RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 36.
A.5
B.4
C.12
D.32
Answer: A.5
Explanation: First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.
Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the form
n = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etc
and
n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etc
So when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)
Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the form
n = 5a + 1
and
n = 7b + 3
Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10.
Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)
Now this question is exactly like the question above. So when you divide n by 36, remainder will be -4 i.e. n will be 4 less than a multiple of 36. So you must add 5 to n to make it a multiple of 36
A
Question: Including Cara and Dan, there are seven members on the board of directors for a company. If the board is to be split up into a three-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?
A.1/5
B.1/4
C.1/3
D.2/3
Answer: C.1/3
Explanation: The number of possible subcommittees with Cara is 6C2=15.
The number of possible subcommittees with Cara and Dan is 5C1=5.
The fraction of Cara's subcommittees which include Dan is 5/15=1/3.
The answer is C.
Question: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of R?
A. 7
B. 8
C. 9
D. 10
Answer: A. 7
Explanation: A simple and elegant solution.
As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1
39-15 = 24
24 divide by 3 is 8.
Meaning mean of the n terms is 15+8 = 39-16 = 23
Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.
R*23 +39 = 25*(R+1)
R = 7
Ans. (A)
Question: The ratio of the present age of Sandy to that of Molly is 7:2. Eight years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago?
A.18
B.24
C.30
D.36
Answer: D.36
Explanation: Let the present age of Sandy be 7x years and that of Molly be 2x years.
(7x + 8) / (2x + 8) = 5 / 2
4x = 24
x = 6
Six years ago, Sandy's age was 7(6) - 6 = 36
The answer is D.
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
A.22
B.27
C.25
D.99
Answer: C.25
Explanation: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25.Answer: C
Question: What will be the cost of building a fence around a rectangle plot with area equal to 289 sq ft, and a = 1.7*b if the price per foot of building the fence is Rs. 58?
A.A)Rs.3944
B.B)Rs.3948
C.C)Rs.3988
D.D)Rs.4082.65
Answer: D.D)Rs.4082.65
Explanation: Let the side of the rectangle plot be a ft.
a*b = 289 =>1.7 b*b = 289
b = 13.03
a = 22.17
Length of the fence = Perimeter of the plot = 2(a+b) = 70.39 ft.
Cost of building the fence = 70.39 * 58 = Rs.4082.65
Answer: D
Question: Set S has a mean of 16 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?
A.{2, 10}
B.{9, 11}
C.{16, 16}
D.{10, 18}
Answer: C.{16, 16}
Explanation: answer A,B,D, and E mean is not 16 therefore not accepted . C mean is 16 but S.D is more. therefore accepted
answer is C mean is 16 and S.D decreases minimum.
C
Question: In Country C, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
A.50% decrease
B.30% decrease
C.15% decrease
D.30% increase
Answer: B.30% decrease
Explanation: September 1, 1992
The total number of construction workers = 1,000 (assume);
16% are unemployed, thus the number of unemployed workers = 160.
September 1, 1996
The total number of construction workers = 1,200 (20% greater);
9% are unemployed, thus the number of unemployed workers = 108.
Decrease is 52, which is approximately 30% of 160.
Answer: B.
Question: A and B started 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. 25,000 earned at the end of 2 years from the starting of the business?
A.Rs. 7500
B.Rs. 9000
C.Rs. 9500
D.Rs. 10,000
Answer: A.Rs. 7500
Explanation: Explanation:
A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs. 7500.
ANSWER IS A
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
A.33888
B.24000
C.27778
D.27772
Answer: B.24000
Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 52000
Share of B = 6/13 (52000) = Rs. 24000
Answer: B
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 2 employees to 4 different offices?
A.16
B.6
C.7
D.8
Answer: A.16
Explanation: Ans. Each employee can go into any of the two offices. Thus we have
=> 4* 4=16
Answer : A
Question: The average of first five prime numbers greater than 37 is?
