RikoteMaster/aqua-rat-mcqa huggingface dataset:
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
Answer: B.522
Explanation: 1 revolution = 3.14 * diameter.
Number of revolutions in 1km = 1000m / ( 3.14 * 0.61m ) = 522.1. Hence 522 complete revolutions.
Answer B
Question: Find the value for x from below equation: x/3=-7?
A.-6
B.-21
C.-2
D.-3
Answer: B.-21
Explanation: 1. Multiply both sides by 3:
x*3/3= -7/3
Simplify both sides:
x = -21
B
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
Answer: A.twice as much
Explanation: 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.
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
Answer: C.10
Explanation: 1/5 + 1/15 - 1/x = 1/6
x = 10
Answer:C
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
Answer: D.9
Explanation: 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
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
Answer: C.6 days
Explanation: 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
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
Answer: C.0.954
Explanation: 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
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
Answer: B.13
Explanation: 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
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
Answer: C.25 : 144
Explanation: Ratio of the sides = Â³âˆš125 : Â³âˆš1728 = 5 : 12
Ratio of surface areas = 5^2 : 12^2 = 25 : 144
ANSWER:C
Question: Find the value of 72515 x 9999 = m?
A.345434667
B.246465757
C.465767867
D.725077485
Answer: D.725077485
Explanation: 72515 x 9999 = 72515 x (10000 - 1)
= 72515 x 10000 - 72515 x 1
= 725150000 - 72515
= 725077485
D
Question: List I: 3, 6, 8, 9
List II: x, 3, 6, 8, 9
A.7
B.8
C.9
D.10
Answer: A.7
Explanation: 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.
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
Answer: C.75 kg
Explanation: Explanation:
Total weight increased = (10 x 2.5) kg = 25 kg.
Weight of new person = (50 + 25) kg = 75 kg.
Answer: C
Question: how many terms are there in the G.P. 3,6,12,24,...,384?
A.8
B.9
C.10
D.11
Answer: A.8
Explanation: 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.
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
Answer: B.800
Explanation: 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
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
Answer: C.27/75
Explanation: 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
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%
Answer: A.15%
Explanation: 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
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
Answer: A.10 years
Explanation: 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
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
Answer: C.1/9
Explanation: 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
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
Answer: D.12 years
Explanation: 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
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
Answer: B.Rs. 1764
Explanation: 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
Question: What is the remainder when you divide 2^200-1 by 7?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: answer is C. this is very similar to the 32^32^32-1 divided by 7 question.
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
Answer: C.70 Kg
Explanation: 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
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
Answer: C.6
Explanation: 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.
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
Answer: C.2/5
Explanation: 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.
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
Answer: C.1300
Explanation: 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
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
Answer: A.30.68
Explanation: 90 feet/2 seconds = 45 feet/second
(45 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 30.68 (approximately)
The answer is A.
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
Answer: C.3/4
Explanation: 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
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
Answer: A.15 days
Explanation: 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
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
Answer: D.24
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 276 + 2* 150
a + b + c = âˆš576 = 24
Answer D
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.
Answer: A.10.3
Explanation: 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
Question: If |x| = 9x-16, then x = ?
A.1
B.1/2
C.2
D.4
Answer: C.2
Explanation: Substituted option C i.e x=2. Inequality satisfied.
This eliminates all options except
Answer is C
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
Answer: A.10 min
Explanation: 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
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
Answer: C.18 sec
Explanation: 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
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
Answer: A.17 1/17 min
Explanation: 1/8 + 1/12 - 1/15 = 17/120
120/17 = 7 1/17
Answer:A
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
Answer: A.60
Explanation: Let the number be x.
Then, 4*x/5 â€“(45% of x) = 21
4x/5 â€“ 45x/100 = 21
x = 60.
Answer A.
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‚†
Answer: B.6! * â·Pâ‚†
Explanation: 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
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
Answer: B.1200
Explanation: l * 30 = 1200 è l = 40
40 + 30 + 50 = 120
120 * 10 = 1200
Answer: B
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
Answer: D.13.6 seconds
Explanation: Distance travelled = 90 + 80m = 170mSpeed = 20 * 5/8 = 25/2mTime = 170 * 2/25 = 13.6 SecondsAnswer : D.
