mathewhe/aqua_rat huggingface dataset:
Question: A boy gives 15 percent of a pie to his mother, 10 percent to his father and 25 percent to his sister. What fraction of the pie is leftover?
(A) 4/5
(B) 3/5
(C) 1/2
(D) 1/5
(E) 1/10
Rationale: 100%-(15%+10%+25%)=50% of the pie remains --> 50% = 20/100 = 1/5.
Answer: C.
Answer: (C) 1/2
Question: How many times are the hands of a clock at right angle in a day?
(A) 11
(B) 22
(C) 33
(D) 44
(E) 55
Rationale: Sol.
In 12 hours, they are at right angles 22 times.
∴ In 24 hours, they are at right angles 44 times.
Answer D
Answer: (D) 44
Question: If xy > 0, 1/x + 1/y = 2, and 1/xy = 8, then (x+y)/4 = ?
(A) 1/16
(B) 1/6
(C) 1/5
(D) 5
(E) 6
Rationale: (1/X+1/Y)=2 canbe solved as {(x+y)/xy}=8. Substituting for 1/xy=8, we get
x+y=2/8
==> (x+y)/4= 2/(8*4)=1/16.
A
Answer: (A) 1/16
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 5 years older than B, the present age of B is
(A) 35
(B) 37
(C) 39
(D) 41
(E) 42
Rationale: Explanation:
Let B's age = x years.
Then, As age = (x+ 5) years.
(x+5+10)=2(x—10)
hence x=35.
Present age of B = 35 years
Answer: Option A
Answer: (A) 35
Question: Harriet planned to complete a certain task on Friday, January 1, but because of illness the completion date was postponed 48 days. On which day of the week in February was the task completed?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday
Rationale: This type of story problem is essentially just about a repeating pattern and a 'remainder.'
We're told that Harriet planned to complete a certain task on FRIDAY, January 1, but because of illness the completion date was postponed 48 DAYS. We're asked on what day of the week the task was actually completed on.
Since the task was supposed to be completed on a Friday....
A 1 day postponement would be Saturday
A 2 day postponement would be Sunday
A 3 day postponement would be Monday
A 4 day postponement would be Tuesday
A 5 day postponement would be Wednesday
A 6 day postponement would be Thursday
A 7 day postponement would be Friday
A 8 day postponement would be Saturday
Etc.
So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 48 days.
48/7 = 6 remainder 6
This means that there are 6 full weeks AND 6 extra days after a Friday....Thus, the task was completed on a Thursday.
D
Answer: (D) Thursday
Question: what is 66.67% of 804 of 0.1666 ?
(A) 19.33
(B) 54.55
(C) 89.33
(D) 97.21
(E) 68.77
Rationale: 66.67 % = 2/3
2/3 of 804 = 2/3 * 804 = 536
536 of 0.166 = 536 * (1/6) = 89.33
.... Ans - C
Answer: (C) 89.33
Question: 397 x 397 + 104 x 104 + 2 x 400x 104 = x?
(A) 234341
(B) 235633
(C) 234677
(D) 315656
(E) 251501
Rationale: Given Exp.	= (397)2 + (104)2 + 2 x 397 x 104
= (397 + 104)2
= (501)2 = (500 + 1)2
= (5002) + (1)2 + (3 x 500 x 1)
= 250000 + 1 + 1500
= 251501
E
Answer: (E) 251501
Question: A table is bought for Rs.1000/- and sold at Rs.1200/- find the loss percentage
(A) 10% Loss
(B) 10% Gain
(C) 20% Loss
(D) 20% Gain
(E) 30% Gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (1200 ~ 1000)/1000 = 20% Gain
D
Answer: (D) 20% Gain
Question: What is the place value of 8 in the numeral 8259
(A) A)2700
(B) B)2800
(C) C)2900
(D) D)2980
(E) E)8000
Rationale: 8 * 1000 = 8000
E
Answer: (E) E)8000
Question: A bicycle wheel has a diameter of 0.61m. How many complete revolutions does it make in 1km?
