- A. Between -5.5 and -4.5

B. Between -4.5 and -3.5

C. Between -3.5 and -2.5

D. Between -2.5 and -1

E. Greater than -1

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

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### GMAT/MBA Expert

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If x and y are non-zero integers and |x - 3| â‰¤ 2 and -1 â‰¤ y â‰¤ 8 then the least value of x/y lies in which of the following range?

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**Solution**

**Given:**

In this question, we are given that

- "¢ The numbers x and y are non-zero integers.

"¢ Also, |x - 3| â‰¤ 2 and -1 â‰¤ y â‰¤ 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| â‰¤ 2

Or, -2 â‰¤ x - 3 â‰¤ 2

Or, 1 â‰¤ x â‰¤ 5

Similarly, for the non-zero integer y,

- "¢ -1 â‰¤ y â‰¤ 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.

Maximum value of x = 5

- "¢ Therefore, the minimum value of x/y = 5/-1 = -5

"¢ This value lies between -5.5 and -4.5

**Answer: A**

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