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
Answer: D.54
Explanation: 8/9 + 6/x = 1
X = 54 days
Answer:D
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.
Answer: A.5.
Explanation: 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
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
Answer: C.6250
Explanation: X * (90/100) * (80/100) = 4500
X = 6250
Answer: C
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
Answer: A.2/7
Explanation: 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.
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
Answer: C.16
Explanation: Sol.
Average = (12 + 14 + 16+ 18+ 20 / 5) = 80 / 5 = 16.
Answer C
Question: For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.267] = 1 and [1.999] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
A.0
B.0
C.27
D.54
Answer: B.0
Explanation: K=[lCM of 80 and 45] * (any integer)
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
for value of k(60) * any integer unit value will be always zero .
B
Question: A circular path of 13 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 25p per m2?
A.Rs.45
B.Rs.48
C.Rs.44
D.Rs.43
Answer: C.Rs.44
Explanation: π (152 - 132) = 176
176 * 1/4
= Rs.44
Answer:C
Question: Set E consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set E by 50, set Y is derived by multiplying each term in set E by 1.5, and set Z is derived by dividing each term in set E by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?
A. X, Y, Z
B. X, Z, Y
C. Y, Z, X
D. Y, X, Z
Answer: D. Y, X, Z
Explanation: Set E - {2, 4, ..., 100};
Set X - {-48, -46, ..., 50};
Set Y - {3, 6, ..., 150};
Set Z - {-2/4, -4/4, ..., -100/4} = {-1/2, -1, -3/2, ..., -25}.
If we add or subtract a constant to each term in a set the SD will not change, so sets E and X will have the same SD.
If we increase or decrease each term in a set by the same percent (multiply by a constant) the SD will increase or decrease by the same percent, so set Y will have 1.5 times greater SD than set E and set Z will have 4 times less SD than set E (note SD can not be negative so SD of Z wil be SD of E divided by 4 not by -4).
So, the ranking of SD's in descending order is: Y, E=X, Z.
Answer: D.
Question: The average age of a husband and a wife is 30 years when they were married ten years ago but now the average age of the husband, wife and child is 30 years(the child was born during the interval). What is the present age of the child?
A.2 years
B.5 years
C.10 years
D.4 years
Answer: C.10 years
Explanation: 40 * 2 = 80
30 * 3 = 90
-----------
10 years
Answer:C
Question: If f(x) = 1 - x if x > 0
= 1/(1 - x) if x≤≤0.
A.1102
B.2767
C.2667
D.1998
Answer: A.1102
Explanation: Let x≤≤0
f(x) = 11−x11−x
f(f(x)) = 1 - 11−x11−x (As 11−x11−x x≥0x≥0
= −x1−x−x1−x (Observe −x1−x−x1−x is Positive for x is negitive)
f3(x)f3(x) = 1−−x1−x=1−x−(−x)1−x=11−x1−−x1−x=1−x−(−x)1−x=11−x
So f1(x)=f3(x)=f5(x)=.....f101(x)f1(x)=f3(x)=f5(x)=.....f101(x)
f101(x)=f1(x)=11−x=11−(−101)=1102
Answer:A
Question: The sum of first 45 natural numbers is?
A.1030
B.1034
C.1035
D.1037
Answer: C.1035
Explanation: Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.
Sn =	n	[2a + (n - 1)d]	=	45	x [2 x 1 + (45 - 1) x 1]	= 45	x 46 = (45 x 23)
2	2	2
= 45 x (20 + 3)
= 45 x 20 + 45 x 3
= 900 + 135
= 1035.
C)
Question: A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
A.
B.
C.
D.
E.
