divelab/Sys2Bench huggingface dataset:
Question: In a theatre the ratio of car & two wheeler is 1:8. Total Number of tyres are 100. Find how many are cars and how many are two wheelers?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: let the no of cars be 1x and no of two wheelers be 8x
(1x*4)+(8x*2)=100
20x=100 ...x=5
1x=no of cars=5 8x=no of two wheelers=40
ANSWER:C
Answer: C
Question: A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 54 km downstream
Options:
A)5 hours
B)4 hours
C)3 hours
D)2 hours
E)None of these
Rationale: Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 54 km
Time taken = distance/speed = 54/27 = 2 hours. Answer : Option D
Answer: D
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:
Options:
A)5324
B)5334
C)6300
D)6356
E)6400
Rationale: Divisor = (5 * 50) = 250
= 10 * Quotient = Divisor
=> Quotient = 250/10 = 25
Dividend = (Divisor * Quotient) + Remainder
Dividend = (250 * 25) + 50 = 6300
C
Answer: C
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?
Options:
A)2 1/4
B)2 1/6
C)2 1/0
D)2 1/2
E)2 1/1
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer: A
Answer: A
Question: What is the value of 17^2 + 18^2 + 19^2 + 20^2 + 21^2 + 22^2 + 23^2 ?
Options:
A)2898
B)2808
C)2818
D)2828
E)2838
Rationale: This is what I did, all the nos are close to 20, and squared, so 20^2 plus there are 7 numbers, so (20)^2 x 7 =2800,
now squaring the last digits of each no individually comes up to (9+4+1+0+1+4+9) = 28.
when you add the 2 up it gives you a (2800+28) =2828,
Answer is D IMO.
Answer: D
Question: P and Q started a business by investing Rs.4400/- and Rs.5500/- respectively. Find the P’s share out of a total profit of Rs.2700:
Options:
A)800
B)1000
C)1200
D)1400
E)1600
Rationale: P = Rs.4400/-
Q = Rs.5500/-
P share 4 parts & Q share 5 parts
Total 9 parts -----> Rs.2700/-
----> 1 part -------> Rs.300/-
P share = 4 parts -----> Rs.1200/-
C
Answer: C
Question: In honor of the year 2013, a donor has purchased 2016 books to be distributed evenly among the elementary schools in a certain school district. If each school must receive the same number of books, and there are to be no books remaining, which of the following is NOT a number of books that each school could receive?
Options:
A)18
B)36
C)42
D)52
E)56
Rationale: All options other than 'D' are factors of 2013. Hence, 'D' is the answer
Answer: D
Question: Seven people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options:
A)7/8
B)1/8
C)1/3
D)1/6
E)1/9
Rationale: Original share of 1 person =1/7
New share of 1 person =1/6
Increase =1/6 -	1/7	=1/42
Required fraction =	(1/42)/(1/7)=1/6
Answer is D.
Answer: D
Question: A classroom has equal number of boys and girls. 6 girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
Options:
A)16
B)24
C)32
D)48
E)54
Rationale: after 6 girls left remaining 6 girls
now boys 12 are twice as many as remaining girls.
initially boys=12 and girls=12.
ANSWER:B
Answer: B
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
Options:
A)2.86
B)2.88
C)2.29
D)2.24
E)2.97
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x =2.88
Answer:B
Answer: B
Question: A tailor trims 11 feet from opposite edges of a square piece of cloth, and 7 feet from the other two edges. If 84 square feet of cloth remain, what was the length of a side of the original piece of cloth?
Options:
A)26
B)27
C)28
D)29
E)30
Rationale: Let the original side of the square be x.
(x-22)*(x-14) = 84 = 6*14
x = 28
The answer is C.
Answer: C
Question: If −2≤q≤0 and n > 19, which of the following CANNOT be the value of qn?
Options:
A)-48
B)-38
C)-20
D)0
E)19
Rationale: value of qn not equal to -19=E -19....Rest all are achievable
Answer: E
Question: If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 22?
