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

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

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

    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

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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| ≤ 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

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