(A) 246
(B) 522
(C) 1408
(D) 710
(E) 223
Rationale: 1 revolution = 3.14 * diameter.
Number of revolutions in 1km = 1000m / ( 3.14 * 0.61m ) = 522.1. Hence 522 complete revolutions.
Answer B
Answer: (B) 522
Question: Find the value for x from below equation: x/3=-7?
(A) -6
(B) -21
(C) -2
(D) -3
(E) 4
Rationale: 1. Multiply both sides by 3:
x*3/3= -7/3
Simplify both sides:
x = -21
B
Answer: (B) -21
Question: David covered a distance of 50 miles on his first trip. On a later trip he travelled 300 miles while going three times as fast. His new time compared with the old time was:
(A) twice as much
(B) three times as much
(C) the same
(D) half as much
(E) a third as much
Rationale: B
Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer: (A) twice as much
Question: Two taps can separately fill a cistern 5 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 6 minutes. The waste pipe can empty the full cistern in?
(A) 6
(B) 8
(C) 10
(D) 9
(E) 2
Rationale: 1/5 + 1/15 - 1/x = 1/6
x = 10
Answer:C
Answer: (C) 10
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine V is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine V can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
(A) 14
(B) 13
(C) 11
(D) 9
(E) 7
Rationale: machine V finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts
Lets assume total work require 120 shifts
Therefore,
rate of V = 5 shifts/day
rate of B = 4 shifts/day
rate of (V+B) = 9 shifts/day
According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day
Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days=D
Answer: (D) 9
Question: How many words with or without meaning, can be formed by using all the letters of the word, â€˜POWERâ€™, using each letter exactly once?
(A) 700
(B) 720
(C) 750
(D) 800
(E) 120
Rationale: The word â€˜POWERâ€™ contains 5 different letters.
Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time
=5P5
= 5!
= 5*4*3*2*1
= 120
ANSWER:E
Answer: (E) 120
Question: Ramesh can finish a piece of work in 18 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?
(A) 8/3 days
(B) 9/3 days
(C) 6 days
(D) 3 days
(E) 7 days
Rationale: Ramesh can finish a piece of work in 18 days. Rohan is twice as efficient as Ramesh.
So Rohan can finish a piece of work in 9 days.
days needed to finish the same amount of work = 1/(1/9+1/18)=6 days
ANSWER:C
Answer: (C) 6 days
Question: If log 27 = 1.431, then the value of log 9 is
(A) 0.95
(B) 0.952
(C) 0.954
(D) 0.951
(E) 0.9323
Rationale: log 27 = 1.431
{\color{Black} \Rightarrow \log (3^{3})=1.431}
3 log 3 = 1.431
log 3 = 0.477
log 9 = {\color{Black} \log (3^{2})} = 2 log 3 = (2 x 0.477) = 0.954
Answer: C) 0.954
Answer: (C) 0.954
Question: If n is an integer and 5^n > 400,000,000, what is the least possible value of n?
(A) 7
(B) 13
(C) 9
(D) 10
(E) 11
Rationale: When you seperate the 400000000 into factors of 5 and 2 you get - > 10^8 x 2^2 = 5^8 x 2^10
2 to the ^ 8 = 1024 so its 1024 x 5^8
that means 5^8 x 5^x must be greater
5^x > 1024
5^1=5
5^2=25
5^3= 125
5^5= 3125 - > so x must be at least 5
5^(8+5)= 5^13
B
Answer: (B) 13
Question: The ratio of the volumes of two cubes is 125 : 1728. What is the ratio of their total surface areas?
