divelab/Sys2Bench huggingface dataset:
Question: In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different Y sets can be produced by this process?
Options:
A) 41
B) 89
C) 125
D) 243
E) 512
Rationale: Case 1: 1 used envelope => 1 way
Case 2: 2 used envelopes
- 4-1-0: Choose 4 from 5 cards: 5 ways
- 3-2-0: Choose 3 from 5 cards: 10 ways
Case 3: All envelopes used
- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways
- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15
Total Y: 1+5+10+10+15=41 => Answer: A
Answer: A
Question: Of the 200 employees at company X, 80 are full-time, and 150 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
Options:
A)20
B)30
C)50
D)80
E)100
Rationale: 200 employees
80 are full-time
150 have worked at company X for at least a year
20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
200-80=120 employees not full time
120-20= 100 employees not full time who worked over a year
150 employees have worked at company X for at least a year-100 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year
C. 50
Answer: C
Question: The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 300% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?
Options:
A)4N
B)6N
C)8N
D)10N
E)12N
Rationale: In 1992, the company's assets were N.
In 1993, the company's assets were N + 3N =4N.
In 1994, the company's assets were 4N + 4N = 8N.
The answer is C.
Answer: C
Question: If n = 8^8 – 5, what is the units digit of n?
Options:
A)0
B)1
C)2
D)3
E)5
Rationale: 8 ^ 8 - 8 = 8 (8 ^ 7 - 1)
==> 8 (2 ^ 21 - 1)
Last digit of 2 ^ 21 is 2 based on what explanation LiveStronger is saying. 2 ^ 24 - 1 yields 2 - 1 = 1 as the unit digit. Now on multiply this with 5, we get unit digit as 5
Answer : E
Answer: E
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 5. What could be the ratio of Cats to dogs in the pet store?
Options:
A)1:3
B)20:25
C)1:5
D)2:5
E)4:6
Rationale: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.
We are told that ax - bx = 5 --> x(a - b) = 5. Since 5 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*5.
The above implies that either x = 1 and a - b = 5 or x = 5 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 = 5*4 = 20 and dogs = 5*5 = 25.
Answer: B.
Answer: B
Question: A and B together have Rs. 1210. If of A's amount is equal to of B's amount, how much amount does B have?
Options:
A)484
B)460
C)550
D)664
E)None of them
Rationale: 4/15 A = 2/5 B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
Therefore, B's share = Rs. (1210 x 2/5)= Rs. 484.
Answer is A.
Answer: A
Question: When 24 is divided by the positive integer d, the remainder is 4. Which of the following statements about d must be true?
I. d is even
II. dis a multiple of 5
III. d is a factor of 20
Options:
A)III only
B)I and II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: 24= m*d + 4
m*d=20
put values of m
m=1 d=20
m=2 d=10
m=4 d=5
I. not true
II. true
III. true
D. correct
Answer: D
Question: Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 34 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
Options:
A)20
B)21
C)22
D)23
E)25
Rationale: Check two extreme cases:
Jane = 18, child = 9, years ago = 34-18 = 16 --> child's age now = 9+16 = 25;
Jane = 24, child = 12, years ago = 34-24 = 10 --> child's age now = 12+10 = 22.
Answer: E.
Answer: E
Question: When 40 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
Options:
A)3 : 4
B)4 : 3
C)1 : 1
D)Data inadequate
E)None of these
Rationale: Let the first and the second numbers be x and y respect then
y + 40% of x = 140% of y
or, y + 0.4x = 1.4y
or, 0.4x = 0.4y
∴ x : y = 0.4 : 0.4 = 4 : 4
Answer C
Answer: C
Question: In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?
Options:
A)$50
B)$320
C)$150
D)$100
E)$400
Rationale: Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.
4x + 4y + 2z = 560 :
9x + 9y + 6z = 1,290
3x + 3y + 2z = 430 : divide all terms of equation C by 3
x + y = 130 : subtract equation D from equation B
3(x + y) + 2z = 430 : equation D with factored terms.
3*130 + 2z = 430
z = 20 : solve for z
x + y + z = 130 + 20 = $150
correct answer C
Answer: C
Question: One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
Options:
A)31
B)32
C)33
D)36
E)35
Rationale: Let the age of Sooraj and Vimal, 1 year ago, be 6x and 7x respectively.
Given that, four years hence, this ratio would become 7:8
⇒(6x+5):(7x+5)=7:8⇒8(6x+5)=7(7x+5)⇒48x+40=49x+35⇒x=5
Vimal's present age
=7x+1=7×5+1=36
Answer is D.
Answer: D
Question: If a and b are unique prime integers, which of the following must be odd?