Options:
A)101
B)187
C)191
D)201
E)242
Rationale: ok, not sure if this is the best explanation, but here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 22 = t 3 + 3 + 4 + 5 + 6....+ 21
the 3 + 4 + 5 + ... + 21 sequence is equal the sequence 1 + 2 + ... + 21, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 21 sequence is equal to n*(n+1)/2 with n being 21, so equal to 21 * 22 / 2 = 231
so :
t 22 = t 3 + 231 - 3
t 22 = 14 + 231 - 3 = 231 + 11 = 242, hence answer E
Answer: E
Question: 36 welders work at a constant rate they complete an order in 3 days. If after the first day, 12 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
Options:
A)3
B)2
C)8
D)4
E)6
Rationale: 1. We need to find out the time taken by 24 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 36*3 = 108 days
4. But on day 1 thirty-six workers had already worked finishing 1/3 of the job. So 24 workers have to finish only 2/3 of the job.
5. Total time taken by 24 workers can be got from formula used at (2). i.e., 24* total time taken = 108. Total time taken by 6 workers to finish the complete job is 108/ 24 = 4.5 days.
6. Time taken by 24 workers to finish 2/3 of the job is 2/3 * 4.5 = 3 days.
The answer is choice A
Answer: A
Question: Rohan spends 40% of his salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If his savings at the end of a month are Rs. 500. then his monthly salary is
Options:
A)Rs. 2500
B)Rs. 3500
C)Rs. 1500
D)Rs. 500
E)Rs. 2000
Rationale: Sol.
Saving = [100 - (40 + 20 + 10 + 10]% = 20%.
Let the monthly salary be Rs. x.
Then, 20% of x = 500
â‡” 20 / 100x = 500
â‡” x = 500 Ã— 5 = 2500.
Answer A
Answer: A
Question: What is the probability of rolling four six-sided dice, and getting a different number on each die?
Options:
A)1/12
B)1/3
C)4/9
D)5/9
E)5/13
Rationale: MAGOOSHOFFICIAL SOLUTION
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.
6 x 5 x 4 x 3 = 360 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6x6 = 1296).
360/1296 = 5/13
Answer: E.
Answer: E
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)165
B)771
C)245
D)177
E)121
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C
Answer: C
Question: The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)29
B)15
C)16
D)17
E)19
Rationale: 10 * 15 + 36 – 26 = 160/10
= 16
Answer:C
Answer: C
Question: At a school, three-fifths of the male students and one-half of the female students speak a foreign language. If the number of males is equal to the number of females, what fraction of the students speak a foreign language?
Options:
A)11/20
B)13/20
C)7/10
D)3/5
E)2/5
Rationale: Let x be the number of students in the school.
The number of males who speak a foreign language is (3/5)(1/2)x = (3/10)x
The number of females who speak a foreign language is (1/2)(1/2)x = (1/4)x
The total number of students who speak a foreign language is (3/10)x + (1/4)x = (11/20)x
The answer is A.
Answer: A
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent. Overall he make a.
Options:
A)228
B)288
C)500
D)200
E)881
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 2/100) = 15000 - 300
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -300 + 800 = Rs. 500
As this is positive, an overall profit of Rs. 500 was made.Answer:C
Answer: C
Question: Two friends are training for a marathon together. Billie is faster than Joey, so they agree to giving Joey a half-hour head start, Joey leaving their warm up at 1:30. Joey runs a 3 minute mile (an average of 20 mph), and Billie runs at an average of 50 mph. When will Billie catch up to Joey?
Options:
A)3:00
B)3:30
C)4:00
D)4:30
E)5:00
Rationale: Distance covered by the Joey in 1/2 hour = 20 miles
Now, 10 miles is compensated in 1 hour
Therefore 20 miles will be compensated in 2 hours
So, Billie meets Joey at 4 p.m.
Correct Answer: C
Answer: C
Question: In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?
Options:
A)18
B)36
C)45
D)55
E)None of these
Rationale: Explanation:
Let R, G and B represent the number of balls in red, green and blue boxes respectively.
Then, .
R + G + B = 108 ...(i),
G + R = 2B ...(ii)
B = 2R ...(iii)
From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.
Putting G = 3R and B = 2R in (i), we get:
R + 3R + 2R = 108 6R = 108 R = 18.
Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.