A.32.2
B.32.98
C.42.3
D.48.6
Answer: D.48.6
Explanation: 41 + 43 + 47 + 53 + 59
= 243/5
= 48.6
Answer: D
Question: A rectangular box of volume x has width, depth and height in the ratio of 2:3:3 (in that order). What is the width as a function of x?
A.(2x/12)^(1/2)
B.(x/2)^(1/2)
C.(x/3)^(1/2)
D.(2x/9)^(1/2)
Answer: D.(2x/9)^(1/2)
Explanation: We are given width = 2, depth = 3, height = 3
Then Volume x = Width x Depth x Height = 2*3*3 = 18
i.e. x = 18
i.e. The correct option should result in 2 on substituting the value of x=18
Checking options with x=18
A) (2x/12)^(1/2) = (2*18/12)^(1/2) = 3^(1/2) INCORRECT ANSWER
B) (x/2)^(1/2) = (18/2)^(1/2) = 9^(1/2) = 3 INCORRECT ANSWER
C) (x/3)^(1/2) = (18/3)^(1/2) INCORRECT ANSWER
D) (2x/9)^(1/2) = (2*18/9)^(1/2) = 4^(1/2) = 2 CORRECT ANSWER
E) (x)^(1/2) = (18)^(1/2) INCORRECT ANSWER
Answer: Option D
Question: What is the probability that a 4 person committee chosen at random from a group consisting of 6 men, 4 women, and 5 children contains exactly 1 woman?
A.44/91
B.77/832
C.11/77
D.308/1411
Answer: A.44/91
Explanation: Total possible selections = 4 out of 15 group members = 15C4
Favorable selections = 1 out of 4 women and 3 out of 11 (= 6 men + 5 children) = 4C1 * 11C3
Thus the required probability = 4C1*11C3 / 15C4 = 44/91. Thus A is the correct answer.
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.26,000 earned at the end of 2 years from the starting of the business?
A.Rs.7800
B.Rs.9000
C.Rs.9500
D.Rs.10,000
Answer: A.Rs.7800
Explanation: Solution
A : B : C	=(20000×24):(15000×24):(20000×18)
=4 :3 :3
B's share	=Rs.(26000×3/10)
= Rs.7800.
Answer A
Question: A certain box has 9 cards and each card has one of the integers from 1 to 9 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 9 cards?
A.1/36
B.1/15
C.1/18
D.1/9
Answer: C.1/18
Explanation: The average of the numbers is 5.
The total number of ways to choose 2 cards from 9 cards is 9C2 = 36.
The ways to choose 2 cards with a sum less than the average are: {1,2},{1,3}
The probability is 2/36 = 1/18
The answer is C.
Question: You collect pens. Suppose you start out with 20. Mike gives you another 22 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 19 pens. How many pens do you have at the end?
A.39
B.40
C.65
D.42
Answer: C.65
Explanation: Solution
Start with 20 pens.
Mike gives you 22 pens: 20 + 22 = 42 pens.
Cindy doubles the number of pens you have: 42 Ã— 2 = 84 pens.
Sharon takes 19 pens from you: 84 - 19 = 65 pens.
So you have 65 at the end.
Correct answer: C
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days M do they need to finish the same job?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time M= 3 days to finish the task
IMO A
Question: For any 5 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.
A.I only
B.II only
C.I and II only
D.II and III only
Answer: C.I and II only
Explanation: Let the 3 numbers be x, y and z.
Question: Which of the following is equivalent to (x + y + z)/3
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141
II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent
Answer: C
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 400 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 5 units?