A.1/250
B.1/84
C.1/11
D.1/9
Answer: D.1/9
Explanation: Probability of choosing one defective phone from a lot of 250 which ontains 84 defective phones is = (84/250)
Probability of choosing one defective phone from a lot of 249(we already picked one) which ontains 83(we already picked one) defective phones is = (83/249)
Combined probability of series of events = product of the probabilities = (84/250)*(83/249)
84/250 is close to (1/3) and (83/249)= (1/3)
so answer is (1/3)*(1/3) = (1/9)
ANSWER:D
Question: In a mixture of 45 litres, the ratio of acid to base is 3 : 2. How much base must be added to make the ratio 9: 11?
A.10 lts
B.15 lts
C.17 lts
D.20 lts
Answer: B.15 lts
Explanation: Let M = 3K,W = 2K
Thus, 3K + 2K = 45
=> K=9
=> acid = 27 litres and base = 18 litres.
Now suppose x litres of base is added to the mixture such that
27/(18 + X) = 9/11
=>162 +9X = 297
=> 9X = 135
=> X = 15
ANSWER:B
Question: The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.100 and Rs.80 respectively. What is the sum and the time?
A.Sum = Rs.400 and Time = 5 years
B.Sum = Rs.200 and Time = 2.5 years
C.Sum = Rs.400 and Time = 2.5 years
D.Sum = Rs.200 and Time = 5 years
Answer: C.Sum = Rs.400 and Time = 2.5 years
Explanation: Explanation :
BD = Rs.100
TD = Rs.80
R = 10%
F = BD ×TD/(BD – TD)=100×80/(100–80)=100×80/20=Rs. 400
BD = Simple Interest on the face value of the bill for unexpired time =FTR/100
⇒100 = (400×T×10)/100
⇒100 = 4 × T × 10 ⇒10 = 4 × T
⇒ T = 10/4 = 2.5 years Answer : Option C
Question: There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set Q, which cannot be the range of the set Q?
A.8
B.B.11
C.C.14
D.D.17
Answer: B.B.11
Explanation: Let Set A has 1,8 as elements
B has 1,14 as elements.. So Range for Combined set Q becomes 14-1=13
For range to be 14,
A = 1,8
B= 2,15 (Range=14)
For range to be 17
A=1,8
B= 5,18
For range to be 21:
A=1,8
B= 9 ,22
So we are left with A and B.
Now consider A has elements A= -1,-8 and Thus Range =-1-(-8) =7
So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...
Consider Option A
A=-1,-8
B= y,x where y and x are smallest and largest element in Set B
Elements of Combined Set: -8,-1,y and x
Now x-(-8)=8 or x=0, then x-y=13 or y=-13...
Range of Combined Set: 0-(-13)= 13...
I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B
Question: Bob is attempting to feed his pets. He feeds his pets as follows:
- No dog receives more food than any other dog
- No cat receives any less food than any other cat
- The cats, as a group, receive exactly as much food as a single dog
If Bob has seven dogs and four cats, approximately what percentage of the food bag does a cat receive?
A.25.0%
B.8.3%
C.3.1%
D.2.7%
Answer: C.3.1%
Explanation: C. Each cat gets 1/4 as much food as a dog. A dog gets 1/8 of the food. 1/4 of 1/8 is 1/32, which is about 3.1%, so the answer is C.
Question: If a person walks at 12 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
A.50 km
B.100 km
C.60 km
D.70 km
Answer: B.100 km
Explanation: Let the actual distance travelled be x km.
x/10 = (x+20)/12
12x = 10x + 200
2x = 200
x = 100 km.
answer :B
Question: Solve for x: 2x â€“ y = (3/4)x + 7.
A.(y + 6)/5
B.4(y + 7)/5
C.(y + 6)
D.4(y - 6)/5
Answer: B.4(y + 7)/5
Explanation: Solution:
2x â€“ y = (3/4)x + 7.
or, 2x - (3/4)x = y + 7.
or, (8x -3x)/4 = y + 7.
or, 5x/4 = y + 7.
or, 5x = 4(y + 7).
or, 5x = 4y + 28.
or, x = (4y + 28)/5.
Therefore, x = 4(y + 7)/5.
correct answer B