(A) 81 : 121
(B) 9 : 11
(C) 25 : 144
(D) 27 : 121
(E) None of these
Rationale: Ratio of the sides = Â³âˆš125 : Â³âˆš1728 = 5 : 12
Ratio of surface areas = 5^2 : 12^2 = 25 : 144
ANSWER:C
Answer: (C) 25 : 144
Question: Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 14 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 14 questions did Zachary answer correctly?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: i got two equations:
3x-2y=25
x+y=14
3x-2(14-x)=25
3x-28+2x=25
5x=53
x=10.6 or between 10 and 11. (ANS E)
Answer: (E) 10
Question: Find the value of 72515 x 9999 = m?
(A) 345434667
(B) 246465757
(C) 465767867
(D) 725077485
(E) 645354643
Rationale: 72515 x 9999 = 72515 x (10000 - 1)
= 72515 x 10000 - 72515 x 1
= 725150000 - 72515
= 725077485
D
Answer: (D) 725077485
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
(A) XB > AB
(B) XB < YD
(C) AX > XB
(D) AX < XB
(E) YD < AB
Rationale: A--X------B
C-----Y---D
YD < AB.
Answer: E.
Answer: (E) YD < AB
Question: List I: 3, 6, 8, 9
List II: x, 3, 6, 8, 9
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.
Answer: A.
Answer: (A) 7
Question: The average weight of 10 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What might be the weight of the new person?
(A) 76 kg
(B) 76.5 kg
(C) 75 kg
(D) Data inadequate
(E) None of these
Rationale: Explanation:
Total weight increased = (10 x 2.5) kg = 25 kg.
Weight of new person = (50 + 25) kg = 75 kg.
Answer: C
Answer: (C) 75 kg
Question: how many terms are there in the G.P. 3,6,12,24,...,384?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 7
Rationale: Here a=3 and r=6/3=2. let the number of items be n
then, t^n=384=> ar^n-1=384
= 3 x 2^n-1=384
=2^n-1=128 = 2^7
=n-1=7=>n=8
Therefore, number of terms is 8
Answer is A.
Answer: (A) 8
Question: If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265
(A) 344
(B) 800
(C) 388
(D) 377
(E) 289
Rationale: Explanation:
Let the cost of Production = Rs. P
Then, as per question,
\fn_jvn {\color{Black} \Rightarrow (\frac{125}{100}\times \frac{115}{100}\times \frac{110}{100}\times p)=1265}
\fn_jvn {\color{Black} \Rightarrow \frac{253}{160}\; p=1265}
\fn_jvn {\color{Blue} \Rightarrow p=800}
Answer: B) Rs. 800
Answer: (B) 800
Question: A and B form a study group and divide a 75 question study guide. If A answer 7 questions per hour, while B answer 5 every hour, what fraction of the study guide is incomplete after 4 hours?
(A) 48/75
(B) 20/75
(C) 27/75
(D) 28/75
(E) 16/75
Rationale: Number of questions A can answer per hour: 7
Number of questions B can answer per hour: 5
Number of questions A and B can answer per hour: 7+5=12
Number of questions A and B can answer in 4 hours: 4x12=48
Fraction of the study guide that is incomplete = 1-48/75=27/75
Answer is C
Answer: (C) 27/75
Question: 15 lts of water containing 20% alcohol, then added 5 lts of water. What is % alcohol
(A) 15%
(B) 18%
(C) 20%
(D) 22%
(E) 25%
Rationale: in 15 ltr of mixure, 3 ltr alcohal and 12 ltr pure water.
when 5 ltr water is added, then
3 ltr alcohal in 20 ltr mixture means 15% alcohal in mixture.
ANSWER:A
Answer: (A) 15%
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 40 years now, the son's age 10 years back was:
(A) 10 years
(B) 19 years
(C) 33 years
(D) 38 years
(E) 39years
Rationale: Let the son's present age be x years. Then, (40 - x) = x
2x = 40.
x = 20
Son's age 5 years back (20 - 10) = 10 years.
Answer:A
Answer: (A) 10 years
Question: What is the probability of getting a sum 9 from two throws of a dice?
