- 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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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?
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Solution
Given:
In this question, we are given that
We need to determine
For the non-zero integer x,
Similarly, for the non-zero integer y,
Now, for x/y to be least, we should take one of them as positive and the other one as negative.
Maximum value of x = 5
Answer: A
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.
We need to determine
- "¢ The least value of x/y lies in which of the given ranges.
For the non-zero integer x,
- "¢ |x - 3| ≤ 2
Or, -2 ≤ x - 3 ≤ 2
Or, 1 ≤ x ≤ 5
Similarly, for the non-zero integer y,
- "¢ -1 ≤ y ≤ 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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