divelab/Sys2Bench huggingface dataset:
Question: Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?
Options:
A)Rs. 32,000
B)Rs. 34,000
C)Rs. 36,000
D)Rs. 36,500
E)Rs. 38,000
Rationale: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, 2x + 4000 = 40
3x + 4000 57
57(2x + 4000) = 40(3x + 4000)
6x = 68,000
3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
E
Answer: E
Question: There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the thicker one. Ramesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How long ago did Ramesh light the two candles .
Options:
A)3 hr
B)4 hr
C)2 hr
D)1 hr
E)5 hr
Rationale: Thicker candle - 6hr
thinner candle -4hr
lcm of (6,4)=12
thinner candle burn in 1 hour= 3part
thicker candle burn in 1 hour= 2part
in 1 hr length of candle left : (thicker,thinner):(10,9)
in 2 hr (8,6)
in 3 hr (6,3)
so, 3 hr
ANSWER:A
Answer: A
Question: 2 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
Options:
A)1
B)2
C)5
D)0
E)4
Rationale: the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 2(2-1)/2 = 2*1/2 = 2/2 = 1
=> the answer is A(1)
Answer: A
Question: After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 4725. What was the number of original inhabitants?
Options:
A)5000
B)7000
C)4000
D)8000
E)9000
Rationale: Let the total number of original inhabitants be x.
(75/100) * (90/100) * x = 4725
(27/40) * x = 4725
x = 4725 * 40 / 27 = 7000
The answer is B.
Answer: B
Question: 38 69 55 73 31 47 91 82
Which of the following numbers is greater than three fourths of the numbers but less than one fourth of the numbers in the list above?
Options:
A)56
B)68
C)69
D)71
E)79
Rationale: Arrange the numbers in ascending order:
31, 38, 47, 55, 69, 73, 82, 91 (Just cross check the count to ensure that you didn't miss anything)
How many numbers do we see?
8, alright.
What's (1/4)8?
2.
What's (3/4)8?
6.
We're asked to find a number that are greater than 6 numbers in the list AND smaller than the remaining two.
31, 38, 47, 55, 69, 73, 82, 91
31, 38, 47, 55, 69, 73: Find a number greater than any of these numbers.
82, 91: Find a number smaller than any of these numbers.
Only 79 fits the description.
Ans:E
Answer: E
Question: Average weight of 10 people increased by 1.5 kg when one person of 45 kg is replaced by a new man. Then weight of the new man is
Options:
A)50
B)55
C)60
D)65
E)66
Rationale: Explanation:
Total weight increased is 1.5 * 10 = 15.
So weight of new person is 45+15 = 60
Answer: Option C
Answer: C
Question: Entry fee in an examination was Re. 1. Later, this was reduced by 25% which increased the sale by 20%. The percentage increase in the number of visitors is
Options:
A)60
B)50
C)66
D)54
E)None
Rationale: Sol.
Let the total original sale be Rs. 100. Then, original number of visitors = 100.
New number of visitors = 120 / 0.75 = 160.
∴ Increase% = 60%.
Answer A
Answer: A
Question: If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 102 to 198, inclusive?
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: 102 x 104 x 106 x 108 => unit digit 4
112 x 114 x 116 x 118 => unit digit 4
192 x 194 x 196 x 198 => unit digit 4
So we have 10 numbers ending by 4 to multiply.
Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply
Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply
So the unit digit is 6
Answer: A
Answer: A
Question: Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 15 from the product of their ages a year from today. What is their age today?
Options:
A)2.
B)4.
C)5.
D)7.
E)9.
Rationale: ad = (a+1) (d+1) -15
0= a+d-14
a+d = 14
a=d (as they are twin brothers)
a=d=7
D is the answer
Answer: D
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 7, or 9. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?