(A) 1/6
(B) 1/8
(C) 1/9
(D) 1/12
(E) 1/7
Rationale: Explanation:
In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =n(E)/n(S)= 4/36 =	1/9	.
ANSWER : C
Answer: (C) 1/9
Question: Five years back, a father was 36 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?
(A) 15 years
(B) 14 years
(C) 13 years
(D) 12 years
(E) 11 years
Rationale: Using linear equations to convert the word problem:
** F = fathers current ageS = sons current age
#1 Five years back, a father was 36 years older than his son: F-5 = 30 + (S - 5)
#2 At present the father is 5 times as old as the son: F = 5*S
How old will the son be three years from now?: S + 3 = ?
With two variables and two linear equations we are able to solve the problem:
(S*5) - 5 = 36 +S -5
4S=36
S = 9
S + 3 = 9 + 3 = 12
Answer: D
Answer: (D) 12 years
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189.The amount of the bill is :
(A) Rs. 1386
(B) Rs. 1764
(C) Rs. 1575
(D) Rs. 2268
(E) None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.189.
∴ x 16x9/12x1/100= 189 or x = 1575.
∴ P.W. = Rs. 1575.
∴Sum due =P.W. + T.D. =Rs.(1575 + 189)=Rs.1764.
Answer B
Answer: (B) Rs. 1764
Question: What is the remainder when you divide 2^200-1 by 7?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: answer is C. this is very similar to the 32^32^32-1 divided by 7 question.
Answer: (C) 3
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg. What is the weight of the new person?
(A) 75 Kg
(B) 50 Kg
(C) 70 Kg
(D) 80 Kg
(E) 60 KG
Rationale: Explanation:
Total increase in weight = 8 Ã— 2.5 = 20
If x is the weight of the new person, total increase in weight = xâˆ’50
=> 20 = x - 50
=> x = 20 + 50 = 70
Answer: Option C
Answer: (C) 70 Kg
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 4567
(B) 4689
(C) 5004
(D) 5678
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: If x and y are positive integers and 11 + x + y + xy = 25, what is the value of x + y?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Try each answer choices.
For A: 11 + 3 + xy = 25; xy = 11 (impossible, 11 prime number. 1 + 11 doesn't equal 3)
For B: 11 + 5 + xy = 25; xy = 9 (no combination of xy = 9 and x + y = 5)
For C: 11 + 6 + xy = 25; xy = 8 (x + y = 6; x = 2, y = 4 or x = 4, y = 2)
For D: 11 + 8 + xy = 25; xy = 6 (no combination of xy = 6 and x + y = 8)
For E: 11 + 9 + xy = 25; xy = 5 (impossible, 5 prime number. 1 + 5 doesn't equal 9)
Therefore, answer C.
Answer: (C) 6
Question: A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the possibility that the 2 apples selected will include the spoiled apple?
(A) 1/5
(B) 3/10
(C) 2/5
(D) 1/2
(E) 3/5
Rationale: p (both apples are not spoiled) = 4C2/5C2 = 4*3/5*4 = 3/5
p (one of the apple spoiled) = 1-3/5 = 2/5
Answer is C.
Answer: (C) 2/5
Question: A boat can move upstream at 25 kmph and downstream at 45 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7
(D) 4
(E) 10
Rationale: US = 25
DS = 45
M = (45 - 25)/2 = 10
Answer: E
Answer: (E) 10
Question: At Bala's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
(A) 700
(B) 1000
(C) 1300
(D) 1600
(E) 2000
Rationale: At Bala's firm's annual revenue grows twice as fast as its costs. First solve for how much revenue is increasing each year:
R2008= R2007*(1+x)
R2009= R2007*(1+x)^2=1.44*R2007
(1+x)^2 = 1.44
1+x=1.2
x=0.2 aka revenue increases 20% each year and cost increases 10% annually
Next solve for R2007and C2007:
R2007= C2007- 1000
1.2*R2007- 1.1*C2007= 0
1.2*[C2007- 1000] - 1.1*C2007= 0
0.1*C2007= 1,200
C2007= 12,000
R2007= 11,000
Finally find 2009 profits:
Profit2009= 1.44*11,000 - 1.21*12,000
Profit2009= 15,840 - 14,520
Profit2009= 1320
Answer: C
Answer: (C) 1300
Question: If an object travels 90 feet in 2 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
(A) 30.68
(B) 32.34
(C) 34.56
(D) 36.72
(E) 38.95
Rationale: 90 feet/2 seconds = 45 feet/second
(45 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 30.68 (approximately)
The answer is A.
