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2a + 5b = 103. How many pairs of positive integer values can a, b take such that a > b?
- a)12
- b)9
- c)7
- d)8
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
2a + 5b = 103. How many pairs of positive integer values can a, b take...
Let us find the one pair of values for a, b.
a = 4, b = 19 satisfies this equation.
2*4 + 5*19 = 103.
Now, if we increase ‘a’ by 5 and decrease ‘b’ by 2 we should get the next set of numbers. We can keep repeating this to get all values.
Let us think about why we increase ‘a’ by 5 and decrease b by 2.
a = 4, b = 19 works.
Let us say, we increase ‘a’ by n, then the increase would be 2n.
This has to be offset by a corresponding decrease in b.
Let us say we decrease b by ‘m’.
This would result in a net drop of 5m.
In order for the total to be same, 2n should be equal to 5m.
The smallest value of m, n for this to work would be 2, 5.
a = 4, b = 19
a = 9, b = 17
a = 14, b = 15
..
And so on till
a = 49, b = 1
We are also told that ‘a’ should be greater than ‘b’, then we have all combinations from (19, 13) … (49, 1).
7 pairs totally.
a = 4, b = 19 satisfies this equation.
2*4 + 5*19 = 103.
Now, if we increase ‘a’ by 5 and decrease ‘b’ by 2 we should get the next set of numbers. We can keep repeating this to get all values.
Let us think about why we increase ‘a’ by 5 and decrease b by 2.
a = 4, b = 19 works.
Let us say, we increase ‘a’ by n, then the increase would be 2n.
This has to be offset by a corresponding decrease in b.
Let us say we decrease b by ‘m’.
This would result in a net drop of 5m.
In order for the total to be same, 2n should be equal to 5m.
The smallest value of m, n for this to work would be 2, 5.
a = 4, b = 19
a = 9, b = 17
a = 14, b = 15
..
And so on till
a = 49, b = 1
We are also told that ‘a’ should be greater than ‘b’, then we have all combinations from (19, 13) … (49, 1).
7 pairs totally.
Hence the answer is "7"
Choice C is the correct answer.
Most Upvoted Answer
2a + 5b = 103. How many pairs of positive integer values can a, b take...
Explanation :
The word 'BIHAR' has 5 letters and all these 5 letters are different.
Total words formed by using all these 5 letters = 5P5 = 5!
= 5 x 4 x 3 x 2 x 1 = 120
Total words formed by using all these 5 letters = 5P5 = 5!
= 5 x 4 x 3 x 2 x 1 = 120
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Community Answer
2a + 5b = 103. How many pairs of positive integer values can a, b take...
Analysis:
To find the number of words that can be formed using all the letters of the word 'BIHAR', we need to calculate the permutations of the letters.
Solution:
To solve this problem, we can follow the steps below:
Step 1: Identify the number of letters:
The word 'BIHAR' has 5 letters.
Step 2: Find the number of permutations:
To find the number of permutations, we use the formula for permutations of n objects taken all at a time, which is given by n!.
In this case, n = 5, so the number of permutations is 5!.
Step 3: Calculate the factorial:
To calculate 5!, we multiply all the numbers from 5 down to 1.
5! = 5 * 4 * 3 * 2 * 1 = 120.
Therefore, there are 120 different words that can be formed by using all the letters of the word 'BIHAR'.
Answer:
The correct answer is option C) 120.
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2a + 5b = 103. How many pairs of positive integer values can a, b take such that a > b?a)12b)9c)7d)8Correct answer is option 'C'. Can you explain this answer?
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