divelab/Sys2Bench huggingface dataset:
Question: The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
Options:
A)3 and 5
B)3 and 6
C)3 and 7
D)3 and 8
E)3 and 9
Rationale: Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.
15 = x y and 16 = 2 x + 2 y
Solve the second equation for x
x = 8 - y
Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as
15 = (8 - y) y
Solve for y to find
y = 3 and y = 5
Use x = 8 - y to find x
when y = 3 , x = 5 and when y = 5 , x = 3.
The dimensions of the rectangle are 3 and 5.
As an exercise, check that the perimeter of this rectangle is 16 and its area is 15.
Answer A
Answer: A
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)230
B)240
C)250
D)270
E)280
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: Option D
Answer: D
Question: A number increased by 20% gives 1080. The number is?
Options:
A)800
B)700
C)500
D)900
E)600
Rationale: Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 20 % = 120 %
120 % -------> 1080 (120 Ã— 9 = 1080)
100 % -------> 900 (100 Ã— 9 = 900)
Option 'D'
Answer: D
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
Options:
A)2 Hrs
B)3 Hrs
C)1 Hr
D)4 Hrs
E)5 Hrs
Rationale: |-----------20--------------------|
50 40
D = 20
RS = 50 â€“ 40 = 10
T = 20/10 = 2 hours
ANSWER A
Answer: A
Question: John has taken four (4) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 86. What will he need to average on his final two tests to achieve this grade?
Options:
A)87
B)90
C)92
D)94
E)97
Rationale: Traditional Method:
Total scored till now 82*4=328
Total score to avg 86 in 6 tests = 86*6=516
Total to be scored on 2 tests = 516-328=188
Avg on 2 tests = 188/2 = 94
Answer: D
Answer: D
Question: If 6<x<10<y<17, then what is the greatest possible positive integer difference of x and y?
Options:
A)3
B)4
C)10
D)6
E)7
Rationale: Let x=6.1 and y=16.1
Greatest possible difference=16.1-6.1=10
Answer C
Answer: C
Question: Joshua is fifth from the bottom in a queue of 100 boys.
What is the position of Joshua from the top of the queue?
Options:
A)51
B)52
C)53
D)54
E)55
Rationale: Solution:
51
Explanation:
The position of boys higher than Joshua in the queue is 100 - 50 = 50.
Therefore, the position of Joshua from the top is 50 + 1 = 51.
Answer A
Answer: A
Question: Robert's salary was decreased by 30% and subsequently increased by 30%. how much percentage does he lose?
Options:
A)10%
B)9%
C)25%
D)30%
E)50%
Rationale: let original salary be $100
Salary after decreasing 30% = 100 - 100 x 30/100 = $70
Salary after increasing 30% on $70 = 70 + 70 x 30/100 = $91
Percentage of loss = 100 - 91 = 9%
Answer : B
Answer: B
Question: The average of temperatures at noontime from Monday to Friday is 45; the lowest one is 42, what is the possible maximum range of the temperatures?
Options:
A)15
B)25
C)40
D)45
E)75
Rationale: there are 5 days so the sum of temperature can be 45*5=225
lowest is 42. to find the maximum range we can say the temperature was the lowest for 4 of the 5 days
so 4*42=168.
on the fifth day it is 225-168=57
range is therefore 57-42=15
answer A
Answer: A
Question: A certain taxi company charges $2.50 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
Options:
A)15.6
B)18.1
C)17.5
D)18.7
E)19.1
Rationale: A certain taxi company charges $2.50 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
A. 15.60
B. 16.00
C. 17.50
D. 18.70
E. 19.10
1/5 miles = 0.2 miles.
The cost of 8 miles long ride would be $2.50 for the first 0.2 miles plus (8-0.2)/0.2*0.4 = $2.50 + $15.6 = $18.1.
Answer: B.