Answer: (A) 30.68
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
(A) 2/7
(B) 3/10
(C) 3/4
(D) 1/9
(E) 7/9
Rationale: In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E) = 27.
P(E) =n(E)/n(S)=27/36=3/4.
hence:C
Answer: (C) 3/4
Question: P, Q and R can do a piece of work in 20, 30 and 60 days respectively. In how many days can P do the work if he is assisted by Q and R on every third day?
(A) 15 days
(B) 18 days
(C) 20 days
(D) 25 days
(E) 10 days
Rationale: P 2 days work = 1/20*2 = 1/10
(P + Q+ R)'s 1 day work ( 1/20 + 1/30 + 1/60) = 6/60 = 1/10
work done in 3 days = 1/5
so 1/5 work done in 3 days
whole work ( 3* 5) = 15 days
ANSWER A
Answer: (A) 15 days
Question: Sum of the squares of 3 no. is 276 and the sum of their products taken two at a time is 150. Find the sum?
(A) 22
(B) 18
(C) 26
(D) 24
(E) 32
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 276 + 2* 150
a + b + c = âˆš576 = 24
Answer D
Answer: (D) 24
Question: From the starting point in a boat race, one competitor started to sail north at a speed of 1.6 Km/h, the other competitor started to sail west at a speed of 1.3 Km/h. What is the distance in Km between the two competitors after 5 hours?
(A) 10.3
(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 = 1.6 *5= 8 KM
And, other competitor will cover a distance of = 1.3*5= 6.5KM
distance between them after 5 hrs = (8^2+ 6.5^2)^1/2= 10.3 KM
A is the answer
Answer: (A) 10.3
Question: If |x| = 9x-16, then x = ?
(A) 1
(B) 1/2
(C) 2
(D) 4
(E) -1/2
Rationale: Substituted option C i.e x=2. Inequality satisfied.
This eliminates all options except
Answer is C
Answer: (C) 2
Question: speed of a bus is 54kmph and including stoppages, it is 45kmph. For how many minsdoes the bus stop per hour?
(A) 10 min
(B) 20 min
(C) 30 min
(D) 50 min
(E) 60 min
Rationale: speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distancespeed=954 hour=16 hour = 606 min=10 min
A
Answer: (A) 10 min
Question: On a certain scale of intensity, each increment of 10 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 135?
(A) 40
(B) 100
(C) 400
(D) 1000
(E) 10 000
Rationale: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:
If intensity for 135 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 165 it'll be 10*10*10*10*x=10^4*x.
Answer: E.
Answer: (E) 10 000
Question: Look at this series: 0.05, 0.2, ____, 3.2, 12.8, ... What number should fill the blank?
(A) 0.5
(B) 0.6
(C) 0.9
(D) 0.7
(E) 0.8
Rationale: This is a simple multiplication series. Each number is 4 times greater than the previous number.
Answer: E
Answer: (E) 0.8
Question: Two persons start running simultaneously around a circular track of length 200 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
(A) 27 sec
(B) 17 sec
(C) 18 sec
(D) 22 sec
(E) 37 sec
Rationale: Explanation:
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 200 / (15 + 25)5/18 = 200x 18 / 40 x 5 = 18 seconds.
