divelab/Sys2Bench huggingface dataset:
Question: Rahul and Bharti are partners in a business. Rahul contributes 1/4th capital for 15 months and Bharti received 2/3 of profit. For how long Bharti money was used.
Options:
A)8 months
B)10 months
C)11 months
D)17 months
E)None of these
Rationale: Explanation:
Let the total profit be Rs. Z
Bharti's share = (2/3)Z
Rahul's Share = Z-(2/3)Z = Z/3
Rahul:Bharti = Z/3:(2/3)Z = 1:2
Now let the total capital be Rs X, and Bharti capital was used for Y months
then, Rahul capital will be (1/4)X and Bharti capital wil be X-(1/4)X = 3X/4
14X∗15/ 3/4X∗Y=1/2
Y=15∗2/3=10
So Bharti's money was used for 10 months
Option B
Answer: B
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
Options:
A)35%
B)30%
C)40%
D)42 6/7%
E)None of these
Rationale: Explanation:
SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer IS D
Answer: D
Question: If n divided by 7 has a remainder of 2, what is the remainder when 2 times n is divided by 7?
Options:
A)1
B)2
C)3
D)4
E)6
Rationale: As per question => N=7P+2 for some integer p
hence 2N => 14Q + 4 => remainder => 4 for some integer Q
Alternatively => N=2 > 2N=> 4 =>4 divided by 7 will leave a remainder 4
hence D
Answer: D
Question: A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball?
Options:
A)5⁄7
B)10⁄21
C)2⁄7
D)11⁄21
E)None of these
Rationale: Reqd probability = 5C2/7C2=5×4/7×6=10/21
Answer B
Answer: B
Question: If the product of the integers r, s, t and u is 770, and if 1 < r< s< t< u, what is the value of r+ u?
Options:
A)10
B)13
C)16
D)18
E)21
Rationale: 770 = 2 * 5 * 7 * 11
So r= 2, s= 5, t= 7, u= 11
r+ u= 2 + 11 = 13
Answer - B
Answer: B
Question: At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 11'o clock.
Options:
A)60sec
B)62sec
C)66sec
D)64sec
E)76sec
Rationale: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
.
.
.
10'o clock 9 *6=54sec
11'o clock 10*6=60sec
So, 60sec at 11'o clock.
ANSWER:A
Answer: A
Question: In how many different R ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?
Options:
A)70
B)288
C)576
D)10,080
E)20,160
Rationale: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways
And there are 4! ways to arrange ladies among themselves
Answer R= (4!)^2 = 576 or C
Answer: C
Question: The integers 1, 2, …, 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the sum of the numbers left on the board at the end?
Options:
A)820
B)821
C)781
D)819
E)780
Rationale: Explanation :
Initial sum of the numbers is 1 + 2 + …40.
Initial sum = 40 * 41/2 = 820. (A.P. with common difference 1 and 1st term 1, last term 40).
Two numbers, a, b are erased and replaced by a+b-1, that means, the sum is now 819.
This is done 39 times. So, sum after 39 time replacement is 820 – 39 = 781.
Answer : C
Answer: C
Question: If December 3rd, 1999 is a Friday, what day is January 7th, 2000?
Options:
A)Wednesday
B)Thursday
C)Friday
D)Saturday
E)Sunday
Rationale: There is difference of 35 days from Dec. 3rd 1999 to Jan. 7th 2000.
35/7 has a remainder of 0.
Jan. 7th is: Friday + 0 days = Friday
The answer is C.
Answer: C
Question: Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm.
Options:
A)221 cm2
B)211 cm2
C)231 cm2
D)236 cm2
E)241 cm2
Rationale: Given: length = 17 cm, breadth = 13 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (17 + 13) cm
= 2 × 30 cm
= 60 cm
We know that the area of rectangle = length × breadth
= (17 × 13) cm22
= 221 cm2 ANSWER :A
Answer: A
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options:
A)87 days
B)20 days
C)66 days
D)77 days
E)44 days
Rationale: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer: B
Answer: B
Question: The difference between a number and its two-fifth is 45. What is the number?