Answer: B
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
Options:
A)43 kmph
B)45 kmph
C)47 kmph
D)49 kmph
E)42 kmph
Rationale: B
Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: B
Question: What will be the product of (25-1)*(25-2)*(25-3)*..............*(25-49)*(25-50)?
Options:
A)0
B)1
C)625
D)less than -100,000
E)more than 100,000
Rationale: One of the terms is (25-25) so the product is 0.
The answer is A.
Answer: A
Question: 0.9999+0.1111=?
Options:
A)1
B)1.0001
C)1.0021
D)1.111
E)1.1111
Rationale: 0.9999 + 0.1111
= 0.9999 + 0.111 + 0.0001
= (0.9999 + 0.0001) + 0.111
= 1 + 0.111
= 1.111
D
Answer: D
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 3. What could be the ratio of Cats to dogs in the pet store?
Options:
A)12:15
B)1:4
C)1:5
D)2:5
E)1:3
Rationale: Say theratio of cats to dogs is a/b. Then the numberof cats would be ax and the number of dogs bx, for some positive integer x.
We are told that ax - bx = 3 --> x(a - b) = 3. Since 3 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*13.
The above implies that either x = 1 and (a - b) = 3 or x = 3 and (a - b )= 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13.
For the original question only option which fits is E, 4:5. Cats = 3*4 = 12 and dogs = 3*5 = 15.
Answer: A.
Answer: A
Question: How many ways could five people sit at a table with eight seats in which three of the eight seats will remain empty?
Options:
A)6720
B)6520
C)56
D)120
E)40
Rationale: ways in which 5 seats out 8 can be selected = 8C5
ways in which 5 people can be arranged in 5 seats = 5!
Total ways of arrangement = 8C5*5!
=(8!/(5!*3!))*5!
=56*120
=6720
Ans = A
Answer: A
Question: What is the difference between local value & face value of 7 in the numeral 65793?
Options:
A)693
B)656
C)691
D)9890
E)10000
Rationale: (Local value of 7) - (Face value of 7)
= (700 - 7) = 693
A
Answer: A
Question: A cube of volume 1000 cm 3 is divided into small cubes of 1 cm 3 ..& all the outer surfaces are painted how many cubes will be there with (at least one side painted or no side painted)
Options:
A)477
B)488
C)456
D)425
E)495
Rationale: Number of cubes with No side painted = 8*8*8 = 512
Number of cubes with atleast one side painted = 1000-512= 488
ANSWER:B
Answer: B
Question: From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine?
Options:
A)1/168
B)1/8
C)1/4
D)1/3
E)3/4
Rationale: "one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine"
The above statement is NOT clear
Still a solution:
For 8 students we have 3 posts
one post can be occupied by only one member
no two posts can be occupied by the same member
probability(P) for a member getting selected for particular 2 of the 3 posts=
probable outcomes=1(Caine)+1(Abel)=2
total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8
=2/8=1/4
Probability required for the given case= 1-P=1-1/4=3/4
Answer: E
Answer: E
Question: If A speaks the truth 60% of the times, B speaks the truth 50% of the times. What is the probability that at least one will tell the truth
Options:
A)0.8
B)0.9
C)1.0
D)1.2
E)1.3
Rationale: probability of A speaks truth p(A)=6/10;false=4/10
probability of B speaks truth p(B)=5/10;false=5/10.For given qtn
Ans=1-(neither of them tell truth).Because A & B are independent events
=1-[(4/10)*(5/10)]=4/5=0.8
ANSWER:A
Answer: A
Question: The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100000 years is:
Options:
A)111 × 1827 miles
B)999× 1238 miles
C)346 × 1012 miles
D)587 x 10^15 miles
E)587 × 1012 miles
Rationale: The distance of the light travels in one years is:
5,870,000,000,000 = 587 * 10 ^10
The distance of the light travels in 100000 years is:
= 587 * 10^10 x 10 ^5 = 587 x 10^15 miles
Answer :D
Answer: D
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 151 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
Options:
A)1289
B)1198
C)281
D)1208
E)282
Rationale: Explanation:
B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 151 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 151 = 3k + 151 => 2k = 302 => k = 151
The initial quantity of water in A = 8k = 8 * 151 = 1208 liters.