Answer: C
Answer: (C) 18 sec
Question: Two pipes A and B can fill a cistern in 8 and 12 minutes respectively, and a third pipe C can empty it in 15 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
(A) 17 1/17 min
(B) 28 1/7 min
(C) 17 1/7 min
(D) 17 1/8 min
(E) 17 5/7 min
Rationale: 1/8 + 1/12 - 1/15 = 17/120
120/17 = 7 1/17
Answer:A
Answer: (A) 17 1/17 min
Question: Forty five percent of a number is 21 less than four fifth of that number. What is the number ?
(A) 60
(B) 140
(C) 230
(D) 130
(E) 125
Rationale: Let the number be x.
Then, 4*x/5 â€“(45% of x) = 21
4x/5 â€“ 45x/100 = 21
x = 60.
Answer A.
Answer: (A) 60
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is
(A) 8! * â·Pâ‚†
(B) 6! * â·Pâ‚†
(C) 4! * â·Pâ‚†
(D) 2! * â·Pâ‚†
(E) 3! * â·Pâ‚†
Rationale: Explanation:
We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in â·Pâ‚† ways.
Hence required number of ways = 6! * â·Pâ‚†
Answer:B
Answer: (B) 6! * â·Pâ‚†
Question: A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
(A) 1218
(B) 1200
(C) 1688
(D) 6996
(E) 2791
Rationale: l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
Answer: B
Answer: (B) 1200
Question: A train 90m long is running at 20kmph. In how much time will it pass a platform 80m long?
(A) 15.6 seconds
(B) 24.6 seconds
(C) 28.6 seconds
(D) 13.6 seconds
(E) 35.6 seconds
Rationale: Distance travelled = 90 + 80m = 170mSpeed = 20 * 5/8 = 25/2mTime = 170 * 2/25 = 13.6 SecondsAnswer : D.
Answer: (D) 13.6 seconds
Question: A can do a piece of work in 9 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) 18
(B) 77
(C) 66
(D) 54
(E) 12
Rationale: 8/9 + 6/x = 1
X = 54 days
Answer:D
Answer: (D) 54
Question: The distance from Steve's house to work is 10 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
(A) 5.
(B) 10.
(C) 14.
(D) 15.
(E) 20.
Rationale: Time is in the ratio 2:1 :: to: fro office
Therefore, 2x+1x=6 hrs
Time take to come back - 2 hrs, distance travelled - 10km => Speed = 5kmph
A
Answer: (A) 5.
Question: A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 120 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 120 feet of frontage each, what is the value of x ?
(A) 400
(B) 3,200
(C) 3,700
(D) 4,400
(E) 5,200
Rationale: Total number of plots,be T
Plots with 80ft is (1/9)th of total plots.
Plots with 120ft frontage = (8/9) X total number of plots
i.e 8/9 X T = 40 T = 45
Total lake frontage = 40X120 + 5X80 = 5200
Answer : E
Answer: (E) 5,200
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 4500, how much was it in the beginning?
(A) 5999
(B) 6788
(C) 6250
(D) 4559
(E) 6989
Rationale: X * (90/100) * (80/100) = 4500
X = 6250
Answer: C
Answer: (C) 6250
Question: A committee is to be formed by randomly choosing 3 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?
(A) 2/7
(B) 3/7
(C) 2/35
(D) 3/35
(E) 4/35
Rationale: The total number of ways to form a committee is 7C3=35.
The number of committees which include Alice but not Bob is 5C2=10.
The probability that Alice is selected but Bob is not selected is 10/35=2/7.
The answer is A.
Answer: (A) 2/7
Question: Find the average of all the numbers between 11 and 21 which are divisible by 2.
(A) 15
(B) 18
(C) 16
(D) 22
(E) None
Rationale: Sol.
Average = (12 + 14 + 16+ 18+ 20 / 5) = 80 / 5 = 16.
Answer C
Answer: (C) 16