Answer: E
Answer: E
Question: A and B invests Rs.2000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)3:5
B)3:4
C)9:2
D)9:9
E)3:1
Rationale: (2*6 + 4*6): (4*12)
36:48 =>
3:4
Answer:B
Answer: B
Question: A mixture of 125 gallons of wine and water contains 20% of water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?
Options:
A)10 gallons
B)8.5gallons
C)8gallons
D)8.33gallons
E)9.33gallons
Rationale: In 125 gallons of the solution there are 0.2∗125=25 gallons of water. We want to add w gallons of water to 125 gallons of solution so that 25+w gallons of water to be 25% of new solution: 25+w=0.25(125+w) --> w=253≈8.33.
ANSWER:D
Answer: D
Question: What is the least valueof y. So that 23x57 is divisible by 3?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
A
Answer: A
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 16. Find their present ages.
Options:
A)20,35,45
B)8,14,18
C)16,28,36
D)16,28,46
E)None of these
Rationale: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 16
20K = 40
K = 2
Therefore, then present ages are 8,14,18.
ANSWER:B
Answer: B
Question: The length of a rectangle is 18 cm and its breadth is 10 cm. When the length is increased to 25 cm, what will be the breadth of the rectangle if the area remains the same ?
Options:
A)7 cm
B)7.1 cm
C)7.2 cm
D)7.3 cm
E)None of these
Rationale: Solution
Let the breadth be b. Then,
⇒ 25b = 18 × 10 ⇒ b = (18x10/25)cm= 7.2 cm Answer C
Answer: C
Question: Statement: According to a survey, the current water reservoir will deplete by 50% by 2050
Action:
I. Government of all the countries should appeal to all the citizens to use water carefully and avoid wastage.
II. Scientists should start finding an alternative solution to water.
Options:
A)Only I follows
B)Only II follows
C)Either I or II follows
D)Neither I nor II follows
E)Both I and II follow
Rationale: Explanation:
Second option is not at all justifiable. Water is a basic necessity for survival. So, wasting money and efforts for finding something which doesn’t even exist makes no sense. 2nd option would have been a good and preferable option if it would have been something other than water like petrol or any such thing.
ANSWER IS A
Answer: A
Question: The ratio of the cost price and the selling price is 4:5. The profit percent is:
Options:
A)10%
B)20%
C)25%
D)30%
E)40%
Rationale: Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
ANSWER:C
Answer: C
Question: Which of the following is true about 0<|x|-3x<5?
Options:
A)-1<x<0
B)0<x<1
C)1<x<2
D)2<x<3
E)3<x<4
Rationale: when can be |x|-4x be greater than 0..
NEVER when x is positive..
ONLY A is left..
you can also substitute any value within the given range to check for answer
Example - put x as -0.5 for A. -1<x<0..
so |x|-3x = |-0.5|- 3*(-0.5) = 0.5+15. = 2 and it satisfies 0<|x|-4x<5
A
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 44 years now, the son's age 10 years back was:
Options:
A)10 years.
B)14 years.
C)17 years.
D)16 years.
E)12 years.
Rationale: Let the son's present age be x years. Then, (44 - x) = x
2x = 44.
x = 22
Son's age 10 years back (22 - 10) = 12 years.
ANSWER :E
Answer: E
Question: If x is negative and y is positive, which of the following cannot be positive?
Options:
A)x^2+y
B)x/-y
C)x/y
D)-xy
E)x^4+y
Rationale: -/+ = - x/y is not positive
Answer : C
Answer: C
Question: There are 10 books on a shelf: 6 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?
Options:
A)31/90
B)3/10
C)4/5
D)31/45
E)28/90
Rationale: Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)
Favourable Outcomes
Case-1: One book is English (out of 6 English books) and one book is Spanish (out of 3 Spanish books) i.e. 6C1*3C1
Case-2: One book is Spanish (out of 3 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 3C1*2C1
Case-3: One book is English (out of 6 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 6C1*2C1
Total favourable Outcomes = 6C1*3C1+3C1*2C1+6C1*2C1 = 18+6+12 = 36
Total Possible Outcomes = 10C2 = 45
i.e. Probability = 36/45=4/5
C
Answer: C
Question: A man, a woman or a boy can do a job in 20 days, 30 days or 60 days respectively. How many boys must assist 2 men and 8 women to do the work in 2 days?
