If 2 andle; -x andndash; 1- andtimes; -y + 3- andle; 5 and both x and y are negative integers, find the number of possible combinations of x and y.a)10b)5c)6d)4Correct answer is option 'A'. Can you explain this answer?

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If 2 ≤ |x – 1| × |y + 3| ≤ 5 and both x and y are negative integers, find the number of possible combinations of x and y.

a)
10
b)
5
c)
6
d)
4

Correct answer is option 'A'. Can you explain this answer?

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If 2 ≤ |x – 1| × |y + 3| ≤ 5 and both x and y are ne...

2 ≤ |x – 1| × |y + 3| ≤ 5
The product of two positive number lies between 2 and 5.
As x is a negative integer, the minimum value of |x – 1| will be 2 and the maximum value of |x – 1| will be 5 as per the question.

When, |x – 1| = 2, |y + 3| can be either 1 or 2
So, for x = -1, y can be – 4 or – 2 or – 5 or -1.
Thus, we get 4 pairs of (x, y)

When |x – 1| = 3, |y + 3| can be 1 only
So, for x = – 2, y can be -4 or -2
Thus, we get 2 pairs of the values of (x, y)

When |x – 1| = 4, |y + 3| can be 1 only
So, for x = – 3, y can be -4 or -2
Thus, we get 2 pairs of the values of (x, y)

When |x – 1| = 5, |y + 3| can be 1 only
So, for x = – 4, y can be -4 or -2
Thus, we get 2 pairs of the values of (x, y)

Therefore, we get a total of 10 pairs of the values of (x, y)
Hence, option A is the correct answer.

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If 2 ≤ |x – 1| × |y + 3| ≤ 5 and both x and y are negative integers, find the number of possible combinations of x and y.a)10b)5c)6d)4Correct answer is option 'A'. Can you explain this answer?

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