Options:
A)a−b
B)2a+2b
C)2a−2b
D)2a / 2b
E)ab^2
Rationale: Any number multiplied by 2 has to be an even number. hence
Answer A
Answer: A
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
Options:
A)44 sec
B)49 sec
C)42 sec
D)47 sec
E)None of these
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
ANSWER:D
Answer: D
Question: A man can row downstream at the rate of 18 Kmph and upstream at 6 Kmph. Find the man’s rate in still water and rate of current?
Options:
A)8.5
B)6.0
C)9.5
D)9.0
E)8.25
Rationale: Rate of still water = 1/2 (down stream + upstream)
= 1/2 (18 + 6) = 12 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (18 - 6)
= 1/2 (12)
= 6 kmph
Answer is B.
Answer: B
Question: A tank is filled by 3 pipes A,B,C in 3 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
Options:
A)25hr
B)35hr
C)40hr
D)20hr
E)21hr
Rationale: Suppose pipe A alone take x hours to fill the tank
Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/3
7/x = 1/3
x = 21 hours
Answer is E
Answer: E
Question: An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are
Options:
A)10 cm, 50 cm
B)20 cm, 100 cm
C)40 cm, 200 cm
D)None of these
E)Cannot be determined
Rationale: Solution
Let the sides of the sheet be x and 5x.
Then,volume of the sheet= volume of the cube
‹=› x × 5x ×1/2
‹=› 10×10×10
‹=› 5x2= 2000
‹=› x2= 400
‹=› x = 20.
The sides are 20 cm and 100 cm.
Answer B
Answer: B
Question: Pipe A can fill a tank in 10 hr, pipe B in 20hr and pipe C in 40hr. If all the pipes are open in how many hours will tank be filled?
Options:
A)1hr
B)30min
C)15min
D)17min
E)10min
Rationale: Part filled by (A+B+C) in 1hour = 1/10 + 1/20 + 1/40 = 7/40
All the 3 pipes together will fill the tank in 17min Approximately
Answer is D
Answer: D
Question: If for any number N, f(N) is defined as the least integer that is greater than or equal to N^2, then what is the value of f(-1.5)?
Options:
A)-4
B)-3
C)1
D)2
E)3
Rationale: If N=-1.5, then N^2=2.25.
The least integer that is greater than or equal to 2.25 is 3, thus f(-1.5) = 2.25.
The answer is E.
Answer: E
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
Options:
A)15
B)46
C)71
D)75
E)78
Rationale: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46
B
Answer: B
Question: The function f(x) is defined for all positive integers x as the number of even factors of x and the function g(x) is defined for all positive integers x as the number of odd factors of x. For positive integers a and b if f(b)*g(a) = 0 and f(a) = 1, which of the following could be the least common multiple of a and b?
Options:
A)12
B)16
C)20
D)30
E)36
Rationale: f(b)∗g(a)=0 : any positive integer has at least one odd factor: 1. Thus, g(a) cannot be 0, which implies that f(b) = 0. This on the other hand means that b is an odd integer (odd integers does not have even factors).
f(a)=1f(a)=1: aa has 1 even factor. This means that aa must be 2 (the only positive integer which has only 1 even factor is 2).
The least common multiple of a=2a=2 and b=odd is 2∗odd. Only option D can be represented this way: 30=2∗1530=2∗15.
Answer: D
Answer: D
Question: The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 55% profit?
Options:
A)$480
B)$450
C)$992
D)$870
E)$660
Rationale: C
Let C.P. = $ x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 155% of $ 640 = 150/100 * 640 = $ 992.
Answer: C
Question: In filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be?
Options:
A)100 cu.m
B)1000 cu.m
C)10000 cu.m
D)100000 cu.m
E)10000000 cu.m
Rationale: 100 * 10 * 10 = 10000
ANSWER:C
Answer: C
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is r, what is the difference between the probability that r is even and the probability that r is odd?
Options:
A) 1/9
B) 1/6
C) 2/9
D) 1/4
E) 1/2
Rationale: Age of Boys r:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11)(13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Answer: A
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)3.6 sec
B)18 sec
C)36 sec
D)72 sec
E)None
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec
ANSWER:C
Answer: C
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
Options:
A)1/26
B)1/52
C)2/62
D)2/26
E)3/26
Rationale: Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E) = n(E)/n(S)
= 2/52
= 1/26
Answer should be A
Answer: A
Question: Today Chris ate 15 jellybeans. Bella ate 2/3 of the jellybeans Chris did, Frances ate 5 more jellybeans than Bella did , and Sandhya ate 20% more than Frances. How many jellybeans did Sandhya eat?