Options:
A)51/625
B)50/625
C)4/625
D)25/625
E)53/625
Rationale: I think most of the answers are missing a point. Let me try to put it across:
Total number of possible numbers are : 5x5 = 25
Correct number =1
Case 1: When he gets it right in first attempt: P(E1) = 1/25
Case 2: He gets 1st attempt wrong and second right:
When he gets it wrong then the probability of getting wrong is 24/25.
Now there are 24 cases with him and he chooses the right one this time.
Probability of right case is 1/24
Thus, P(E2) = 24/25 x 1/24
=1/25
Probability of getting it right in at most two cases = P(E1) + P(E2)
= 1/25 + 1/25
= 2/25
= 50/625
Option (B) is therefore right as most of you mentioned but the method employed was wrong.
Answer: B
Question: If a + b + c = 0 and a,b,c, are rational numbers then the roots of the equation
(b + c – a)x2 + (c + a – b) x + (a + b – c) = 0 are
Options:
A)rational
B)irrational
C)non real
D)real
E)none of these.
Rationale: Sol.(a) The sum of coefficients
= (b + c - a) + (c + a - b) + (a + b - c) = a + b + c = 0 (given)
∴ x = 1 is a root of the equation
∴ The other root is a+b−cb+c−aa+b−cb+c−a , which is rational as a,b, c, are rational
Hence, both the roots are rational.
ALTERNATIVE :
D = (c + a - b)2 - 4(b + c - a)(a + b - c)
= (-2b)2 - 4(-2a)(-2c) = 4b2 - 16ac
= 4(a + c)2 - 16ac = 4[(a + c)2 - 4ac] = 2[(a - c)2]
D is a perfect square. Hence, the roots of the equation are rational.
Answer A
Answer: A
Question: In a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes
Options:
A)12:7
B)10:7
C)8:7
D)4:3
E)none
Rationale: Solution: Boys: girls = 8:5; (let the boys = 8x; girl = 5x)
Total strength = 286;
8x+5x = 286;
13x = 286;
Or, x = 286/13 = 22;
Boys = 176 and girls = 110;
22 more girls get admitted then number of girls become,
(5x+22) = 110+22 = 132;
Now, new ratio of boys and girls = 176:132 = 4:3.
Answer: Option D
Answer: D
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
Options:
A)3630
B)3877
C)2667
D)2977
E)2378
Rationale: Explanation:
6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer: A
Answer: A
Question: A & B are two places. C & D start walking from A and B respectively. Before meeting D, C travel 18m more than D. then C takes 13 and half minute and D take 24 minute to reach their destination.
Options:
A)124
B)126
C)127
D)128
E)129
Rationale: their speed in ratio 4:3
7*18=126
ANSWER:B
Answer: B
Question: UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 9:1. If 90% of the Toyota bought and 10% of the Honda bought were SUVÃ¢â‚¬â„¢s. How many SUVÃ¢â‚¬â„¢s did UBA capital buy in the aforementioned purchase?
Options:
A)82%
B)64%
C)28%
D)69%
E)80%
Rationale: let total no of Vehicles bought be 100, Toyota 90 and Honda 10, so total number of SUV's bought for Toyota and Honda respectively 90* 90/100=81 and 10* 10/100=1
so total 82 SUV's were bought out of 100 Vehicles bought..so required % is 82%
ANSWER:A
Answer: A
Question: How many factors of 220 are odd numbers greater than 1?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: When factorized, 220 has 4 prime factors. Of these prime factors 2 are odd and 2 are even. Hence total number of odd factors is 2*2(4), which includes 1. The total number of odd factors greater than 1 are 3.(option A)
Answer: A
Question: What is the 4 digit no.in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
Options:
A)1200
B)1256
C)1349
D)1456
E)1590
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Answer: C
Question: W(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point W?
Options:
A)(1, 2).
B)(2, 0).
C)(0, -2).
D)(-2, 0).
E)(2, 2).