Options:
A)76
B)56
C)88
D)66
E)75
Rationale: Explanation:
Let the number be x.
x – (2 / 5) x = 45
(3/5) x = 45
x = 75
ANSWER: E
Answer: E
Question: What is the total number of prime numbers less than 50?
Options:
A)17
B)18
C)19
D)15
E)21
Rationale: Solution
Prime numbers less than 50 are	=15.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
Their number is 15.
Answer D
Answer: D
Question: What will be the compound interest on Rs. 30000 after 3 years at the rate of 12 % per annum
Options:
A)Rs 10123.20
B)Rs 12147.84
C)Rs 10123.40
D)Rs 10123.50
E)None of these
Rationale: Explanation:
(30000×(1+12/100)3)
=>30000×28/25×28/25×28/25
=>42147.84
So Compound interest will be 42147.84 - 30000
= Rs 12147.84
Option B
Answer: B
Question: A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the physics club and 3/4 attend the chemistry club. 3/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.
Options:
A)80
B)70
C)60
D)50
E)30
Rationale: A-Club has 200 members (1/2 of 400)
B-Club has 250 members (5/8 of 400)
C-Club has 300 members (3/4 of 400)
We can create an equation to solve this:
200+250+300 = n + x + 2y
where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.
The question provides y for us (150).
750 = 400 + x + 300
x = 50
D
Answer: D
Question: In how many different ways can the letter of the word 'JUDGE ' be arranged in such a way that the vowels always come together?
Options:
A)48
B)89
C)56
D)74
E)25
Rationale: It has 5 different letters.
when the vowels UE are always together, they can be supposed to form one letter.
then we have to arrange the letter JD
now 4 letters can be arranged in 4!=24ways
the vowels UE can be arranged amoung themselves in 2!=2 ways
required number of ways =24*2=48
Answer(A)
Answer: A
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 2000, the number of valid votes that the other candidate got, was:
Options:
A)900
B)750
C)250
D)600
E)800
Rationale: Number of valid votes = 80% of 2000 = 1600
Valid votes polled by other candidate = 45% of 2000
=(45/100)X2000 =900
ANSWER = A
Answer: A
Question: Set S has a mean of 9 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
Options:
A){2, 10}
B){16, 16}
C){9, 11}
D){7, 13}
E){10, 18}
Rationale: answer A, B,C, and D mean is not 9 therefore not accepted . E mean is 9 but S.D is one unit. therefore accepted
answer is E mean is 9 and S.D decreases minimum.
E
Answer: E
Question: if the ratio of s.i earned on certain amount on same rate is 4:5.what is the ratio of time?
Options:
A)1:2
B)6:9
C)4:5
D)2:3
E)not possible to calculate
Rationale: s.i1/s.i2=[(p*r*t1)/100]/[(p*r*t2)/100]
4/5=t1/t2
ratio=4:5
answer C
Answer: C
Question: A man sitting in a train which is traveling at 36 kmph observes that a goods train, traveling in opposite direction, takes 10 seconds to pass him. If the goods train is 240 m long, find its speed
Options:
A)50 kmph
B)56 kmph
C)58 kmph
D)62 kmph
E)72 kmph
Rationale: Explanation:
Relative speed = 240/10 m / sec = ((240/10)×(18/5)) kmph = 86 kmph.
Speed of goods train = (86 - 36) kmph = 50 kmph
Answer: Option A
Answer: A
Question: If P and Q are positive integers and P = 10Q + 3, what is the remainder when P is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: This question asks what IS...(the answer), so we know that the answer will be consistent. As such, we can TEST VALUES to quickly get the solution.
We're told that P and Q are POSITIVE INTEGERS and P = 10Q + 3. We're asked for the REMAINDER when X is divided by 5.
IF....
Q = 1
P= 13
13/5 = 3 remainder 3
Final Answer:
D
Answer: D
Question: John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Q that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
Options:
A)a. 3/5
B)b.2/3
C)c.7/10
D)d.3/4
E)e.4/5
Rationale: X(10) --- Net(0) --- Q(-15) = -15/-10 = 3/2.
So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
Answer: A
Question: Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.
Options:
A)Rs. 4000
B)Rs. 5000
C)Rs. 6000
D)Rs. 7000
E)None
Rationale: Solution: Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A:B:C =6 x : 4x : x
= 6 : 4 : 1
B's share = 16500 * (4/11) = 1500*4 = 6000.
