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A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair?- a)3
- b)20
- c)39
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair?
a)
3
b)
20
c)
39
d)
None of these
|
Raksha Das answered |
Explanation:
Scenario:
- The man has 20 black socks and 20 brown socks in a drawer.
- He needs to take out socks in the dark.
To ensure a matching pair, the man must take out at least 3 socks:
- The worst-case scenario for the man would be if he first picks out 2 socks of different colors.
- In this case, the next sock he picks will definitely match one of the socks he already has.
- Therefore, he needs to take out 3 socks to be sure that he has a matching pair.
Therefore, the correct answer is option A) 3.
The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?- a)15
- b)29
- c)61
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner?
a)
15
b)
29
c)
61
d)
None of these
|
Ias Masters answered |
Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1 = 29.
There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?- a)20
- b)30
- c)50
- d)60
Correct answer is option 'D'. Can you explain this answer?
There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?
a)
20
b)
30
c)
50
d)
60
|
Gayatri Basak answered |
**Problem Solving:**
To solve this problem, we can use a system of linear equations. Let's assume that the number of deer is represented by 'x' and the number of peacocks is represented by 'y'.
**Step 1: Formulate the Equations:**
We are given two pieces of information:
1. The total number of heads is 80.
2. The total number of legs is 200.
From these two pieces of information, we can form two equations:
Equation 1: x + y = 80 (since the total number of heads is 80)
Equation 2: 4x + 2y = 200 (since each deer has 4 legs and each peacock has 2 legs)
**Step 2: Solve the Equations:**
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's solve it using the method of substitution.
From Equation 1, we can express x in terms of y: x = 80 - y
Substituting this value of x into Equation 2, we get:
4(80 - y) + 2y = 200
Simplifying the equation, we have:
320 - 4y + 2y = 200
Combining like terms, we get:
-2y = 200 - 320
-2y = -120
Dividing both sides by -2, we get:
y = 60
**Step 3: Find the Number of Peacocks:**
From our solution, we found that y = 60, which represents the number of peacocks.
Therefore, the correct answer is option D) 60.
To solve this problem, we can use a system of linear equations. Let's assume that the number of deer is represented by 'x' and the number of peacocks is represented by 'y'.
**Step 1: Formulate the Equations:**
We are given two pieces of information:
1. The total number of heads is 80.
2. The total number of legs is 200.
From these two pieces of information, we can form two equations:
Equation 1: x + y = 80 (since the total number of heads is 80)
Equation 2: 4x + 2y = 200 (since each deer has 4 legs and each peacock has 2 legs)
**Step 2: Solve the Equations:**
To solve the system of equations, we can use the method of substitution or elimination. In this case, let's solve it using the method of substitution.
From Equation 1, we can express x in terms of y: x = 80 - y
Substituting this value of x into Equation 2, we get:
4(80 - y) + 2y = 200
Simplifying the equation, we have:
320 - 4y + 2y = 200
Combining like terms, we get:
-2y = 200 - 320
-2y = -120
Dividing both sides by -2, we get:
y = 60
**Step 3: Find the Number of Peacocks:**
From our solution, we found that y = 60, which represents the number of peacocks.
Therefore, the correct answer is option D) 60.
In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?- a)6
- b)12
- c)18
- d)24
Correct answer is option 'B'. Can you explain this answer?
In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?
a)
6
b)
12
c)
18
d)
24
|
Aarav Saini answered |
To solve this problem, we need to break it down into smaller steps and use logical reasoning to find the solution.
Let's start by understanding the given information:
1. There are 18 boys who are over 160 cm tall, and this constitutes three-fourths of the boys.
2. The total number of boys is two-thirds of the total number of students in the class.
Now, let's find the total number of boys in the class:
We know that 18 boys constitute three-fourths of the boys, so we can set up the equation:
(3/4) * Total boys = 18
To find the total number of boys, we need to multiply both sides of the equation by (4/3):
Total boys = (18 * 4) / 3
Total boys = 72 / 3
Total boys = 24
So, there are 24 boys in the class.
Next, let's find the total number of students in the class:
We know that the total number of boys is two-thirds of the total number of students. So, we can set up the equation:
(2/3) * Total students = Total boys
Plugging in the value we found for the total number of boys:
(2/3) * Total students = 24
To find the total number of students, we need to multiply both sides of the equation by (3/2):
Total students = (24 * 3) / 2
Total students = 72 / 2
Total students = 36
So, there are 36 students in the class.