Options:
A)15 boys
B)8 boys
C)10 boys
D)11 boys
E)None of these
Rationale: Man’s two day’s work = 2 × 1⁄20 th work = 1⁄10 th work
Woman’s two days’s work
= 2 × 1⁄30 th work = 1⁄15 th work
Boy’s two day’s work = 2 × 1⁄60 th work = 1⁄30 th work
Now, let 2 men, 8 women and x boys can complete work in 2 days. Then ,
2 men’s work + 8 women’s work + x boy’s work = 1
2(1⁄10) + 8(1⁄15) + x(1⁄30) = 1
⇒ x = (1 - 1⁄5 - 8⁄15) × 30 ⇒ x = 8 boys
Answer B
Answer: B
Question: An amount of Rs.20,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
Options:
A)Rs. 5000
B)Rs. 4570
C)Rs. 2750
D)Rs. 2950
E)None of these
Rationale: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 20,000
Thus we get, 2Q + Q + Q + 4Q = 20,000
8Q = 20,000 or Q = Rs. 2500
Thus, R = Rs. 2500, P = 5000 & S = Rs. 10000
Hence, the required difference = (S – P) = (10000 – 5000) = Rs. 5000
ANSWER:A
Answer: A
Question: ?% of 360 = 115.2
Options:
A)277
B)36
C)64
D)32
E)None of these
Rationale: ?% of 360 = 115.2
or, ? = 115.2×100/360=32
Answer D
Answer: D
Question: How many multiples of 3 are there between 10 and 100, exclusive ?
Options:
A)30
B)29
C)28
D)31
E)33
Rationale: 3 * 4 = 12
3 * 33 = 99
Total multiples = (33 - 4) + 1 = 30
Exclude 10 and 100 = 30
Answer is A
Answer: A
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 3 and that the product of the given number and the sum of its digits is equal to 517, then the number is:
Options:
A)14
B)36
C)47
D)58
E)63
Rationale: Let the ten's digit be x. Then, unit's digit = x + 3. Number = 10x + (x + 3) = 11x + 3
(11x + 3)(2x + 3) = 517
22(x)(x)+ 39x- 508 = 0
(x - 4)(22x + 127) = 0
x = 4
Hence, required number = 11x + 3 = 47.
ANSWER:C
Answer: C
Question: There is an increase of 30% in the production of milk chocolates in Amul Dairy in one month. If now it is 9,100 milk chocolates per month, what was it one month ago?
Options:
A)10,000 chocolates
B)9000 chocolates
C)8000 chocolates
D)7000 chocolates
E)None of these
Rationale: Let one month ago, production be x chocolates.
Then, 130 % of x = 9100
⇒ x = 9100×100/130=7000 chocolates
Answer D
Answer: D
Question: Which of the following cannot be the range of a set consisting of 5 odd multiples of 13?
Options:
A)52
B)100
C)104
D)208
E)416
Rationale: Solution: sequence of 13 lets say sequence is 13n, 13(n+1), 13(n+2), 13(n+3), 13(n+4)
so range is 13n+52-13n = 52
if we put the different values of n we will get different but the range will be multiple of 52
and only 100 is not multiple of 52
Answer : B
Answer: B
Question: A and B started a business with an investment of Rs.26000 and Rs.28000. After two months C joined in the business with an investment of Rs.32000, what is share of C in the half year profit of Rs.9040 ?
Options:
A)Rs.3360
B)Rs.3120
C)Rs.2940
D)Rs.2560
E)Rs.3550
Rationale: Investment x Time.
A = 26000 x 6 = 156000.
B = 28000 x 6 = 168000.
C = 32000 x 4 = 128000.
Ratio of shares A : B : C = 39 : 42 : 32 = [ Total 113 units ]
Share of C in the profit = 9040 × 32 / 113 = 2560
Option D
Answer: D
Question: A shopkeeper has 280 kg of apples. He sells 40% of these at 10% profit and remaining 60% at 30% profit. Find his % profit on total.
