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 \(\frac{x}{y}\) 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,
Therefore, possible values of y = -1, 1, 2, 3, 4, 5, 6, 7, 8
Now, for \(\frac{x}{y}\) 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 \(\frac{x}{y}\) = \(\frac{5}{-1}\) = -5
• This value lies between -5.5 and -4.5
Hence, the correct answer is option A.
Answer: A
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