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Question of the Week - 41 (If x and y are non-zero integers and...)

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Question of the Week - 41 (If x and y are non-zero integers and...)  [#permalink]

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New post 30 Mar 2019, 02:36
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Question Stats:

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e-GMAT Question of the Week #41


If x and y are non-zero integers and |x – 3| ≤ 2 and -1 ≤ y ≤ 8 then the least value of \(\frac{x}{y}\) 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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Re: Question of the Week - 41 (If x and y are non-zero integers and...)  [#permalink]

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New post 30 Mar 2019, 02:59
If x and y are non-zero integers and |x – 3| ≤ 2 and -1 ≤ y ≤ 8 then the least value of \(\frac{x}{y}\) lies in which of the following range?

We know the range of y, and now we will work on range of x by solving |x – 3| ≤ 2..
Two cases for |x – 3| ≤ 2 : (I) x-3≤ 2...x≤ 5, and (II) -(x-3)≤ 2...3-x≤ 2......1≤ x
Range of x = > x-3≤ 2........1≤x≤ 5

Now, for the least value of \(\frac{x}{y}\), we will take y as negative, that is -1. The denominator should have the largest possible value, so 5..
\(\frac{x}{y}\)=>\(\frac{5}{-1}=-5\).

-5 is between -5.5 and -4.5, and so the answer is A
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Re: Question of the Week - 41 (If x and y are non-zero integers and...)  [#permalink]

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New post 30 Mar 2019, 05:38
solve for
|x – 3| ≤ 2
x<=5
and -x<=1 ; x>=1
so 1>=x<=5
and
-1 ≤ y ≤ 8
so to get least value of x/y ; x = 5 and y = -1
-5
IMO A


EgmatQuantExpert wrote:
e-GMAT Question of the Week #41


If x and y are non-zero integers and |x – 3| ≤ 2 and -1 ≤ y ≤ 8 then the least value of \(\frac{x}{y}\) 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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Question of the Week - 41 (If x and y are non-zero integers and...)  [#permalink]

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New post 02 Apr 2019, 21:41

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,
    • -1 ≤ y ≤ 8

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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Question of the Week - 41 (If x and y are non-zero integers and...)   [#permalink] 02 Apr 2019, 21:41
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