Rationale: A quick glance at the options,W(x, y) and we can see that A and E do not satisfy the circle equation. Now we are left with B, C and D. Now B and C do not satisfy the line equation. So we are just left with D. And thats the answer=D
Answer: D
Question: If –3 < x < 3 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x^2
Options:
A) I only
B) II only
C) III only
D) II and III only
E) I, II, and III
Rationale: Answer is D. Let's look at the statements one by one
Stmt I. x^3 < x
if 0<x<1 then x^3< x but if -1<x<0 then x^3>x
So this statement is not always true
Stmt II. x^2 < |x|
Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.
Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2
So Stmt II is always true
Stmt III. x^4 – x^5 > x^3 – x^2
This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).
Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 which means that (1-x)>0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.
So Stmt III is always true
E
Answer: E
Question: A cylindrical can has a radius of 4 centimeters and a height of 24 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
Options:
A)16 pi
B)64 pi
C)96 pi
D)192 pi
E)576 pi
Rationale: They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*4*24=192 pi
Answer is D.
Answer: D
Question: A train running at the speed of 90 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)225 meter
B)200 meter
C)250 meter
D)210 meter
E)230 meter
Rationale: Speed = 90*(5/18) m/sec = 25 m/sec
Length of Train (Distance) = Speed * Time
(25) * 9 = 225 meter
Answer:A
Answer: A
Question: Josh spends a total of $5.5 buying S items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then S may be which of the following?
Options:
A)99
B)100
C)101
D)112
E)113
Rationale: S items in the convenience store$5.5 = 550 cents
550 = 50a + 5b
=>110 = 10a + b
b = 110 - 10a = 10(11-a)
Hence b is even and multiple of 10.
Possible values of b:
b = 10,20,30,40,50,60,70,80,90,100
a = 11,9,8,7,6,5,4,3,2,1
The total (a+b) is 21,29,38,47,56,65,74,83,92,101
The only option is 101. Hence C.
Answer: C
Question: There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 15, then find the smaller number?
Options:
A)25
B)66
C)88
D)89
E)53
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 15
3x = 15 => x = 5
=> Smaller number = 5x = 25.
Answer: A
Answer: A
Question: Evaluate :
28% of 400 + 45 % of 250
Options:
A)220.3
B)224.5
C)190.3
D)150
E)None of these
Rationale: Explanation:
28% of 400 + 45 % of 250
= (28/100 *400 + 45/100 * 250)
= (112 + 112.5)
= 224.5
ANSWER B
Answer: B
Question: Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 45?
Options:
A)1/16
B)5/42
C)1/8
D)3/16
E)1/4
Rationale: 210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=5/42.
Answer: B.
Answer: B
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/6 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
Options:
A)12 greater
B)12 fewer
C)28 fewer
D)36 fewer
E)44 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/6 * 480 =80
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 80-68 =12>>> therfore answer is 28 fewer
B
Answer: B
Question: If x-y=8, which of the following must be true?
I. If x is negative, y must be negative
II. If x is positive, y must be positive
III.Both x and y are positive
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D
2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E
A) I only
B) II only
C) III only
D) I and II
E) II and III
Answer A
Answer: A
Question: Runner A passed a post running at a constant speed of 50 miles per hour. Then, 15 minutes later, Runner B passed the same post at a constant speed of 60 miles per hour. If both runners maintained their speeds and both remained on the highway for at least 2 hours, how long after Runner B passed the gas station did he catch up with Runner A?
Options:
A)30 min
B)45 min
C)1 hr
D)1 hr 15 min
E)1 hr 30 min
Rationale: When Runner B is at the post, Runner A is 50/4 miles ahead on the highway. (the distance covered in 15 min)
every hour, Runner B runs 10miles more than Mary. how many hours will it takes him to run 50/4 miles more? the answer is (50/4)/10 = 25/20=1h15min.
Answer D
Answer: D
Question: At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $ 2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $ 1.70. What is the price of 2 doughnuts?
