he have to choose from?
(A) 4
(B) 15
(C) 36
(D) 27
(E) 35
Rationale: A military commander has to choose 2 soldiers out of a company of 9.
different group combinations of 2
He can do this in 9C2 ways
9*8/2*1= 36 ways
ANSWER:C
Answer: (C) 36
Question: A trail mix company keeps costs down by employing the peanuts:cashews:almonds ratio of 10:4:1 in each bag of up to 75 total nuts. What is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts?
(A) 40%
(B) 48%
(C) 49%
(D) 50%
(E) 58%
Rationale: Peanuts = 50
Cashews = 20
Almonds = 5
We want to remove as many peanuts as possible while still having peanuts represent MORE than half of the mixture...
The number of cashews and almonds will stay the same though, so we have 20 + 5 = 25 of those non-peanuts in total.
If we had 25 peanuts and 25 non-peanuts, then that would be 50% EXACTLY. We want MORE than 50% though, so we need to add in 1 more peanut. This gives us...
Peanuts = 26
Cashews = 20
Almonds = 5
The question asked for the decrease in the number of peanuts as a percentage. We started with 50 peanuts and removed 24 = 24/50 = 48% ;ANSWER:B
Answer: (B) 48%
Question: x - y = 5
2x = 2y + 10
The system of equations above has how many solutions?
(A)  Infinitely many
(B)  Exactly one
(C)  Exactly two
(D)  Exactly three
(E)  None
Rationale: x-y=5 ---------------1
2x=2y+10 ---------------2
Divide equation 2 by 2:
2x/2=(2y+10)/2
x=y+5
x-y=5----------------3
Equation 1 and 3 are equal and thus have infinitely many solutions:
x-y=5
x=5, y=0
x=6, y=1
x=7, y=2
Ans:A
Answer: (A)  Infinitely many
Question: In the list 3, 3, 4, 4, 5, 5, 5, 5, 7, 11, 21, what fraction of the data is less than the mode?
(A) 2/9
(B) 1/3
(C) 4/11
(D) 2/3
(E) 7/9
Rationale: Mode: The mode of any set is the term which has the highest frequency (Occurrence)
Highest frequent term in the set is 5 (with frequency 4) hence
Mode = 5
two terms (3, 3, 4, 4) out of a total of 11 terms are less than mode of the set.
Fraction of set that are less than Mode of set = 4/11
Answer: Option C
Answer: (C) 4/11
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 60 Kmph
(B) 70 Kmph
(C) 80 Kmph
(D) 85 Kmph
(E) 90 Kmph
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
A
Answer: (A) 60 Kmph
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 11
(B) 20
(C) 28
(D) 26
(E) 21
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer: B
Answer: (B) 20
Question: A grocer buys apples for 100¢ per pound. If 20% of the apples goes bad and he still wants to make a 10% profit over his purchase price, what should be the sales price?
(A) 136¢
(B) 130¢
(C) 140¢
(D) 137.5¢
(E) 142¢
Rationale: for making calculation simple let us consider he buys 10pounds @ 100/pound=1000¢ in total .
20% apples lost...means 8 pounds left.
further he wants 10% profit on 1000 ¢
means he wants to earn 1100¢
sales price should be 1100/8=¢ 137.5
Ans D
Answer: (D) 137.5¢
Question: A and B invests Rs.3000 and Rs.5000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 9:6
(B) 9:8
(C) 9:10
(D) 9:9
(E) 9:5
Rationale: (3*6 + 6*6): (5*12)
54:60 => 9:10.Answer:C
Answer: (C) 9:10
Question: Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 88, and the three numbers in order are?
(A) 116,58,36
(B) 98,49,33
(C) 126,63,36
(D) 144,72,48
(E) None of these
Rationale: Explanation :
Solution: Let A =x,
B =x/2, C = x/3.
=x + x/2 + x/3 / 3 = 88
By solving we will get x = 144.
Hence A= 144
B= 144/2= 72
C= 144/3 = 48
Answer : D
Answer: (D) 144,72,48
Question: If two numbers are in the ratio 4:3. If 20 is added to both of the numbers then the ratio becomes 5:4 then find the smallest number?
