mathewhe/aqua_rat huggingface dataset:
Question: In a class of 100 students, there are 50 who play soccer, 45 who play
basketball, and 50 who play volleyball. Only 15 of these students play all
three sports. Everyone plays at least one of these sports. How many of
the students play exactly two of these sports?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Let S1 be the number of students who play exactly one of the three sports; S2 - the
number of students who play exactly two of the three sports; and let S3 be the number
of students who play all three sports. We know that S3 = 15 and S1 + S2 + S3 = 100
(the total number of students). Also in the sum 50+45+50 (soccer players + basketball
players + volleyball players), each student who plays exactly one sport is counted once,
the ones who play exactly two sports are counted twice, and those who play all three
sports are counted three times. Thus, 50 + 45 + 50 = S1 + 2S2 + 3S3. Note that
S2 = (S1 + 2S2 + 3S3) − (S1 + S2 + S3) − 2S3 = 15
correct answer A
Answer: (A) 15
Question: Pipes A and B can fill a tank in 2 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
(A) 3 9/97 hrs
(B) 3 9/77 hrs
(C) 3 9/17 hrs
(D) 1 5/7 hrs
(E) 3 9/19 hrs
Rationale: Net part filled in 1 hour = 1/2 + 1/6 - 1/12
= 7/12
The tank will be full in 12/7 hrs, i.e., 1 5/7 hrs.
Answer:D
Answer: (D) 1 5/7 hrs
Question: Tom can do a piece of work in 5 days and Ben alone can do it in 10 days. How much time will both take to finish the work ?
(A) A)3.3333
(B) B)4.3333
(C) C)7.3333
(D) D)5.3333
(E) E)2.3333
Rationale: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 5 x 10 / (5 + 10)
= 50 / 15
= 3.3333 days
Answer: A
Answer: (A) A)3.3333
Question: From the starting point in a boat race, one competitor started to sail north at a speed of 1.5 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours?
(A) 9.6
(B) 12.
(C) 12.5.
(D) 14.
(E) 15.4.
Rationale: Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.5 *5= 7.5 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (7.5^2+ 6^2)^1/2= 9.6 KM
A is the answer
Answer: (A) 9.6
Question: Which of the following fractions E, if written as a decimal, would have a 2 in the thousandths place ?
(A)  3/11
(B)  7/9
(C)  1/8
(D)  4/7
(E)  1/6
Rationale: (A) E=3/11 = 0.2727272727....
Answer: A
Answer: (A)  3/11
Question: Milk contains 5% water.What quantity of pure milk should be added to 10 litres of milk to reduce this 2%?
(A) 15 litres
(B) 16 litres
(C) 17 litres
(D) 25 litres
(E) 35 litres
Rationale: Present Ration of MIlK TO WATER IS 95:5
Amount of Milk is 10 litres
Hence, Pure milk content is 9.5 litre
and water content is 0.5 litres
Now, we should not disturb the water content
So, 0.5 litres of water is equivalent to 2%
So 100% mixture is :(0.5/2)*100=25litre
Thus, milk should be added=25-10=15 litres of pure milk
ANSWER:A
Answer: (A) 15 litres
Question: A card shop contains 5 birthday cards, 5 holiday cards, and 5 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be of the same type?
(A) 6/91
(B) 5/93
(C) 4/95
(D) 3/97
(E) 2/99
Rationale: It might require to be written as "5 different birthday cards, 5 different holiday cards, and 5 different graduation cards" rather than "5 birthday cards, 5 holiday cards, and 5 graduation cards"..
If the cards are same there will be ONLY 1 way to pick from each type and thus overall 3..
so numerator has to be 3, or 1 if 3 cancels out..
If I take all as different cards--
ways to pick 3 cards of same type = 5C3 * 3= 30
ways to pick 3 cards out of 15 = 15C3 = 455
Prob = 30/455 = 6/91
Ans: A
Answer: (A) 6/91
Question: The age of the two friends were in the ration of 6:5. If the sum of their ages is 55. Then after how many years their ratio will become 8:7?