Options:
A)18
B)20
C)13
D)25
E)15
Rationale: A
13
Chris ate 15 jellybeans
Bella ate 2/3 of the jellybeans Chris did.
Bella= 2/3 x 15
=10
Frances ate 5 more jellybeans than Bella.
Frances= 10+5 jellybeans.
=15
Sandhya ate 20% more jellybeans than Frances.
Sandhya = 15 + 15 × 20%
= 15 + 15 × 0.20
= 15 + 3
= 18
Sandhya ate 18 jellybeans.
The correct answer is A.
Answer: A
Question: In a shop 40% of the articles are sold at a profit of 20% and the remaining at a loss of 10%.what is the overall profit/loss?
Options:
A)6% loss
B)4% loss
C)2% profit
D)10% loss
E)none
Rationale: 40*1.2+60*0.9/100=1.02
ANSWER:C
Answer: C
Question: Vijay bought 160 shirts at the rate of Rs. 205 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)s.225
B)s.288
C)s.485
D)s.261
E)s.282
Rationale: Total CP per shirt = 205 + 1400/160 + 1.75 + 320/160 = Rs. 217.5
SP = CP[(100 + profit%)/100]
= 217.5 * [(100 + 20)/100] = Rs.261.
Answer:D
Answer: D
Question: A number is increased by 10% and then decreased by 10%, the final value of the number is ?
Options:
A)decreases by 1%
B)decreases by 2%
C)decreases by 3%
D)decreases by 4%
E)none of the above
Rationale: Here, x = 10 and y = - 10
Therefore, the net % change in value
= ( x + y + xy/100)%
= [10 - 10 + (10 * -10)/100]% or - 1%
Since the sign is negative, there is a decrease in value by 1%.
ANSWER:A
Answer: A
Question: Mangala completes a piece of work in 9 days, Raju completes the same work in 21 days. If both of them work together, then the number of days required to complete the work is
Options:
A)6 days
B)7 days
C)8 days
D)9 days
E)11 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 9 Ã— 21/30 = 6 days.
A
Answer: A
Question: What is the probability of getting a sum 9 from two throws of a dice?
Options:
A)1/6
B)1/8
C)1/9
D)1/12
E)None of these
Rationale: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =n(E)/n(S)=4/36=1/9	.
Answer:C
Answer: C
Question: In a covering a certain distance the speed of A and B are in the ratio of 6: 9, A takes 20 min more, than B to reach the destination. The time taken by A to reach the destination is:
Options:
A)1 Hour
B)2 Hours
C)1.5 Hours
D)2.5 Hours
E)3 Hours
Rationale: Let the speed of A and B are 6x Kmph
and 9x Kmph respectively,
Let the total distance to travel = y Km
y/6x - y/9x = 1/3
y/x(1/18 = 1/3
y = 6x
Required time = 6x/6x = 1 hour
Answer A.
Answer: A
Question: In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
Options:
A) 215,000
B) 216,000
C) 217,000
D) 218,000
E) 219,000
Rationale: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 7-2 = 5 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 5 = 216,000. Hence B.
Answer: B
Question: 9 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
Options:
A)40587
B)60451
C)16152
D)24325
E)40320
Rationale: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 9
hence ans = 8 factorial = 40320
hence E
Answer: E
Question: A is twice as fast as B. If B alone can do a piece of work in 24 days, in what time can A and B together complete the work?
Options:
A)10
B)12
C)6
D)2
E)8
Rationale: A can do the work in 24/2 i.e., 12 days.
A and B's one day's work = 1/12+ 1/24 = (2 + 1)/24 = 1/8
So A and B together can do the work in 8 days.
Answer: E
Answer: E
Question: The expression (5x-2)/(x+3) is equivalent to which of the following?
Options:
A)(5-2)/3
B)5 – (2/3)
C)5 – (x)/(x+3)
D)5 – (17)/(x+3)
E)5 + (17)/(x+3
Rationale: iven asked to find the value of (5x-2)/(x+3)...
Now take X as 1 then we get 3/4...
From the options check which one gets the same 3/4.
From option D = 5 – (17)/(x+3) => 5 - (17)/(1+3) => 3/4.. All other options will result in some other value..
Answer: D is the correct option
Answer: D
Question: From a group of 7 women and 6 men, five persons are to be selected to form a committee so that at least 3 women are there in the committee. In how many ways can it be done?
Options:
A)A)650
B)B)656
C)C)696
D)D)724
E)E)756
Rationale: From a group of 7 women and 6 men, five persons are to be selected with at least 3 men.
Hence we have the following 3 options.