Answer: Option C
Answer: C
Question: The length of a rectangle is two third of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 4761 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 13 units?
Options:
A)598 sq.units
B)556 sq.units
C)589 sq.units
D)958 sq.units
E)985 sq.units
Rationale: Given that the area of the square = 4761sq.units
=> Side of square = âˆš4761 = 69 units
The radius of the circle = side of the square = 69 units
Length of the rectangle = 2/3 * 69 =46units
Given that breadth = 13 units
Area of the rectangle = lb = 46 * 13= 598 sq.units
Answer:A
Answer: A
Question: A man is 12 years older than his brother. In two years, his age will be twice the age of his brother. The present age of his brother is:
Options:
A)10
B)21
C)22
D)23
E)24
Rationale: Let the brother's present age be x years. Then, man's present age = (x + 12) years.
(x + 12) + 2 = 2(x + 2)
x + 14 = 2x + 4
x = 10.
Answer:A
Answer: A
Question: P alone can complete a piece of work in 14 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
Options:
A)6 (1/4) days
B)21/2 days
C)7 (3/4) days
D)8/5 days
E)9 (3/4) days
Rationale: Work done by P alone in one day = 1/14th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/14 of the total) = 1/42 of the total.
Work done by P and Q, working together in one day = 1/14 + 1/42 = 4/42 of the total
They would take 42/4 days = 21/2 days to complete the work working together.
ANSWER:B
Answer: B
Question: If 20% of a number = 400, then 120% of that number will be?
Options:
A)20
B)120
C)360
D)2400
E)2820
Rationale: Let the number x. Then,
20% of x = 400
x = (400 * 100)/20 = 2000
120% of x = (120/100 * 2000) = 2400.
ANSWER:D
Answer: D
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit ?
Options:
A)Rs. 660
B)Rs. 560
C)Rs. 1060
D)Rs. 960
E)None of these
Rationale: Explanation:
Let C.P. = Rs. C.
Then, 832 - C = C - 448
2C = 1280 => C = 640
Required S.P. = 150% of Rs. 640 = 150/100 x 640 = Rs. 960.
ANSWER IS D
Answer: D
Question: Mohan has 8 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 16 shoes, what is the probability that she will select 2 shoes of the same color?
Options:
A)2/5
B)1/15
C)1/9
D)1/10
E)1/25
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 16 shoes = 16/16 = 1
Probability of selecting the next shoe (out of 16 available) having the same color = 1/16 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/15=1/15.
B is the correct answer.
Answer: B
Question: Three maths classes: A, B and C take an algebra test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. What is the average score of classes A, B, C ?
Options:
A)81.8
B)81.1
C)81.2
D)81.5
E)81.9
Rationale: Let the number of students in classes A, B and C be P, Q and R respectively.
Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R.
Also given that,
(83P + 76Q) / (P + Q) = 79
=>4P = 3Q.
(76Q + 85R)/(Q + R) = 81
=>4R = 5Q,
=>Q = 4P/3 and R = 5P/3
Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12 = 81.5
Answer: D
Answer: D
Question: In a class of students, the ratio of girls to boys is 1:2. If 2 more girls joined the class, the ratio would be 2:3. How many students are in the class?
Options:
A)18
B)20
C)22
D)24
E)26
Rationale: Let x be the number of students in the class.
(1/3)*x=(2/5)(x+2)-2
5x=6x+12-30
x=18
The answer is A.
Answer: A
Question: The ages of two persons differ by 16 years. 8 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person
Options:
A)15
B)20
C)25
D)30
E)32
Rationale: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x � 16
(x � 8) = 3 (x-16-8)
=> x � 8 = 3x � 72
=> 2x = 64
=> x = 64/2 = 32
Answer: Option E
Answer: E
Question: A dozen eggs and 10 pounds of oranges are currently at the same price. If the price of a dozen eggs rises by 9 percent and the price of oranges rises by 6 %. How much more will it cost to buy a dozen eggs and 10 pounds of oranges .