Options:
A)$ 0.55
B)$ 1.00
C)$ 1.10
D)$ 1.30
E)$ 1.80
Rationale: Joe ordered 3 Dougnuts and Cup of Coffee. Stella ordered 2 Doughnuts and cup of coffee which means Joe ordered 1 doughnut more than stella only. So 1 doughnut must be 2.25 - 1.7 = 0.55
Price of 1 Doughnut = 0.55
Price of 2 Doughnut = 0.55*2 = 1.1
ANSWER:C
Answer: C
Question: Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.45, b = 2.95, and c = 3.75, what is y – x?
Options:
A)-0.1
B)0
C)0.2
D)0.1
E)0.3
Rationale: To find x, we first sum a, b, and c, then round to the tenths place. 5.45 + 2.95 + 3.75 = 12.15, which rounds to 12.2.
To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 2.9 + 3.7 = 12.0.
We are looking for y - x, which gives us 12.3 - 12.2 = 0.2, or answer choice C.
C
Answer: C
Question: In track last week, the boys ran 34 laps. The girls ran 20 more
laps. Each lap is a 1/6th of a mile. How many miles did the girls run?
Options:
A)9 miles
B)10 miles
C)11 miles
D)12 miles
E)13 miles
Rationale: The girls ran 34 + 20 = 54 laps. 54 x 1/6 = 54/6, which reduces to 9.
The girls ran 9 miles
correct answer A
Answer: A
Question: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible?
Options:
A) 2
B) 4
C) 6
D) 8
E) 10
Rationale: Mother has a fixed place and father, so there are 2! ways to arrange the children, hence A
Answer: A
Question: A and B invests Rs.3000 and Rs.10000 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)9:6
B)9:8
C)9:20
D)9:9
E)9:5
Rationale: (3*6 + 6*6): (10*12)
54:120 => 9:20.Answer:C
Answer: C
Question: Which of the following fractions T has a decimal equivalent that is a terminating decimal?
Options:
A)10/189
B)15/196
C)16/225
D)25/144
E)39/128
Rationale: The fraction T will terminate if and only if the denominator has prime divisors only 2 and 5 or both.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: E
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 5
Options:
A)1/2
B)7/12
C)5/13
D)5/12
E)3/8
Rationale: Total number of cases = 4*4 = 16
Favourable cases = [(2,4),(3,3),(3,4),(4,2),(4,3),(4,4)] = 6
So Probability = 6/16 = 3/8
Answer is E
Answer: E
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
Options:
A)5/17
B)5/12
C)5/19
D)5/29
E)5/13
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Answer: B
Question: In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate?
Options:
A)69
B)70
C)71
D)72
E)73
Rationale: number of ways = 2*3!*3! = 72
Answer is D
Answer: D
Question: If Rs. 510 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively:
Options:
A)Rs.260
B)Rs.360
C)Rs.350
D)Rs.364
E)Rs.362
Rationale: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A;s share = 510 * 2/17 = Rs. 60
B's share = 510 * 3/17 = Rs. 90
C's share = 510 * 12/17 = Rs.360.
Answer: B
Answer: B
Question: How many different ways can 2 students be seated in a row of 4 desks, so that there is always at least one empty desk between the students?
Options:
A)2
B)3
C)4
D)6
E)12
Rationale: Total cases : 12 ( student one has 4 options and student two has three options, 4x3=12)
Non-favourable cases : 6 (when two students sit together. students in desk 1 and desk 2 , in desk 2 and desk 3, in desk 3 and desk 4) for each of these cases there are two possibilities because the positions can be interchanged. hence 2x3=6.
SO favourable cases : 12-6=6. ANSWER:D
Answer: D
Question: A women in her conversation said " if u reverse my own age, in figures represent my husbands age. he is of course senior to me and difference between our age is one 0ne-eleventh of their sum. what is the woman's and her husbands age?
Options:
A)45,54
B)46,57
C)84,57
D)34,58
E)52,54
Rationale: let man,s age be xy
the woman's age is yx
then 10x+y-10y-x=1/11(10x+y+10y+x)
9x-9y=x+y
8x=10y
x/y=10/8=5/4
so xy=54 and yx=45
ANSWER:A
Answer: A
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)88
C)77
D)62
E)52
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: A
Question: A certain barrel, which is a right circular cylinder, is filled to capacity with 200 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?
