Question of the Week - 2 (If x and y are non-zero integers )

Solution

Given:
In this question, we are given that

• • The numbers x and y are non-zero integers.
  • Also, |x – 3| ≤ 2 and -1 ≤ y ≤ 8.

To find:
We need to determine

• • The least value of x/y lies in which of the given ranges.

Approach and Working:
For the non-zero integer x,

• • |x – 3| ≤ 2
  Or, -2 ≤ x – 3 ≤ 2
  Or, 1 ≤ x ≤ 5

Therefore, possible values of x = 1, 2, 3, 4, 5

Similarly, for the non-zero integer y,

• • -1 ≤ y ≤ 8

Therefore, possible values of y = -1, 1, 2, 3, 4, 5, 6, 7, 8

Now, for x/y to be least, we should take one of them as positive and the other one as negative.

• • As we can see from the derived values of x and y, x can be positive only whereas y can be negative.
  • Hence, we should take negative value of y, with maximum possible magnitude, and maximum value of x.

Negative value of y, with maximum magnitude = -1
Maximum value of x = 5

• • Therefore, the minimum value of x/y = 5/-1 = -5
  • This value lies between -5.5 and -4.5

Hence, the correct answer is option A.

Answer: A