Answer: Option D
Answer: D
Question: John bought 2 shares and sold them for $24 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
Options:
A)a profit of $10
B)a profit of $2
C)a loss of $2
D)a loss of $10
E)neither a profit nor a loss
Rationale: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss
Total Selling Price = 24*2 = $48
Total Cost Price = 48/(0.96) = $50
Loss = 50-48 = $2
Answer: Option C
Answer: C
Question: Dan can do a job alone in 12 hours. Annie, working alone, can do the same job in just 9 hours. If Dan works alone for 8 hours and then stops, how many hours will it take Annie, working alone, to complete the job?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Dan can complete 1/12 of the job per hour.
In 8 hours, Dan completes 8(1/12) = 2/3 of the job.
Annie can complete 1/9 of the job per hour.
To complete the job, Annie will take 1/3 / 1/9 = 3 hours.
The answer is B.
Answer: B
Question: The ratio of the radius of two circles is 1: 5, and then the ratio of their areas is?
Options:
A)1:7
B)2:9
C)1:25
D)3:7
E)3:4
Rationale: r1: r2 = 1: 5
Î r1^2: Î r2^2
r1^2: r2^2 = 1:25
Answer: C
Answer: C
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.120000, find the cost of a camel?
Options:
A)s.9800
B)s.3800
C)s.9800
D)s.4800
E)s.6880
Rationale: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.120000
P = Rs.[(24 * 4 * 4 * 120000)/(10 * 16 * 6 * 10)]
P = Rs.(46080000/9600) => P = Rs.4800
Answer:D
Answer: D
Question: A certain car uses 12 gallons of gasoline in traveling 360 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: 360/10 = 36. The difference is 36 - 30 = 6.
Answer C
Answer: C
Question: In a group of ducks and cows, the total number of legs are 26 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)11
B)12
C)13
D)16
E)18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 26
=> 2x = 26=> x = 13
C
Answer: C
Question: (((13!)^16)-((13!)^8))/(((13!)^8)+((13!)^4))=a
then what is the units digit for a/((13!)^4)=
Options:
A)7
B)8
C)9
D)6
E)5
Rationale: (((13!)^16)-((13!)^8))/(((13!)^8)+((13!)^4))=a
solving it , we get
a/((13!)^4)= ((13!)^4-1)
last digit of (13!)^4 will be 0.
so last digit of ((13!)^4-1) will be 9.
ANSWER:C
Answer: C
Question: Find the value for x from below equation: x/2=-2?
Options:
A)-6
B)1
C)-2
D)-3
E)-4
Rationale: 1. Multiply both sides by 2:
x*2/2= -2/2
Simplify both sides:
x = -4
E
Answer: E
Question: The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Options:
A)1520 m2
B)2420 m2
C)2480 m2
D)2520 m2
E)None of these
Rationale: Explanation:
We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m2.
Answer: D
Answer: D
Question: John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $58000 and Ingrid makes $72000, what is their combined tax rate?
Options:
A)32%
B)34.4%
C)35%
D)35.6%
E)37.4%
Rationale: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.
(2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.
(3) Get 72000/130000 = 36/65. 36/65 is a little above 36/72 = 1/2. Thus, our answer is just a little above 35.
Answer: D
Answer: D
Question: There are 9 executives, including the CEO and CFO, that are asked to form a small team of 4 members. However, the CEO and CFO may not both be assigned to the team. Given this constraint, how many ways are there to form the team?
Options:
A)97
B)99
C)101
D)103
E)105
Rationale: The total number of ways to form a team of 4 is 9C4=126.
We need to subtract the number of teams that have both the CEO and the CFO.
The number of teams with both the CEO and CFO is 7C2=21.