Options:
A)5%
B)10%
C)15%
D)20%
E)25%
Rationale: Say currently both a dozen eggs and 10 pounds of oranges cost $100 (they are at the same price). So, to buy a dozen eggs and 10 pounds of oranges we need $100.
After the increase, the price of a dozen eggs will be $109 and the price of 10 pounds of oranges will be $106. So after the increase, to buy a dozen eggs and 10 pounds of oranges we'll need $215.
Increase = 15%.
Answer: C.
Answer: C
Question: Two children want to walk together to visit their aunt, who lives exactly 9 blocks north and 7 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 16 blocks. How many different 16-block routes may they take to travel the shortest possible distance to their aunt’s house?
Options:
A)9!*7!
B)16*9*7
C)16!*9!*7!
D)16!/(9*7)
E)16!/(9!*7!)
Rationale: If they need to walk 9 blocks north and 7 blocks east, we can express this route as NNNNNNNNNEEEEEEE. The question thus asks us how many ways we can arrange those letters.
The number of arrangements of 16 things is 16!
We then divide by the repetitions of N's and E's, which are 9! and 7! respectively.
The number of walking routes is 16!/(9!*7!).
The answer is E.
Answer: E
Question: Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
Options:
A)99:61
B)99:160
C)61:160
D)61:99
E)99:160
Rationale: Vessel A = 300 gallons --> milk = 120, water = 180;
Vessel B = 500 gallons --> milk = 375, water = 125;
Vessel A + B = 800 gallons --> milk = 495, water 305.
The ratio = 495/305 --> reduce by 5 = 99/61.
Answer: A.
Answer: A
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 30,000
B)Rs. 50,000
C)Rs. 60,000
D)Rs. 90,000
E)Rs. 80,000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
(1/3)x= (1/2)(150000-x)
x/3+x/2=75000
5x/6=75000
x=75000*6/5= 90000
Therefore, Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000
ANSWER:C
Answer: C
Question: If 1/12 of the passengers on a ship are from North America, 1/8 are Europeans, 1/3 are from Africa, 1/6 are from Asia and the remaining 35 people are citizens of other continents, then how many passengers are on board the ship?
Options:
A)110
B)115
C)120
D)125
E)130
Rationale: 1/12 + 1/8 + 1/3 + 1/6 = (2+3+8+4)/24 = 17/24
Let x be the number of passengers on the ship.
35 = (7/24)x
x = 120
The answer is C.
Answer: C
Question: The avg age of an adult class is 40years. 12new students with an avg age of 32years join the class. Therefore decreasingthe avg by 4year. Find what was the original strength of class?
Options:
A)8
B)12
C)15
D)16
E)19
Rationale: Let original strength = y
Then , 40y + 12 x 32 = ( y + 12) x 36
⇒ 40y + 384 = 36y + 432
⇒ 4y = 48
∴ y = 12
B
Answer: B
Question: In a survey about potential presidential candidates A and B, 37% of the public like A and 55% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither?
Options:
A)27%
B)31%
C)41%
D)22%
E)69%
Rationale: Let x be the percentage of people who like both.
Then the percentage of people who like only 1 but not both is 2x.
37% + 55% = 2x + 2(x) because the percentage who like both are counted twice.
Then x = 23% and 2x = 46%
100% = 23% + 46% + Neither
Neither = 31%
The answer is B.
Answer: B
Question: On a baseball team, 7 players including Alice want to play 1st base, 2nd base, or 3rd base. Before every game, the coach chooses a name randomly from a bag and this person plays 1st base. Then the coach chooses the next name randomly and this person plays 2nd base. The coach then chooses a third name randomly and this person plays 3rd base. What is the probability that Alice plays 1st, 2nd, or 3rd base?
Options:
A)2/3
B)3/5
C)4/5
D)3/7
E)4/7
Rationale: The total number of ways to choose three players is 7C3=35.
Excluding Alice, the number of ways to choose three players is 6C3=20.
P(Alice is not chosen)=20/35=4/7.
P(Alice is chosen)=1 - 4/7 = 3/7.
The answer is D.
Answer: D
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: five letters -> 5 blanks ....
First and last--> N and A
remaining three blanks --> remaining 3 letters in 3!
req no of words ==>6
ANSWER C
Answer: C
Question: Catherina works 5 hours per day on Monday, Wednesday and Friday, and 10 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $420 per week. How much does she earn in dollars per hour?