Finally, let's find the number of girls in the class:
We know that the total number of students in the class is 36, and the number of boys is 24. To find the number of girls, we can subtract the number of boys from the total number of students:
Number of girls = Total students - Total boys
Number of girls = 36 - 24
Number of girls = 12
Therefore, the number of girls in the class is 12.
Hence, the correct answer is option 'B' - 12.
Let's start by understanding the given information:
1. There are 18 boys who are over 160 cm tall, and this constitutes three-fourths of the boys.
2. The total number of boys is two-thirds of the total number of students in the class.
Now, let's find the total number of boys in the class:
We know that 18 boys constitute three-fourths of the boys, so we can set up the equation:
(3/4) * Total boys = 18
To find the total number of boys, we need to multiply both sides of the equation by (4/3):
Total boys = (18 * 4) / 3
Total boys = 72 / 3
Total boys = 24
So, there are 24 boys in the class.
Next, let's find the total number of students in the class:
We know that the total number of boys is two-thirds of the total number of students. So, we can set up the equation:
(2/3) * Total students = Total boys
Plugging in the value we found for the total number of boys:
(2/3) * Total students = 24
To find the total number of students, we need to multiply both sides of the equation by (3/2):
Total students = (24 * 3) / 2
Total students = 72 / 2
Total students = 36
So, there are 36 students in the class.
Finally, let's find the number of girls in the class:
We know that the total number of students in the class is 36, and the number of boys is 24. To find the number of girls, we can subtract the number of boys from the total number of students:
Number of girls = Total students - Total boys
Number of girls = 36 - 24
Number of girls = 12
Therefore, the number of girls in the class is 12.
Hence, the correct answer is option 'B' - 12.
A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes?- a)32 rolls
- b)54 rolls
- c)108 rolls
- d)120 rolls
Correct answer is option 'D'. Can you explain this answer?
A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes?
a)
32 rolls
b)
54 rolls
c)
108 rolls
d)
120 rolls
|
Lakshya Ias answered |
Number of cuts made to cut a roll into 10 pieces = 9.
Therefore Required number of rolls = (45 x 24)/9 = 120.
Therefore Required number of rolls = (45 x 24)/9 = 120.
A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?- a)28
- b)29
- c)31
- d)35
Correct answer is option 'A'. Can you explain this answer?
A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?
a)
28
b)
29
c)
31
d)
35
|
|
Raghav Kumar answered |
Understanding the Problem
To determine how many cards C has, we need to establish equations based on the information given.
Let’s Define Variables
- Let A, B, C, D, and E represent the number of cards each player has.
- The total number of cards is 150:
A + B + C + D + E = 150
From A's Statement
1. If B gives A 3 cards:
A + 3 = B - 3
This implies:
B = A + 6
2. If D takes 5 cards from B:
D + 5 = E
This implies:
E = D + 5
Relationship Between A, C, and E
- A and C together have twice as many cards as E:
A + C = 2E
By substituting E:
A + C = 2(D + 5)
A + C = 2D + 10
Equality Between B&D and A&C
- B and D together have the same number of cards as A and C:
B + D = A + C
Substituting B from earlier:
(A + 6) + D = A + C
This simplifies to:
D = C - 6
Substituting Values
Now, substitute D in the earlier equations:
- From E = D + 5, we have:
E = (C - 6) + 5 = C - 1
Now, substitute E into A + C = 2E:
- A + C = 2(C - 1)
- A + C = 2C - 2
- A = C - 2
Final Calculation
Substituting A, B, D, and E in the total equation:
A + (A + 6) + C + (C - 6) + (C - 1) = 150
This gives:
2A + 3C - 1 = 150
2A + 3C = 151
Using A = C - 2:
2(C - 2) + 3C = 151
2C - 4 + 3C = 151
5C = 155
C = 31
Thus, the number of cards C has is 31, confirming that the correct answer is option 'A'.
To determine how many cards C has, we need to establish equations based on the information given.
Let’s Define Variables
- Let A, B, C, D, and E represent the number of cards each player has.