(A) 11
(B) 7
(C) 10
(D) 12
(E) 13
Rationale: since given ratio is 6:5 of their ages.
6x+5x=55(given)
11x=55
x=5. so present ages are: 6*5=30 and 5*5=25
after few yrs ratio becomes 8:5.
so,their ages will become 8x and 7x respectively, ie. 40 and 35 respectively.
nw difference of their current ages and further ages is clear from above... ie. 10 yrs.
ANSWER:C
Answer: (C) 10
Question: A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/4. What is the difference of the numerator and denominator of the original fraction?
(A)  49
(B)  35
(C)  28
(D)  24
(E)  21
Rationale: x/y = 2/5 -> 1
(x+4)/2y = 1/4 -> 2
Divide 1 by 2 :
=> 2x/(x+4) = 8/5
=> 5x = 4x + 16
=> x = 16
=> y = 5/2 *16 = 40
so x - y = 24
The answer is D
Answer: (D)  24
Question: The ratio of Male to Female in last week Calvary Church attendance was 4:6. If 60% of the Male and 40% of the Female were Under 35 years, How many people under 35 years of age attended Calvary Church last Sunday.
(A) 51%
(B) 50%
(C) 48%
(D) 54%
(E) 46%
Rationale: let total no of last week Calvary church attendance be 100, Male 40 and Female 60, so total number of last week Calvary church attendance below 35 years for both male and female respectively 40* 60/100=24 and 60* 40/100=24
so total 48 Calvary church attendance last week out of a Total of 100 attendance is under 35 years......so required % is 48%
ANSWER:C
Answer: (C) 48%
Question: A man complete a journey in 20 hours. He travels first half of the journey at the rate of 10 km/hr and second half at the rate of 15 km/hr. Find the total journey in km.
(A) 220 km
(B) 240 km
(C) 230 km
(D) 232 km
(E) 234 km
Rationale: 0.5x/10 + 0.5x/15 = 20
--> x/10+ x/15= 40
--> 5x = 30x40
--> x = (30x40)/5 = 240 km.
Answer : B.
Answer: (B) 240 km
Question: Sum of 49 odd numbers is?
(A) 2398
(B) 2399
(C) 2400
(D) 2401
(E) 2402
Rationale: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 49 odd numbers = 49^2 = 2401
ANSWER:D
Answer: (D) 2401
Question: What is the smallest number K which when increased by 5 is completely divisible by 8, 11 and 24?
(A) 264
(B) 259
(C) 269
(D) 270
(E) 282
Rationale: This question includes a number of great Number Property shortcuts that you can take advantage of:
1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.
2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.
3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.
The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.
Final Answer:
B
Answer: (B) 259
Question: Ayesha's father was 38 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 10 years
Rationale: Explanation:
Mother's age when Ayesha's brother was born = 34 years.
Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 34) years = 8 years.
Answer: D
Answer: (D) 8 years
Question: A is a working partner and B is a sleeping partner in a business. A puts in 20,000 and B 90,000. A gets 20% of the profit for managing the business, and the rest is divided in proportion to their capitals. Find the share of B in profit of 11000.
(A) 3500
(B) 7200
(C) 6800
(D) 4800
(E) None of these
Rationale: The amount A gets for managing
= 20% of Rs. 11000 = 2200
Remaining profit = 11000 – 2200 = 8800
This is to be divided in the ratio 2 : 9.
Share of B = 9/11 of 8800 = 7200
Answer B
Answer: (B) 7200
Question: A bullet train 150 m long is running with a speed of 30 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the bullet train is going?
(A) 23 sec
(B) 15 sec
(C) 12 sec
(D) 11 sec
(E) 15 sec
Rationale: E
15 sec
Speed of the bullet train relative to man = (30 + 6) kmph
= 36 *5/18 m/sec = 30/3 m/sec.