The number of ways to form an acceptable team is 126-21=105.
The answer is E.
Answer: E
Question: If x is divisible by 6 and 5, which of the following must divide evenly into x? I. 64 II. 32 III. 15
Options:
A)I only
B)II only
C)III only
D)II,III only
E)none of these
Rationale: If x is divisible by 6,5 means it will be = or > 30, 60,90 etc...
That are not divisible by 32, 64.
So, the answer is C
Answer: C
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)65 km/hr
B)50 km/hr
C)21 km/hr
D)25 km/hr
E)76 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec
= (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer: B
Answer: B
Question: How many numbers between 400 and 1000 can be made with the digits 2,3,4,5,6 and 0?
Options:
A)30
B)60
C)90
D)120
E)150
Rationale: Required number = 3 * 5P2 = 3*20 = 60
Answer is B
Answer: B
Question: If there are half as many women as men in a group and an equal number of men and women do not own cars - a group that is 40% of the total. What fraction of the total is women who own cars?
Options:
A)3⁄20
B)11⁄60
C)9⁄40
D)1⁄5
E)2⁄15
Rationale: Consider a group of 200 men and 100 women, a total of 300 people. 40% of them, which is 120, form a group of people who don't own a car.
Half of them are men, and the other half are women, more precisely 60.
It means that there are 100-60 = 40 women who own a car, and this represents 40/300 = 2/15 of the total.
Answer E
Answer: E
Question: The length of a train and that of a platform are equal. If with a speed of 144 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)757
B)758
C)718
D)1200
E)738
Rationale: Speed = [144 * 5/18] m/sec = 40 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 40 è x = 40 * 60 / 2
=1200
Answer:D
Answer: D
Question: If a boat goes 6km upstream in 36 minutes and the speed of the stream is 4 kmph, then the speed of the boat in still water is ?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Rate upsteram =(6/36*60)kmph=10kmph.
speed of the stream =4kmph let speed in still water be xkm/hr. then speed upstream=(x-4)km/hr. x-4=10==>x=14km/hr Answer(E)
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
Options:
A)118
B)150
C)277
D)250
E)191
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 250 m
Answer: D
Answer: D
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.6270.What was his original salary?
Options:
A)6000
B)2999
C)1000
D)2651
E)1971
Rationale: X * (110/100) * (95/100) = 6270
X * (11/10) * (1/100) = 66
X = 6000
Answer: A
Answer: A
Question: The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:
Options:
A)1%
B)2%
C)3%
D)5%
E)4%
Rationale: D
5%
Increase in 10 years = (262500 - 175000) = 87500.
Increase% = (87500/175000 x 100)% = 50%.
Required average = (50/10)% = 5%.
Answer: D
Question: Find the cost of fencing around a circular field of diameter 42 m at the rate of Rs.3 a meter?
Options:
A)138
B)390
C)393
D)279
E)222
Rationale: 2 * 22/7 * 21 = 131
131 * 3
= Rs.393
Answer: C
Answer: C
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Options:
A)4 years
B)6 years
C)8 years
D)10 years
E)12 years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
Answer: Option A
Answer: A
Question: A, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)270
B)279
C)276
D)261
E)262
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 841 = 261
Answer: D
Answer: D
Question: Find the numbers which are in the ratio 3 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 21 ?
Options:
A)9, 6, 11
B)9, 6, 17
C)9, 6, 19
D)9, 6, 12
E)9, 6, 10
Rationale: Let the numbers be a, b and c.
Given that a, b and c are in the ratio 3 : 2 : 4.
let, a = 3x, b = 2x and c = 4x
Given, (a+b) + (c - b) = 21
= > a + b + c - b = 21 = > a + c = 21
= > 3x + 4x = 21 = >7x = 21 = > x = 3
a , b , c are 3x, 2x, 4x.
a, b, c are 9 , 6 , 12.