- The total number of cards is 150:
A + B + C + D + E = 150
From A's Statement
1. If B gives A 3 cards:
A + 3 = B - 3
This implies:
B = A + 6
2. If D takes 5 cards from B:
D + 5 = E
This implies:
E = D + 5
Relationship Between A, C, and E
- A and C together have twice as many cards as E:
A + C = 2E
By substituting E:
A + C = 2(D + 5)
A + C = 2D + 10
Equality Between B&D and A&C
- B and D together have the same number of cards as A and C:
B + D = A + C
Substituting B from earlier:
(A + 6) + D = A + C
This simplifies to:
D = C - 6
Substituting Values
Now, substitute D in the earlier equations:
- From E = D + 5, we have:
E = (C - 6) + 5 = C - 1
Now, substitute E into A + C = 2E:
- A + C = 2(C - 1)
- A + C = 2C - 2
- A = C - 2
Final Calculation
Substituting A, B, D, and E in the total equation:
A + (A + 6) + C + (C - 6) + (C - 1) = 150
This gives:
2A + 3C - 1 = 150
2A + 3C = 151
Using A = C - 2:
2(C - 2) + 3C = 151
2C - 4 + 3C = 151
5C = 155
C = 31
Thus, the number of cards C has is 31, confirming that the correct answer is option 'A'.
A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?- a)4
- b)8
- c)12
- d)24
Correct answer is option 'D'. Can you explain this answer?
A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?
a)
4
b)
8
c)
12
d)
24
|
|
Akshita Joshi answered |
To determine the total number of routes the motorist knows from Bristol to Carlisle, we need to find the product of the number of routes from Bristol to Birmingham, Birmingham to Sheffield, and Sheffield to Carlisle.
Number of routes from Bristol to Birmingham: 4
Number of routes from Birmingham to Sheffield: 3
Number of routes from Sheffield to Carlisle: 2
To calculate the total number of routes from Bristol to Carlisle, we multiply these numbers together.
4 routes * 3 routes * 2 routes = 24 routes
So, the correct answer is option 'D' - 24.
Number of routes from Bristol to Birmingham: 4
Number of routes from Birmingham to Sheffield: 3
Number of routes from Sheffield to Carlisle: 2
To calculate the total number of routes from Bristol to Carlisle, we multiply these numbers together.
4 routes * 3 routes * 2 routes = 24 routes
So, the correct answer is option 'D' - 24.
A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?- a)2
- b)3
- c)6
- d)12
Correct answer is option 'C'. Can you explain this answer?
A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
a)
2
b)
3
c)
6
d)
12
|
Valor Academy answered |
Since B and D are twins, so B = D.
Now, A = B + 3 and A = C - 3.
Thus, B + 3 = C - 3
D + 3 = C - 3 
C - D = 6.
Now, A = B + 3 and A = C - 3.
Thus, B + 3 = C - 3
D + 3 = C - 3 C - D = 6.A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?- a)100
- b)104
- c)108
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
A farmer built a fence around his square plot. He used 27 fence poles on each side of the square. How many poles did he need altogether?
a)
100
b)
104
c)
108
d)
None of these
|
|
Rahul Mehta answered |
Since each pole at the corner of the plot is common to its two sides, so we have :
Total number of poles needed = 27 x 4 - 4 = 108 - 4 = 104.
A bird shooter was askgd how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?- a)9
- b)18
- c)27
- d)36
Correct answer is option 'A'. Can you explain this answer?
A bird shooter was askgd how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?
a)
9
b)
18
c)
27
d)
36
|
|
Rhea Reddy answered |
There were all sparrows but six' means that six birds were not sparrows but only pigeons and ducks.
Similarly, number of sparrows + number of ducks = 6 and number of sparrows + number of pigeons = 6.
This is possible when there are 3 sparrows, 3 pigeons and 3 ducks i.e. 9 birds in all.
Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?- a)£ 300
- b)£ 330
- c)£ 360
- d)£ 420
Correct answer is option 'B'. Can you explain this answer?
Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?
a)
£ 300
b)
£ 330
c)
£ 360
d)
£ 420
|
Nishanth Rane answered |
$50,000 per year, but due to a promotion, he will now earn $65,000 per year.
Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?- a)7 times
- b)8 times
- c)9 times
- d)11 times
Correct answer is option 'B'. Can you explain this answer?
Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start?
a)
7 times
b)
8 times
c)
9 times
d)
11 times
|
|
Baishali Chavan answered |
Let's analyze the problem step by step.