(A) 60
(B) 30
(C) 40
(D) 20
(E) 50
Rationale: 4:3
4x + 20 : 3x + 20 =5 : 4
4[4x + 20] =5[3x + 20]
16x + 80 = 15x + 100
16x -15x = 100 - 80
x = 20
Then smallest number is = 2
3x = 60
A
Answer: (A) 60
Question: If f and t are integers and f^2 – t^2 is an odd integer, which of the following must be an even integer?
I. f + t + 2
II. f^2 + 2ft + t^2
III. f^2 + t^2
(A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III
Rationale: f^2–t^2 is an odd integer means that either f is even and t is odd or f is odd and t is even.
Check all options:
I. f + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. f^2 + 2ft + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. f^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A.
Answer: (A) None
Question: The pages of a report are numbered consecutively from 1 to 9. If the sum of the page numbers up to and including page number x of the report is equal to THREE less than the sum of the page numbers following page number x, then x =
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: sum of the first few numbers =1+2+3+4+5+6 =21
sum of the last few = 7 +8+ 9 =24 page no.6 answer .C
Answer: (C) 6
Question: If 8 cats can kill 8 rats in 8 minutes, how long will it take 100 cats to kill 100 rats?
(A) 6 minutes
(B) 7 minutes
(C) 8 minutes
(D) 9 minutes
(E) 10 minutes
Rationale: It will take 8 minutes for 100 cats to kill 100 rats.
1 cat can kill 1 rat in 8 minutes, so 100 cats can kill 100 rats in 8 minutes
Answer C
Answer: (C) 8 minutes
Question: A cistern is normally filled in 2 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
(A) 4 hours
(B) 20 hours
(C) 30 hours
(D) 40 hours
(E) 50 hours
Rationale: If leakage/hour=1/x, then 1/2 -1/x= 1/4, solving 1/x=1/4
So in 4 hours full cistern will be empty.
ANSWER:A
Answer: (A) 4 hours
Question: The cash difference between the selling prices of an article at a profit of 8% and 6% is Rs. 3. The ratio of the two selling prices is?
(A) 52:56
(B) 52:53
(C) 52:50
(D) 54:53
(E) 52:51
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 108% of x / 106% of x
= 108/106 = 54/53 = 54:53
Answer: D
Answer: (D) 54:53
Question: For which of the following functions is f(q) = f(−q) for all values of q ?
(A) f(x) = x^3 + 3
(B) f(x) = −x
(C) f(x) = 2x + 3
(D) f(q) = −q^2 + 2
(E) f(x) = 5x − 4
Rationale: f(q) = f(−q)
The above is a property of an even function .
f(q) = f^(n)
f(q) = f(−q) will hold when n is an even integer .
The only case when q is even is option D
Answer D
Answer: (D) f(q) = −q^2 + 2
Question: Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?
(A) k m %
(B) (k – m) %
(C) [100(k – m)] / (100 + k) %
(D) [100(k – m)] / (100 + m) %
(E) [100(k – m)] / (100 + k + m) %
Rationale: Price Per Share (PPS) = x
Earning Per Share(EPS) = y
Increased PPS = x(1+k/100)
Increased EPS = y(1+m/100)
% increase in the ratios (PPS/EPS) = {[x(100+k)]/[y(100+m)] - (x/y)} / (x/y)
On Simplifying, % increase = [100(k-m)] / (100 + m) % , ANSWER:D
Answer: (D) [100(k – m)] / (100 + m) %
Question: A bakery sells 4 varieties of pastries. John buys 10 pastries making sure, he gets at least one of each kind.
In how many ways can John make the purchase ?
(A) 84
(B) 86
(C) 88
(D) 90
(E) 82
Rationale: no of 1st variety of pastry: a
no of 2nd variety of pastry: b
no of 3rd variety of pastry: c
no of 4th variety of pastry: d
So, we have a+b+c+d=10 (where a,b,c,d>0)
Remember: Number of positive integer solution of x+y+z+... (r terms) = n is (n-1)C(r-1)
So, the answer to the question would be (10-1)C(4-1) = 9C3 = 84.