Time taken by the bullet train to cross the man = Time taken by it to cover 150 m at (30/3) m / sec
= (150 *3/30) sec = 15 sec
Answer: (E) 15 sec
Question: 99! how many zero's?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: 99!=99/5=19
=19/5=3
so 99! has (19+3=22 zeroes)
ANSWER:C
Answer: (C) 22
Question: A can do a piece of work 30 days. B can do work in 55 days. In how many days they will complete the work together?
(A) 15 days
(B) 16 days
(C) 19.4 days
(D) 17.2 days
(E) 18 days
Rationale: LCM = 330, Ratio= 30:45=6:11
No of days= 330/(6+11) = 330/17 = 19.4 days
ANSWER:C
Answer: (C) 19.4 days
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) 339
(B) 278
(C) 189
(D) 287
(E) 211
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
Answer: C
Answer: (C) 189
Question: Nitin ranks 18th in a class of 49 students. What is rank from the last ?
(A) 33
(B) 38
(C) 32
(D) 28
(E) 19
Rationale: Explanation:
Number students behind the nitin in rank = (49 - 18) = 31
Nitin is 32nd from the last
Answer: C) 32
Answer: (C) 32
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda
spends 30% more time painting the house than Angela, each receives a payment
of m dollars when the work is completed. If Angela decides to pay Linda n
dollars so that they would have received the same compensation per hour
worked, what is n in terms of m?
(A) A)(3/23)m
(B) B)(1/3)m
(C) C)(1/4)m
(D) D)(1/5)m
(E) E)(1/6)m
Rationale: let angela work for 10hrs and get 1150 rs. (m =1150)
According to question, linda works 30% more time and gets the same amount. so let linda work 13 hrs and get 1150 rs.
so they do a total of 13 +10=23 hrs of work and get 2300 rs together . The question basically asks to equalise their payment. so a total of 2300 rs is received by them and they do 23 hrs work together. average rate will be 2300/23 = 100 rs per hr. so linda should get 13*100 =1300 rs. But she got only 1150. so angela should give 150 rs to linda. answer = 150/1150 =3/23
answer A
Answer: (A) A)(3/23)m
Question: Three partners A, B, C in a business invested money such that 2(Aâ€™s capital) = 5(Bâ€™s capital) = 10(Câ€™s capital) then, The ratio of their capitals is
(A) 63 : 45 : 34
(B) 63 : 54 : 34
(C) 5 : 2 : 1
(D) 63 : 45 : 35
(E) None of these
Rationale: Explanation:
Let 2(Aâ€™s capital) = 5(Bâ€™s capital) = 10(Câ€™s capital) = Rs.x
Then, Aâ€™s capital = Rs x/2, Bâ€™s capital = Rs. x/5 and Câ€™s capital = Rs. x/10
A : B : C = x/2 : x/5 : x/10
5 : 2 : 1
Answer: Option C
Answer: (C) 5 : 2 : 1
Question: the walker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the walker continues to walk at her constant rate, how many minutes must the cyclist wait until the walker catches up?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: After passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles/hour.
In those 5 mins the cyclist travels a distance of 5/3 miles.
In those 5 mins the hiker travels a distance of 1/3 miles.
So the hiker still has to cover 4/3 miles to meet the waiting cyclist.
The hiker will need 1/3 hours or 20 mins to cover the remaining 4/3 miles.
So the answer is C.
Answer: (C) 20
Question: Doughnut delivery delivers about 75 orders using 15 fleet bikes in any given day of 15 hours. They need to increase their delivery for Christmas and so they bought 10 more bikes and now work for 4 extra hours. How many more orders will be delivered in the next eight days?
(A) 200
(B) 225
(C) 37.5
(D) 16,875
(E) 95
Rationale: old bikes deliver 75/15= 5 orders per hour, which is 5* (15+4) hours= 95 orders in new day time frame.