A.40 sq.units
B.158 sq.units
C.187 sq.units
D.607 sq.units
Answer: A.40 sq.units
Explanation: Given that the area of the square = 400 sq.units
=> Side of square = √400= 20 units
The radius of the circle = side of the square = 20 units
Length of the rectangle = 2/5 * 20 = 8 units
Given that breadth = 5 units
Area of the rectangle = lb = 8 * 5 = 40 sq.units
Answer: A
Question: 200 college students were asked in a survey if they preferred Windows or Mac brand computers. 70 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 80 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
A.25
B.50
C.57
D.60
Answer: B.50
Explanation: 200 = 70(Mac) + x(Window) + 80(both) => x=50
ANSWER:B
Question: I bought two books; for Rs.300. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
A.175
B.280
C.189
D.278
Answer: A.175
Explanation: x*(85/100)
= (300 - x)119/100
x = 175
Answer: A
Question: If the simple interest on a sum of money for 5 years at 9% per annum is Rs. 800, what is the compound interest on the same sum at the rate and for the same time?
A.Rs. 947.55
B.Rs. 957.55
C.Rs. 857.55
D.Rs. 657.55
Answer: B.Rs. 957.55
Explanation: Sum = (800 * 100) / (5 * 9) = Rs. 1,777.78
C.I. on Rs. Rs. 1,777.78 for 5 years at 9% = Rs. 2,735.33.
= Rs. 2,735.33 - 1,777.78 = Rs. 957.55
ANSWER:B
Question: Ratio between length and breath of a rectangle is 25:16. The area of the rectangle is same with a square whose side is 200. Find the breadth and length of the rectangle?
A.150,200
B.140,300
C.100,300
D.160,250
Answer: D.160,250
Explanation: Let length l = 25x and breadth b = 16x
Area of the square = 200^2 = 40000
16x*25x = 40000
400x^2 = 40000
x^2 = 100
x = 10
length = 25*10 = 250
breadth = 16*10 = 160
Answer :D
Question: P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 3), the remainder is also D. If P/Q = 1020.75 and P/(Q + 3) = 816.6, then which of the following gives the correct set of {D, Q}?
A.{6, 12}
B.{6, 15}
C.{9, 12}
D.{9, 15}
Answer: C.{9, 12}
Explanation: Here, we have to use
decimal part of decimal quotient ={remainder/divisor}
to translate each act of division. The first one tells us 0.75 = D/Q, and the second one tells us that 0.60 = D/(Q + 3). These are also two simultaneous equations. Multiply both to get rid of the fractions.
D = 0.75*Q
D = 0.60*(Q + 3) = 0.60*Q + 1.80
Both are equal to D, so set them equal to each other and solve for Q.
0.75*Q = 0.60*Q + 1.80
0.15*Q = 1.80
Q = 1.80/0.15 = 180/15 = 60/5 = 12
Now that we know Q = 12, we can find D = 0.75*Q = (3/4)*12 = 9. So D = 9 and Q = 12. Answer = C.
Question: 110 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
A.34
B.32
C.30
D.26
Answer: D.26
Explanation: {Total}={Writers}+{Editors}-{Both}+{Neither}.
{Total}=110;
{Writers}=45;
{Editors}>38;
{Both}=x;
{Neither}=2x;
110=45+{Editors}-x+2x --> x=65-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=65-39=26.
Answer: D.
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A.375
B.400
C.600
D.800
Answer: B.400
Explanation: C's 1 day's work =1/3-1/6	+1/7	=1/3	-7/24=1/24	.
A's wages : B's wages : C's wages =	1/6 : 1/8 : 1/24= 4 : 3 : 1.
C's share (for 3 days) = Rs. 3 x	1/24	x 3200 = Rs. 400.
Option B
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 18p, in terms of p?
A.p
B.2p
C.5p
D.6p
Answer: D.6p
Explanation: Y=30p
other number is 18p
then GCF(30p,18P)=6P; D is the correct answer
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
A.2447
B.377
C.667
D.416
Answer: D.416
Explanation: Explanation:
Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 * 32 = 416.
Answer: D
Question: A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen?