Step 1: Find the LCM of the time intervals
The time intervals given are 6, 5, 7, 10, and 12 seconds. To find the least common multiple (LCM) of these intervals, we can list their multiples and find the smallest number that appears in each list.
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, ...
Multiples of 10: 10, 20, 30, ...
Multiples of 12: 12, 24, 36, ...
From the lists, we can see that the smallest number that appears in each list is 30. Therefore, the LCM of the time intervals is 30 seconds.
Step 2: Calculate the number of times they toll together in one hour
In one hour, there are 60 minutes * 60 seconds = 3600 seconds.
To find the number of times the bells toll together, we need to divide the total time (3600 seconds) by the LCM of the time intervals (30 seconds).
3600 seconds / 30 seconds = 120
This means that the bells toll together 120 times in one hour.
However, we need to exclude the one at the start. Therefore, the correct answer is 120 - 1 = 119 times.
So, the correct option is b) 8 times.
Step 1: Find the LCM of the time intervals
The time intervals given are 6, 5, 7, 10, and 12 seconds. To find the least common multiple (LCM) of these intervals, we can list their multiples and find the smallest number that appears in each list.
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, ...
Multiples of 10: 10, 20, 30, ...
Multiples of 12: 12, 24, 36, ...
From the lists, we can see that the smallest number that appears in each list is 30. Therefore, the LCM of the time intervals is 30 seconds.
Step 2: Calculate the number of times they toll together in one hour
In one hour, there are 60 minutes * 60 seconds = 3600 seconds.
To find the number of times the bells toll together, we need to divide the total time (3600 seconds) by the LCM of the time intervals (30 seconds).
3600 seconds / 30 seconds = 120
This means that the bells toll together 120 times in one hour.
However, we need to exclude the one at the start. Therefore, the correct answer is 120 - 1 = 119 times.
So, the correct option is b) 8 times.
What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks?- a)3
- b)5
- c)7
- d)9
Correct answer is option 'A'. Can you explain this answer?
What is the smallest number of ducks that could swim in this formation - two ducks in front of a duck, two ducks behind a duck and a duck between two ducks?
a)
3
b)
5
c)
7
d)
9
|
|
Roshni Sarkar answered |
Explanation:
Formation Description:
- Two ducks in front of a duck
- Two ducks behind a duck
- A duck between two ducks
Minimum Number of Ducks:
- In this formation, we need at least 3 ducks to satisfy all the given conditions:
1. Duck 1: Two ducks in front
2. Duck 2: A duck between two ducks
3. Duck 3: Two ducks behind
Therefore, the smallest number of ducks that could swim in this formation is 3, which is option 'A'.
Formation Description:
- Two ducks in front of a duck
- Two ducks behind a duck
- A duck between two ducks
Minimum Number of Ducks:
- In this formation, we need at least 3 ducks to satisfy all the given conditions:
1. Duck 1: Two ducks in front
2. Duck 2: A duck between two ducks
3. Duck 3: Two ducks behind
Therefore, the smallest number of ducks that could swim in this formation is 3, which is option 'A'.
A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is- a)12
- b)15
- c)18
- d)20
Correct answer is option 'B'. Can you explain this answer?
A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is
a)
12
b)
15
c)
18
d)
20
|
Shreya Das answered |
Given Information:
- Father is now 3 times as old as his son.
- 5 years back, father was 4 times as old as his son.
Let the age of the son be x years.
Calculating Father's age:
- Father's age = 3x (as per the first statement)
Calculating Son's age 5 years ago:
- Son's age 5 years ago = x - 5
Calculating Father's age 5 years ago:
- Father's age 5 years ago = 3x - 5
Using the second statement:
- 3x - 5 = 4(x - 5)
- 3x - 5 = 4x - 20
- x = 15
Therefore, the age of the son is 15 years (option B).
- Father is now 3 times as old as his son.
- 5 years back, father was 4 times as old as his son.
Let the age of the son be x years.
Calculating Father's age:
- Father's age = 3x (as per the first statement)
Calculating Son's age 5 years ago:
- Son's age 5 years ago = x - 5
Calculating Father's age 5 years ago:
- Father's age 5 years ago = 3x - 5
Using the second statement:
- 3x - 5 = 4(x - 5)
- 3x - 5 = 4x - 20
- x = 15
Therefore, the age of the son is 15 years (option B).
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