Options:
A)14
B)15
C)16
D)12
E)18
Rationale: So, she works 15 hours in 3 days
So, she works 20 hours in 2 days
So in a week she works 35 hours ( 15 + 20 ) and earns $420
So, Hourly wage is 420/35 => 12
Hence answer will be (D) 12
Answer: D
Question: If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+3 ?
Options:
A)4
B)-4
C)-1
D)-2
E)-3
Rationale: let we put values. a=1, b=3, c=5
5-3-1=1
1+3 =4
Answer :A
Answer: A
Question: A 300 m long train crosses a platform in 40 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Options:
A)288
B)350
C)889
D)367
E)234
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/40 = 50/3
3x + 900 = 2000 => x = 367 m.
Answer:D
Answer: D
Question: A certain quantity of 60% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
Options:
A)1/4
B)1/3
C)1/2
D)2/3
E)5/7
Rationale: Let's say that the total original mixture A is 100 ml
The original mixture A thus has 60 ml of alcohol out of 100 ml of solution
You want to replace some of that original mixture A with another mixture B that contains 25 ml of alcohol per 100 ml. Thus, the difference between 60 ml and 25 ml is 35 ml per 100 ml of mixture. This means that every time you replace 100 ml of the original mixture A by 100 ml of mixture B, the original alcohol concentration will decrease by 35%. The question says that the new mixture, let's call it C, must be 35% alcohol, a decrease of only 25%. Therefore, 25 out of 35 is 5/7 and E is the answer.
Answer: E
Question: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile, what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles?
Options:
A)1/6
B)3/10
C)1/3
D)1/2
E)2/3
Rationale: The car ends within a half mile of the sign indicating 2 1/2 miles means that the car will end in one mile interval, between the signs indicating 2 and 3 miles.
Now, it doesn't matter where the car starts or what distance it travels, the probability will be P=(favorable outcome)/(total # of outcomes)=1/3 (as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared, so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1/3).
Answer: C.
Answer: C
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 48 years now, the son's age five years back was:
Options:
A)14 years
B)19 years
C)33 years
D)38 years
E)39years
Rationale: Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24.
Son's age 5 years back (24 - 5) = 19 years.
Answer:B
Answer: B
Question: If the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
Options:
A)50
B)52
C)69
D)78
E)84
Rationale: Sum of 5 Integer (a, b, c, d, e) = 5*70 = 350
e - a = 10
i.e. e = a+10
For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers
i.e. a+a+a+a+(a+10) = 350
i.e. 5a = 340
i.e. a = 68
i.e. Largest e = 68+10 = 78
Answer: option D
Answer: D
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)2:5
B)2:9
C)2:2
D)2:9
E)2:1
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer:A
Answer: A
Question: A courtyard is 24 meter long and 14 meter board is to be paved with bricks of dimensions 25 cm by 15 cm. The total number of bricks required is :
Options:
A)6000
B)8000
C)8960
D)2000
E)None of these
Rationale: Explanation:
Number of bricks =Courtyard area /1 brick area
=(2400Ã—1400 /25Ã—15)=8960
Option C
Answer: C
Question: At the store, Sam bought a shirt and a toaster. There was a 9% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?
Options:
A)0.91(K – T)
B)0.91K – T
C)0.91(K – 1.09T)
D)(K – T)/1.09
E)(K/1.09) – T
Rationale: 1.09S + 1.09T = K
1.09S = K - 1.09T
S = (K/1.09) - T
The answer is E.
Answer: E
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be B's share in the total profit of Rs.27,000 earned at the end of 2 years from the starting of the business?
Options:
A)Rs.8100
B)Rs.9000
C)Rs.9500
D)Rs.10,000
E)None
Rationale: Solution
A : B : C	=(20000×24):(15000×24):(20000×18)
=4 :3 :3
B's share	=Rs.(27000×3/10)
= Rs.8100.
Answer A
Answer: A
Question: How much is 80% of 40 is greater than 4/5 of 25?
Options:
A)22
B)77
C)15
D)12
E)88
Rationale: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D
Answer: D