A.119
B.1,200
C.3,240
D.3,600
Answer: B.1,200
Explanation: To meet the conditions we can have only 2 cases:
2 officers and 3 civilians: C25∗C39=840
3 officers and 2 civilians: C35∗C29=360
Total: 840+360=1,200.
Answer: B.
Question: Look at this series: 75, 75, 70, 70, 65, 65, ... What number should come next?
A.14
B.15
C.17
D.60
Answer: D.60
Explanation: In this series, each number is repeated, then 5 is subtracted to arrive at the next number.
The next number is 60
Answer : D
Question: If x is a positive integer less than 30, is 'x' an odd number?
A.87
B.65
C.77
D.56
Answer: B.65
Explanation: Answer:B
Question: A bag of n peanuts can be divided into 9 smaller bags with 6 peanuts left over. Another bag of m peanuts can be divided into 12 smaller bags with 4 peanuts left over. What is the remainder when nm is divided by 9?
A.4
B.2
C.3
D.0
Answer: D.0
Explanation: n = 9x + 6
m = 12y + 4
nm = (9x + 6)*(12y + 4) = 108xy + 36x + 72y + 24
Remainder of nm/9 = (108xy + 36x + 72y + 24)/9
Observe that the all four terms are a multiple of 9
hence nm is divisible by 9
Correct Option: D
Question: A man can row with a speed of 5 kmph in still water. If the stream flows at 30 kmph, then the speed in downstream is?
A.29
B.35
C.20
D.27
Answer: B.35
Explanation: M = 5
S = 30
DS = 5 + 30 = 35
Answer: B
Question: 120 is what percent of 40 ?
A. 5%
B. 20%
C. 50%
D. 300%
Answer: D. 300%
Explanation: 40*x=120 --> x=3 --> 3 expressed as percent is 300%.
Answer: D.
Question: How many times in a day, are the hands of a clock in straight line but opposite in direction?
A.20
B.22
C.24
D.48
Answer: B.22
Explanation: Solution
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
Answer B
Question: A cycle is bought for Rs.675 and sold for Rs.1080, find the gain percent?
A.22
B.60
C.99
D.88
Answer: B.60
Explanation: 675 ---- 180
100 ---- ? => 60%
Answer:B
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 4 hours?
A.125 miles
B.225 miles
C.260 miles
D.425 miles
Answer: C.260 miles
Explanation: During each hour, the car travels 65 miles. For 4 hours it will travel
65 + 65 + 65 + 65 = 4 × 65 = 260 miles
correct answer is C) 260 miles
Question: A man invested Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the rate of dividend be 12%, his annual income is:
A.Rs. 207.40
B.Rs. 534.60
C.Rs. 648
D.Rs. 655.60
Answer: C.Rs. 648
Explanation: Explanation:
Number of shares =4455/8.25 =540
Face value = Rs. (540 x 10) = Rs. 5400.
Annual income = Rs. 12/100*5400 =Rs. 648
ANSWER IS C
Question: Praveen starts business with Rs.3220 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
A.s.7500
B.s.8000
C.s.8280
D.s.9000
Answer: C.s.8280
Explanation: Let Hari’s capital be Rs. x. Then, 3220 * 12/7x = 2/3
=> 14x = 115920
=> x =8280.
ANSWER:C
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.210m
B.240m
C.963m
D.874m
Answer: B.240m
Explanation: Explanation:
Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.
Answer: B)240m
Question: If a certain toy store's revenue in November was 2/5 of its revenue in December and its revenue in January was 1/3 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
A.5/3
B.5/4
C.10/3
D.15/4
Answer: D.15/4
Explanation: N = 2D/5
J = N/3 = 2D/15
The average of November and January is (N+J)/2 = 8D/15 / 2 = 4D/15
D is 15/4 times the average of November and January.
The answer is D.
Question: If x≠6 and (x^2 - 36)/(2y) = (x - 6)/4, then in terms of y, x = ?