Total bikes is 25* 95 orders is 225 orders.
Answer is B.
Answer: (B) 225
Question: If the sides of a triangle are 30 cm, 26 cm and 10 cm, what is its area?
(A) 120
(B) 110
(C) 130
(D) 140
(E) 150
Rationale: The triangle with sides 30 cm, 26 cm and 10 cm is right angled, where the hypotenuse is 30 cm.
Area of the triangle = 1/2 * 26 * 10 = 130 cm2
Answer: Option C
Answer: (C) 130
Question: A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 30 nickles in the bag, how many coins are there in that bag?
(A) 70
(B) 65
(C) 75
(D) 85
(E) 80
Rationale: A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 5x and number of nickels = 3x
But we know the number of nickels, 30. Hence
3x = 30
Solve for x
x = 10
The total number of coins is given by
5x + 3x = 8x = 8 × 10 = 80
E
Answer: (E) 80
Question: The L.C.M. of two numbers is 42. The numbers are in the ratio 2 : 3. Then sum of the number is:
(A) 28
(B) 32
(C) 35
(D) 53
(E) 54
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 42 or x = 7.
The numbers are 14 and 21.
Hence, required sum = (14 + 21) = 35.
Answer: Option C
Answer: (C) 35
Question: Kiran has $100 in her piggy bank. How much will she have in her bank 30 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?
(A) 500
(B) 525
(C) 535
(D) 565
(E) 575
Rationale: The dollar deposits are in an A.P.
1,2,3,4...30 with common difference 1
Sum of the terms is n(n+1) / 2
i.e 30 * (30+1) /2
= 30 * 31/2 = 465
Total deposit therefore with Chiu-Lihas is 100 + 465 = 565$
Answer: (D) 565
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
(A) 304 cm2
(B) 384 cm2
(C) 184 cm2
(D) 284 cm2
(E) 385 cm2
Rationale: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: B
Answer: (B) 384 cm2
Question: A man can row upstream at 7 kmph and downstream at 10kmph.find man’s rate in still water and the rate of current.
(A) 1.5 km/hr
(B) 2.5 km/hr
(C) 3.5 km/hr
(D) 4.5 km/hr
(E) 5.5 km/hr
Rationale: Rate in still water=1/2(10+7)km/hr=8.5 km/hr.
Rate of current=1/2(10-7)km/hr=1.5 km/hr.
ANSWER A 1.5 km/hr
Answer: (A) 1.5 km/hr
Question: A cube of side 5 meter length is cut into small cubes of side 25cm each. How many such small cubes can be obtained?
(A) 10781
(B) 1276
(C) 1000
(D) 8000
(E) 5000
Rationale: Along one edge, the number of small cubes that can be cut
= 500/25 =20
Along each edge 20 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
=20 *20 * 20 = 8000
Answer:D
Answer: (D) 8000
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
(A) 4:8
(B) 1:4
(C) 6:2
(D) 3:1
(E) 1:2
Rationale: Explanation:
d = 3d d = d
aâˆš2 = 3d aâˆš2 = d
a = 3d/âˆš2 a = d/âˆš2 => 3: 1
ANSWER IS D
Answer: (D) 3:1
Question: A male student must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to the student?
(A) 120
(B) 140
(C) 110
(D) 150
(E) 160
Rationale: as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 5 from later half..
ways = 5C2 = 10..
total ways = 10C3 = 120
ans = 120-10 = 110
C
Answer: (C) 110
Question: 70 is subtracted from 30% of a number, the result is 20. Find the number?
(A) 150
(B) 997
(C) 266
(D) 300
(E) 271
Rationale: (30/100) * X – 70 = 20
3X = 900
X = 300
Answer:D
Answer: (D) 300
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 49 years. What will be the age of the B ten years hence?
(A) 22
(B) 77
(C) 26
(D) 98
(E) 51
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 49 => b + c = 98 --- (2)
From (1) and (2), we cannot find b.