ANSWER:A
Answer: (A) 84
Question: A certain protective additive increases from 50 days to 60 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?
(A) 25%
(B) 33 1/3%
(C) 50%
(D) 66 2/3%
(E) 20%
Rationale: General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the time between maintenance checks increased by 60−50/50∗100=20
Answer: E.
Answer: (E) 20%
Question: The relationship between quantities m and n is expressed by the equation 30m = 5(n - 42). If the difference between the two chosen values of n is 30, what is the difference in the corresponding values of m?
(A) 5
(B) 42/11
(C) 60/11
(D) 150/11
(E) 14
Rationale: Another Simple way
30m=5(n-42)
Assume n = 42 to make one side equal to 0
then 30m=0
and m = 0
Repeat it by assuming n as 42+30 i.e 72
30m- 5(72-42)
30m=150
m=150/30
diff = 5 - 0 = 5
Answer : A
Answer: (A) 5
Question: A sock drawer contains five socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. If the socks are laid next to each other, how many different arrangements of socks could be made?
(A) 24
(B) 240
(C) 1,024
(D) 2,520
(E) 120
Rationale: I see no condition for arrangement.
So 5! ways - IMO option E is correct answer..
Answer: (E) 120
Question: Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 16 hours and 25 hours after they passed each other the ratio of the speeds of the two trains was
(A) 2:1
(B) 3:2
(C) 4:3
(D) 5:4
(E) 1:2
Rationale: Explanation:
Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)
Therefore, Ratio of the speeds of two trains = = 5 : 4. Answer: D
Answer: (D) 5:4
Question: At a certain university, the ratio of the number of teaching assistants to the number of students in any course must always be greater than 4:85. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?
(A) 106
(B) 107
(C) 108
(D) 109
(E) 110
Rationale: (5/4)*85=106 plus remainder
The answer is A.
Answer: (A) 106
Question: A, B, and C working alone can finish constructing a house in 6, 12, and 18 hours respectively. A starts alone and works for 1 hour. He is then joined by B and they work together for 1 hour. Finally C joins them and they all work together to finish the work. If they start working at 9 am, at what time will they finish?
(A) 12:05 pm
(B) 12:15 pm
(C) 12:35 pm
(D) 12:55 pm
(E) 1:15 pm
Rationale: A completes 1/6 of the job each hour.
B completes 1/12 of the work each hour.
C completes 1/18 of the work each hour.
A completes 1/6 of the work in the first hour.
Working together, A and B complete another 3/12 for a total of 5/12.
Working together, A, B, and C can complete 11/36 of the work each hour.
To complete 7/12, the time required is (7/12) / (11/36) = 21/11 hours.
The work will be completed at 12:00 plus 10*60/11 minutes which is about 12:55 pm.
The answer is D.
Answer: (D) 12:55 pm
Question: If |20x-10| = 150, then find the product of the values of x?
(A) -45
(B) 56
(C) -62
(D) 35
(E) -30
Rationale: |20x-10| = 150
20x-10 = 150 or 20x-10 = -150
20x = 160 or 20x = -140
x = 8 or x = -7
product = -7*8 = -56
Answer is B
Answer: (B) 56
Question: Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be even?
(A) 3/14
(B) 2/7
(C) 1/3
(D) 1/2
(E) 12/21
Rationale: Probability that the number on first die is even = 3/6 [Because 3 out of 6 faces are even]
Probability that the number on Second die is even = 3/7 [Because 3 out of 7 faces are even]
Probability that Both Dice result in odd numbers = (3/6)*(3/7) = 3/14
Answer: Option A
Answer: (A) 3/14
Question: If the average cost of a house was $70,000 in 1965 and was x in 2005, what was the average increase in home prices per year over this period?