A.(y - 6)/2
B.(y - 3)/2
C.y - 3
D.(y - 12)/2
Answer: D.(y - 12)/2
Explanation: Since (x^2 – 36)=(x-6)(x+6) the original equation can be changed into 4*(x-6)(x+6) = 2y *(x-6).
By cancelling 2(x-6) (we can do it because x≠6) we get :
2*(x+6)=y.
So x=(y-12)/2. So the answer is D).
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?
A.5
B.6
C.8
D.7
Answer: D.7
Explanation: Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 7 times before 9.30 a.m.
ANSWER:D
Question: The population of a town increase annually by 20% . If the present population is 2,00,000, then what is the difference in population after two years and three years
A.63,250
B.48,800
C.60,800
D.57,600
Answer: D.57,600
Explanation: M .F for 2Yrs = 120/100*120/100 =36/25
M .F for 3Yrs =120/100*120/100*120/100 =6/5*6/5*6/5 =216/125
Population after 2Yrs = 2,00,000*36/25 = 2,88,000
Population after 3 Yrs = 2,00,000*216/125 = 3,45,600
Difference = 3,45,600 – 2,88,000 =57,600
ANSWER:D
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount had been offered?
A.28.5
B.27.675
C.30
D.Data inadequate
Answer: C.30
Explanation: Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.
Then printed price = 100×(100+23.5)/(100−5)
= 100×247/190=130
Hence, required % Profit = 130 – 100 = 30%
Answer C
Question: The C.P of 8 books is equal to the S.P of 16 books. Find his gain% or loss%?
A.60%
B.50%
C.70%
D.90%
Answer: B.50%
Explanation: explanation:
8 CP = 16 SP
16 --- 8 CP loss
100 --- ? => 50% loss
Answer: B
Question: A train is running at a speed of 4040 km/hr and it crosses a post in 1818 seconds. What is the length of the train?
A.190 metres
B.160 metres
C.200 metres
D.120 metres
Answer: C.200 metres
Explanation: Explanation:
Speed =40 km/hr =40 km/hr =40Ã—518=1009 m/s=40Ã—518=1009 m/s
Time =18=18 seconds
Distance Covered =1009Ã—18=200 m=1009Ã—18=200 m
Therefore, length of the train =200 m
ANSWER IS C
Question: You are given with two ropes with variable width. However if we start burning both the ropes, they will burn at exactly same time i.e. an hour. The ropes are non-homogeneous in nature. You are asked to measure 45 minutes by using these two ropes.
How can you do it?
Please note that you can’t break the rope in half as it is being clearly stated that the ropes are non-homogeneous in nature.
A.45 minutes
B.40 minutes
C.35 minutes
D.55 minutes
Answer: A.45 minutes
Explanation: A
45 minutes
All you have to do is burn the first rope from both the ends and the second rope from one end only simultaneously. The first rope will burn in 30 minutes (half of an hour since we burned from both sides) while the other rope would have burnt half. At this moment, light the second rope from the other end as well. Where, the second rope would have taken half an hour more to burn completely, it will take just 15 minutes as we have lit it from the other end too.
Thus you have successfully calculated 30+15 = 45 minutes with the help of the two given ropes.
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
A.23
B.27
C.28
D.12
Answer: D.12
Explanation: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5
= 12 seconds.
Answer:D
Question: List K consists of 12 consecutive integers. If -3 is the least integer in list K, what is the range of the positive integers in list K?
A.5
B.6
C.7
D.11
Answer: C.7
Explanation: Answer = C =7
If least = -3, then largest = 8
Range = 8 - 1 = 7
Question: A train running at the speed of 162 km/hr crosses a pole in 9 seconds. Find the length of the train.
A.150 meter
B.286 meter
C.186 meter
D.405 meter
Answer: D.405 meter
Explanation: Speed = 162*(5/18) m/sec
= 45 m/sec
Length of Train (Distance)
= Speed * Time
(45) * 9 = 405 meter
Answer:D