Answer: D
Answer: (D) 98
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 60 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 88
(E) 26
Rationale: We have: l = 20 ft and lb = 60 sq. ft.
So, b = 3 ft.
Length of fencing = (l + 2b) = (20 + 6) ft = 26 ft.
ANSWER:E
Answer: (E) 26
Question: A bag contains 5 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?
(A) 2/5
(B) 3/5
(C) 1/5
(D) 7/15
(E) 5/8
Rationale: Total number of balls = (5 + 5 + 6) = 16.
Therefore, n(S) = 16.
Let E1 = event of drawing a red ball.
and E2 = event of drawing a green ball.
Then, E1 n E2 = f.
P (E1 n E2) = P(E1) + P(E2) = (5/16 + 5/16) = 5/8.
ANSWER:E
Answer: (E) 5/8
Question: A set S = {x, -8, -5, -1, 1, 6, 9, y} with elements arranged in increasing order. If the median and the mean of the set are the same, what is the value of |x|-|y|?
(A) -1
(B) Cannot be determined
(C) 1
(D) 0
(E) 2
Rationale: Median of the set = (-1+1)/2 = 0
As per statement, Mean of the set = 0
Mean of the set
|y|- |x| +16-14 = 0 (where x is negative n y is positive)
|y|- |x| = -2
So the absolute difference between two numbers is 2
Answer E
Answer: (E) 2
Question: Which of the following are roots of an equation (x^-2)-(2x^-1)-35=0
(A) 1/5 and -1/7
(B) -1/5 and 1/7
(C) 1/5 and 1/7
(D) -1/5 and -1/7
(E) -5/2 and -1/7
Rationale: Given: (x^-2) - (2x^-1) - 35 = 0
Rewrite as: 1/(x²) - 2/x - 35 = 0
Remove fractions by multiplying both sides by x² to get: 1 - 2x - 35x² = 0
Rearrange to get: 35x² + 2x - 1 = 0
Factor to get: (5x + 1)(7x - 1) = 0
So, EITHER 5x + 1 OR 7x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If 7x - 1 = 0, then x = 1/7
So, the roots (solutions) are -1/5 and 1/7
The answer is B.
Answer: (B) -1/5 and 1/7
Question: In an increasing sequence of 10 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 6 integers in the sequence?
(A) 885
(B) 888
(C) 889
(D) 884
(E) 880
Rationale: Solution:
In solving this problem we must first remember that when we have 10 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
Integer 4: x + 3
Integer 5: x + 4
Integer 6: x + 5
Integer 7: x + 6
Integer 8: x + 7
Integer 9: x + 8
Integer 10: x + 9
We are given that the sum of the first 4 integers is 570. This means that:
x + x+1 + x+2 + x+3 = 570
4x + 6 = 570
4x = 564
x = 141
The sum of the last 6 integers can be expressed and simplified as:
x+4 + x+5 + x+6+ x+7 +x+8 x+9 = 6x + 39
Substituting 141 for x yields:
(6)(141) + 39 = 885
Answer: A
Answer: (A) 885
Question: P and Q invested in a shop. The profits were divided in the ratio of 4 : 6 respectively. If P invested Rs. 55,000, the amount invested by Q is:
(A) 48000
(B) 40000
(C) 35000
(D) 60000
(E) None
Rationale: Suppose Q invested Rs. y. Then, 50000/y = 4/6 or y = [50000 x 6/ 4] = 75000.
Answer E
Answer: (E) None
Question: A vessel of capacity 2 litre has 40% of alcohol and another vessel of capacity 6 litre had 60% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
(A) 31%.
(B) 44%.
(C) 49%.
(D) 29%.
(E) 51%.
Rationale: 40% of 2 litres = 0.8 litres
60% of 6 litres = 3.6 litres
Therefore, total quantity of alcohol is 4.4 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 44%
B
Answer: (B) 44%.
Question: A textile worker’s wages are increased by 10% and afterwards decreased by 10 %. Find the change percentage in his wages.