Options:
A)There is no empty capacity
B)1100 gallons
C)1300 gallons
D)1400 gallons
E)1800 gallons
Rationale: Radius of first cylinder=r, diameter=2r, height=h
Radius of second cylinder=2r, diameter=2d and height=2h
Volume of first cylinder=pie (r^2)*h=200
Volume of second cylinder=pie(2r^2)2h
Put the value of pie (r^2)*h=200 in the second cylinder,volume= pie (r^2)*4*2=200*8=1600 gallons
Empty capacity=1400
D
Answer: D
Question: Gautami went to the stationers and bought things worth Rs. 100, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 5%. then what was the cost of the tax free items?
Options:
A)Rs. 99.50
B)Rs. 70.50
C)Rs. 89.50
D)Rs. 69.50
E)Rs. 80.50
Rationale: Solution
Let the amount of taxable purchases be Rs.x.
Then, 5% of x	= 50/100
x ‹=› (50/100×100/5)
= 10
Cost of tax free items	= Rs.[100 - (10 + 0.50)]
= Rs. 89.50
Answer C
Answer: C
Question: When a student Joe, weighing 40 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
Options:
A)5 kg
B)11 kg
C)30 kg
D)36.5 kg
E)71 kg
Rationale: After two persons leave the group the average remains the same. That means the weight of the two persons = 40+30 = 70
So, the average the two persons = 35
That gives the answer 40-35 = 5
Answer A
Answer: A
Question: Three men A, B and C working together can do a work in 17 days. They start the work together and A works for 5 days and takes rest on the sixth day, B works for 5 days and takes rest on the next two days and C works for 8 days and takes rest on the next three days. In how many days will the work be completed ? (A, B, C work at the same rate)
Options:
A)24 days
B)23 days
C)22 days
D)21 days
E)20 days
Rationale: Total work is 3*17 = 51 units.
A does 5 days of work every 6 days.
B does 5 days of work every 7 days.
C does 8 days of work every 11 days.
Test the options.
In 20 days:
A will do 5*3 + 2 =17 units (3 complete cycles and 2 days of work).
B will do 5*2+ 5=15 units (2 complete cycles, 5 days of work, and 1 day of rest).
C will do 8*1 + 8 =16 units (1 complete cycle, 8 days of work, and 1 day of rest).
Total = 17 + 15 + 16 = 48 units.
In 21 days:
A will do 5*3 + 3 =18 units (3 complete cycles and 3 days of work).
B will do 5*3 =15 units (3 complete cycles).
C will do 8*1 + 8 =16 units (1 complete cycle, 8 days of work, and 2 days of rest).
Total = 18 + 15 + 16 = 49 units.
In 22 days:
A will do 5*3 + 4 =19 units (3 complete cycles and 4 days of work).
B will do 5*3 + 1= 16 units (3 complete cycles and 1 day of work).
C will do 8*1 + 8 =16 units (1 complete cycle, 8 days of work, and 3 days of rest).
Total = 19 + 16 + 16 = 51 units.
Answer: C.
Answer: C
Question: A double decked bus can accomodate 100 passengers,40 in the upper deck and 60 in the lower deck.In how many ways can the passengers be accomodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck?
Options:
A)1. 85!50!60!/40!45!
B)2. 75!/30!45!
C)3. 110!/50!60!
D)4. 110!50!60!/40!45!
E)5. 110!/40!45!
Rationale: 100 passengers,40 in the upper deck and 60 in the lower deck.
25 passengers have issues as 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck
So those 15 will be put in lower deck and 10 will be in upper deck
So from the rest 75 passengers(100-25), we need to find 30 people to put into upper deck and the rest go to lower deck
So the ways are: C(75,30) = 75!/30!45! . Answer B
Answer: B