We can select 5 women ...(option 1)
Number of ways to do this = 7C5
We can select 4 men and 1 man ...(option 2)
Number of ways to do this = 7C4 × 6C1
We can select 3 women and 2 men ...(option 3)
Number of ways to do this = 7C3 × 6C2
Total number of ways
= 7C5 + (7C4 × 6C1) + (7C3 × 6C2)
= 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ]
=
7
×
6
2
×
1
+
7
×
6
×
5
3
×
2
×
1
×
6
=7×62×1+7×6×53×2×1×6
+
7
×
6
×
5
3
×
2
×
1
×
6
×
5
2
×
1
+7×6×53×2×1×6×52×1
=
21
+
210
+
525
=
756
=21+210+525=756
E)
Answer: E
Question: There are 9 color balls at a row. From that how many ways can 9 different color balls be arranged in a row so that black, white, red and green are never together?
Options:
A)223600
B)214600
C)566600
D)786789
E)345600
Rationale: Total number of ways in which 9 different colour balls can be arranged in a row
=9! ⋯(A)
Now we will find out total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are always together.
We have total 9 balls. Since black, white, red and green balls are always together, group these 4 balls together and consider as a single ball. Hence we can take total number of balls as 6. These 6 balls can be arranged in 6! ways.
We had grouped 4 balls together. These 4 balls can be arranged among themselves in 4! ways.
Hence, total number of ways in which 9 different colour balls be arranged in a row so that black, white, red and green balls are always together
=6!×4! ⋯(B)
From (A) and (B),
Total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are never together
=9!–6!×4!=6!×7×8×9−6!×4!=6!(7×8×9–4!)=6!(504–24)=6!×480=720×480=345600
E
Answer: E
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
Options:
A)76
B)21
C)26
D)28
E)11
Rationale: Explanation:
Lot the total number of workers be v Then,
8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21.
Answer: B
Answer: B
Question: The area of a triangle is with base 4m and height 8m?
Options:
A)11
B)10
C)787
D)16
E)12
Rationale: 1/2 * 4 * 8 = 16 m2
Answer: D
Answer: D
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 400 revolutions. How many revolutions does the second wheel make in covering d feet?
Options:
A)400xy
B)400y - x
C)400x - y
D)400x/y
E)400y/x
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
400 = d/(x*pi)
d = 100 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (400 * x * pi) / (y*pi) = 400x/y
Answer (D)
Answer: D
Question: A pupil's marks were wrongly entered as 73 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
Options:
A)56
B)80
C)20
D)25
E)26
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (73 - 45)
=> X/2 = 28
=> X = 56.
ANSWER:A
Answer: A
Question: Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?
Options:
A)20
B)90
C)10
D)80
E)70
Rationale: D
80
We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300
D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.
Answer: D
Question: The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 180,000. What was the percent increase in the cost of the home?
Options:
A)60%
B)50%
C)55%
D)40%
E)33.3%
Rationale: Percentage Increase = Increase in price / original price *100= (180000-120000)/120000*100=50%
Answer: B
Answer: B
Question: a boy average marks in five subject is 60.he score 90 in math,in physics he scores 95.in rest three in how much maximum subject he can score more than or equal to 95.
Options:
A)1
B)2
C)3
D)0
E)4
Rationale: addition of marks of all five subject=300.
math+physics=185
sum of three subject marks=300-185=115
here it is clearly visible that he can only score more than 95 in one subject if he will score more than 95 in two then it will exceed 115 because marks are not in negative.
answer A
Answer: A
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is?
Options:
A)75
B)78
C)80
D)82
E)86
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86
E)
Answer: E
Question: A and B entered into a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months C joins the business with a capital of Rs. 21000. The share of B exceeds that of C, out of a total profit of Rs. 26400 after one year by
Options:
A)Rs. 3200
B)Rs. 3400
C)Rs. 3600
D)Rs. 3800
E)None of these
Rationale: Explanation:
A:B: C = 16000*3 + 11000*9:12000*3 + 17000*9:21000*6
= 147:189:126 = 7:9:6
Difference of B and C’s shares =
Rs. [26400 * (9/22) — 26400 * (6/22))
= Rs. 3600
Option C
Answer: C
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 500?
Options:
A)4
B)6
C)8
D)10
E)12
Rationale: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^8 = 256 < 500, then the greatest possible length of integer z is 8.
The answer is C.
Answer: C
Question: X and Y are two points respectively on sides AB and AC of triangle ABC such that XY is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium XYCB is 25:144 and BC=13 cm, then find the length of XY.
Options:
A)12
B)13
C)14
D)11
E)5
Rationale: ABC and AXY are similar triangles.
So (side of ABC/side of AXY)^2=169/25
side of ABC/side of AXY = 13/5
So the length of XY = 5
Answer - E
Answer: E