Answer: D
Answer: D
Question: The owner of a furniture shop charges his customer 100% more than the cost price. If a customer paid Rs. 1000 for a computer table, then what was the cost price of the computer table?
Options:
A)800
B)650
C)500
D)600
E)250
Rationale: CP = SP * (100/(100 + profit%))
= 1000(100/200) = Rs. 500.
Answer: C
Answer: C
Question: Find the unit's digit in 264^102+264^103
Options:
A)0
B)2
C)3
D)5
E)6
Rationale: Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102+264103264102+264103
= unit's digit in (6+4)=0
A
Answer: A
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 5:3 and B:C = 5:2. If the total runs scored by all of them are 60, the runs scored by B are?
Options:
A)20.23
B)20.13
C)30.93
D)19.56
E)10.93
Rationale: A:B = 5:3
B:C = 5:2
A:B:C = 25:15:6
15/46 * 60 = 19.56
ANSWER:D
Answer: D
Question: A boy incurs 5% loss by selling a book for Rs. 1000. At what price should the book be sold to earn 5 % profit?
Options:
A)Rs. 1105.26
B)Rs. 1251.50
C)Rs. 1085.13
D)Rs. 1885.13
E)None of these
Rationale: Explanation:
Let the new selling price be Rs. x
(100 – loss %) /1000 = (100 + gain %) / x
(100 – 5) / 1000 = (100 + 5) / x
x = (105 × 1000) / 95 = 105000 / 95
x = 1105.26.
ANSWER A
Answer: A
Question: In a store, the profit is 320% of the cost. If the cost increases by 25% but the SP remains constant, approximately what % of the sellingprice is the profit?
Options:
A)50%
B)70%
C)90%
D)100%
E)120%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
B
Answer: B
Question: The average of ten numbers is 0. In those 10, at the least, how many may be greater than or equal to zero?
Options:
A)0
B)1
C)2
D)3
E)5
Rationale: Explanation :
Average of 10 numbers = 0
Sum of 10 numbers =(0 x 10) =0.
It is quite possible that 9 of these numbers may be negative and if there sum is -a, then 10th number is (a).
Answer : B
Answer: B
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 57 kmph, find the speed of the stream?
Options:
A)16 kmph
B)19 kmph
C)14 kmph
D)11 kmph
E)13 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream
= 57/3 = 19 kmph.
Answer: B
Answer: B
Question: In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only one of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Total Private Schools = 9
Dist A: High Schools = 18 ==> Private Schools = ?
Dist B: High Schools = 17 ==> Private Schools = 1
Dist C: High Schools = 15 ==> Private Schools = 5
Therefore, 9 - 1 - 5 ==> 3
Answer B)
Answer: B
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
Options:
A)8 : 6
B)8 : 7
C)8 : 8
D)8 : 9
E)8 : 3
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
Answer: Option B
Answer: B
Question: A man walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 60 miles?
Options:
A) 300
B) 318
C) 322
D) 324
E) 390
Rationale: To cover 60 miles the man needs (time) = (distance)/(rate) = 60/10 = 6 hours = 360 minutes. He will also rest 5 times (after 10, 20, 30,40 and 50 miles), so total resting time = 5*6 = 30 minutes.
Total time = 360 + 30 = 390 minutes.
Answer: E.
Answer: E
Question: In one hour a boat goes 18 km long the stream and 6 km against the stream.The speed of the boat in still water is?
Options:
A)12
B)14
C)16
D)17
E)18
Rationale: Speed in still water A = ½ ( 18+6) km/hr A= 12 kmph
Answer: A
Answer: A
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.400, find the number of 50 paise coins ?
Options:
A)498
B)488
C)428
D)528
E)418
Rationale: 50*3k + 20*4k + 10*5k = 40000
280k = 40000 => k = 142.85
50p coins = 3k = 3*142.85 = 428
20p coins = 4k = 4*142.85 = 571
10p coins = 5k = 5*142.85 = 714
ANSWER:C
Answer: C