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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3074
Question of the Week - 41 (If x and y are non-zero integers and...)  [#permalink]

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30 Mar 2019, 02:36
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Difficulty:

35% (medium)

Question Stats:

60% (02:25) correct 40% (02:22) wrong based on 43 sessions

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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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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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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:
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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Joined: 04 Jan 2015
Posts: 3074
Question of the Week - 41 (If x and y are non-zero integers and...)  [#permalink]

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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.

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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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