Options:
A)22%
B)25%
C)26%
D)28%
E)35%
Rationale: If the total quantity was 100
Then 40X 10% + 60 X30%= 22
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'A' is the answer
Answer: A
Question: There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure y in inches of the width of the foil covered prism?
Options:
A)4
B)6
C)8
D)9
E)10
Rationale: If the width is w, then length and height would be w/2.
So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)
=> w = 2*4 = 8 in.
Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes
= 8 +2 =y=10
Ans E.
Answer: E
Question: A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $900?
Options:
A)$3,000
B)$3,150
C)$4,000
D)$4,150
E)$5,000
Rationale: We're told that a sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $900.
Since the salesperson receives a $150 salary, the remaining $750 has to be accounted for by the 15% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.
Let's TEST Answer C: $4,000
Since 15% of $1,000 = $150
15% of $4,000 = 4($150) = $600
This is TOO HIGH (it's supposed to be $450), so we need a LOWER total sales figure.
Let's TEST Answer E: $5,000
Since 15% of $1,000 = $150
15% of $5,000 = 5($150) = $750
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
E
Answer: E
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A)18/35
B)18/39
C)18/128
D)18/30
E)18/32
Rationale: Explanation:
If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A
Answer: A
Question: Machine X takes 10 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce
Options:
A)100
B)65
C)25
D)11
E)18
Rationale: Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 10
So, x = 10.
Hence 6x = 6*10 = 60 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/60
= 18
Hence option (E).
Answer: E
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)277 sec
B)190 sec
C)667 sec
D)167 sec
E)176 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.Answer: B
Answer: B
Question: In a race of length L metres, Johnson beats Lewis by P metres and Greene by Q metres, By how many metres does Lewis beat Greene in the same race ? (P<Q)
Options:
A)L(L-Q) / L-P
B)L(Q-P) / L-P
C)L-Q
D)P-Q
E)P+Q
Rationale: As the time is constant, the ratio of distances will be the same as the ratio of speeds.
If Sj,Sl,Sg are the speeds of Johnson, Lewis, and Greene respectively, then
Sj/Sl = L/(L-P)
and Sj/Sg = L/(L-Q)
=> Sg/Sl = (L-Q)/(L-P)
Therefore the speeds of Lewis and Greene are in the ratio (L-P)/(L-Q)
When Lewis finishes the race, the time run by him and Greene are same
=> The ratio of the speeds of Lewis and Greene will be the same as the ratio of distances run by them.
=> Distance run by Greene when Lewis finishes the race = (L-Q)/(L-P) * L
=> Lewis beats Greene by L - L*(L-Q)/(L-P) = L [ 1 - (L-Q)/(L-P)] = L (Q-P) / (L-P)
Option (B) is therefore correct.
Answer: B
Question: The age of father 5 years ago was four times the age of his son. Five years hence, father's age will be twice that of his son. The ratio of their present ages is:
Options:
A)5 : 4
B)7 : 4
C)5 : 2
D)5 : 3
E)7 : 5
Rationale: Let the ages of father and son 5 years ago be 4x and x years respectively.
Then, (4x + 5) + 5= 2[(x + 5) + 5]
4x + 10 = 2x + 20
x = 5.
Required ratio = (4x + 5) : (x + 5) = 25: 10= 5 : 2.
Answer: Option C
Answer: C
Question: A baker filled with a measuring cup with 1/2 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
Options:
A)1/8 cup
B)3/8 cup
C)1/4 cup
D)1/2 cup
E)5/8 cup
Rationale: 1/2 is the original water in cup .half in batter.So left is 1/4 out which 1/8 is spilled out.So again left with 1/8.
so 50% more than what he started was = 1/2+1/2*(1/2)=3/4
Amount of water needed to add = 6/8 - 1/8=5/8
E
Answer: E
Question: The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares
Options:
A)22 cm
B)24 cm
C)26 cm
D)28 cm
E)None of these
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 10*10 - 8*8
= 36 cm
So side of third square = 6 [because area of square = side*side]
Perimeter = 4*Side = 4*6 = 24 cm
Option B
Answer: B