(A) 2 % increase
(B) 4% increase
(C) 1% decrease
(D) 4% decrease
(E) None of these
Rationale: Explanation:
Let workers wages = X
A 10% increase would mean new wages
= (110/100) X
A 10% decrease would mean new wages
= (90/100) (110/100 X)
= 99/100 X which means a decrease of 1 %
ANSWER: C
Answer: (C) 1% decrease
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 3/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
(A) 3/35
(B) 2/3
(C) 7/35
(D) 5/7
(E) 7/5
Rationale: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 3/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 3/7 x 1/5 = 3/35
ANSWER:A
Answer: (A) 3/35
Question: During the months May through October, Teddy the bear doubles his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
(A) 4m - 1300
(B) 9m - 1200
(C) 4m - 1200
(D) 9m - 1300
(E) m - 1200
Rationale: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 2m - 300
April' 75 = 2m - 400
Oct' 75 = 4m - 1200
April'76 = 4m - 1300
Hence answer will be (A) 4m - 1300
Answer: (A) 4m - 1300
Question: The radius of the wheel of a bus is 35 cms and the speed of the bus is 66 km/h, then the r.p.m. (revolutions per minutes)of the wheel is
(A) 200
(B) 250
(C) 300
(D) 500
(E) None of these
Rationale: Radius of the wheel of bus = 35 cm. Then,
circumference of wheel = 2Ï€r = 70Ï€ = 220 cm
Distance covered by bus in 1 minute
= 66â„60 Ã— 1000 Ã— 100 cms
Distance covered by one revolution of wheel
= circumference of wheel
= 220 cm
âˆ´ Revolutions per minute = 6600000/60Ã—220 = 500
Answer D
Answer: (D) 500
Question: When the number 2y31129 is exactly divisible by 11, then what can be the smallest whole number in place of y?
(A) 1
(B) 3
(C) 4
(D) 7
(E) 8
Rationale: The given number =2y31129
Sum of the odd places =9+1+3+2=15
Sum of the even places = 2+1+y
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
15-(3+y) = divisible by 11
12 � y = divisible by 11.
Y must be 1, to make given number divisible by 11.
A
Answer: (A) 1
Question: A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
(A) 1/2
(B) 1/4
(C) 3/8
(D) 5/12
(E) 2/5
Rationale: The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 4/16 = 1/4.
The answer is B.
Answer: (B) 1/4
Question: Man1 does a work in 10 days and Man2 does the same work in 15 days. In how many days they together will do the same work ?
(A) 10 days
(B) 5 days
(C) 6 days
(D) 7 days
(E) 8 days
Rationale: Man1 day work = 1/10
Man2 day work = 1/15
Both work =1/10+1/15
===>3+2/30
==>1/6
ANSWER C
Answer: (C) 6 days
Question: A man's regular pay is $3 per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid $186, how many hours overtime did he work?
(A) 8
(B) 5
(C) 9
(D) 6
(E) 11
Rationale: At $3 per hour up to 40 hours, regular pay = $3 x 40 = $120 If total pay = $168, overtime pay = $186 - $120 = $66 Overtime rate (twice regular) = 2 x $3 = $6 per hour => number of overtime hours = $66/$6 = 11
Ans is E
Answer: (E) 11
Question: Coins are stacked one on top of the other to form a column. The first column has 12 coins and subsequent columns have 2 more coins than the previous one. Find the number of columns if total number of coins is 432.
(A) 27
(B) 16
(C) 15
(D) 26
(E) 11
Rationale: Assume there are n columns. This forms an Arithmetic Progression with first term 12 and nth term (12+2*(n-1)). The average is (12+12+2n-2)/2 or (11+n) and total number of coins will be (11+n)*n = n2+11n-432=0 or (n+27)*(n-16)=0
n=16 or -27. Since n cannot be negative, n=16
Answer is B
Answer: (B) 16