(A) A)(x+50,000)/40
(B) C)(50,000/40)+x
(C) B)(x-50,000)/40
(D) D)(50,000-x)/40
(E) E)x/40
Rationale: Average house price in 2005: x
Average house price in 1965: 50,000
2005-1965=40
Average increase per year: (x-70,000)/40
Answer is C
Answer: (C) B)(x-50,000)/40
Question: A loan has a variable interest rate that fluctuates between 5% and 10% of the base payment per month. If base payments remain at $200 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
(A) $220.00
(B) $222.20
(C) $224.20
(D) $224.40
(E) $225.60
Rationale: The maximum interest in one month is 10%*$200=$20.
The combined payment (base plus interest) is $200 + $20 = $220.
The greatest possible payment is: 1.01*$220=$222.20.
The answer is B.
Answer: (B) $222.20
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?
(A) 27 grams
(B) 28 grams
(C) 29 grams
(D) 42 grams
(E) 32 grams
Rationale: Let original mass be 100
The final mass of that element will be 7
So whatever option we have it will be divisible by 7
Check for the options the one that doesn't produce non terminating decimal is our answer
A. 27 grams
27/7 = 3.857...
B. 25 grams
25/7 = 3.571...
C. 29 grams
29/7 = 4.142.......
D. 42 grams
42/7 = 6
E. 32 grams
32/7 = 4.571....
Hence our answer will be (D)
Answer: (D) 42 grams
Question: Five people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
(A) 7/8
(B) 1/8
(C) 1/4
(D) 1/7
(E) 1/9
Rationale: Original share of 1 person =1/5
New share of 1 person =1/4
Increase =1/4 -	1/5 =1/20
Required fraction =	(1/20)/(1/5)=1/4
Answer is C.
Answer: (C) 1/4
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 42 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
(A) 70
(B) 245
(C) 150
(D) 300
(E) 350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 42, so 0.14*{total} = 42 --> {total} = 300.
Answer: D.
Answer: (D) 300
Question: A can have a piece of work done in 8 days, B can work three times faster than the A, C can work five times faster than A. How many days will they take to do the work together ?
(A) 3 days
(B) 8/9 days
(C) 4 days
(D) can't say
(E) none
Rationale: A's 1 day work is 1/8
B's 1 day work is 3/8
C's 1 day work is 5/8
(A+B+C)'s 1 day work(1/8+3/8+5/8) is 9/8
so, they can finish the work in 8/9 days
ANSWER:B
Answer: (B) 8/9 days
Question: Calculate the sum of first 28 natural numbers.
(A) 426
(B) 406
(C) 401
(D) 409
(E) 405
Rationale: Solution
We know that(1+2+3+.....+28)	= n(n+1)/2
Therefore (1+2+3+....+28)	=(28×29 / 2)
= 406.
Answer B
Answer: (B) 406
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is
(A) 9 years
(B) 11 years
(C) 14 years
(D) 21 years
(E) 25 years
Rationale: Solution
Age of the 15th student	=[15x15-(14x5+16x9)]
= (225 - 214)
= 11 years.
Answer B
Answer: (B) 11 years
Question: The average of seven numbers is 26. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 25
(B) 83
(C) 29
(D) 32
(E) 34
Rationale: The total of seven numbers = 7X26 = 182
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (182 - 99 ) = 83
B
Answer: (B) 83
Question: How many figures are required to number the pages the pages of a book containing 709 pages?
(A) 2020
(B) 2019
(C) 1019
(D) 2029
(E) 2039
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 709 = 610 * 3 = 1830
-----------
2019
ANSWER:B
Answer: (B) 2019
Question: If k is an integer, which of the following must be an even integer?
(A) k^2-k-1
(B) k^2-4k+6
(C) k^2-5k+5
(D) k^2+3k+8
(E) k^2+2k+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: k^2-k-1 = -1 { If k = 1 }
B: k^2-4k+6 = 3 { If k = 1 }
C: k^2-5k+5 = 1 { If k = 1 }
D: k^2+3k+8 = 12 { If k = 1 }k^2+3k+8 = 18 { If k = 2 }
E: k^2+2k+10 = 13 { If k = 1 }
Thus the only possible answer is (D)
Answer: (D) k^2+3k+8
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 22
(B) 99
(C) 24
(D) 66
(E) 887
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer: C
Answer: (C) 24