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If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10,

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If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10,  [#permalink]

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New post Updated on: 30 Jul 2017, 21:39
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If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10, what is the sum of the minimum and the maximum possible values of x/y?

A. -8
B. -4
C. 0
D. 4
E. 8

Originally posted by DHAR on 30 Jul 2017, 20:44.
Last edited by DHAR on 30 Jul 2017, 21:39, edited 1 time in total.
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Re: If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10,  [#permalink]

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New post 30 Jul 2017, 20:46
1
(x/y)min=-12/1 = -12
(x/y)max=-12/-1 = 12
Sum= 0
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Re: If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10,  [#permalink]

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New post 30 Jul 2017, 21:36
DH99 wrote:
If x and y are integers such that -12≤ x ≤ 1 and -4≤ y ≤10, what is the sum of the minimum and the maximum possible values of x/y?

A. -8
B. -4
C. 0
D. 4
E. 8


Mistake in Question The question must mention that y is NOT equal to zero for the x/y to be defined
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Re: If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10,  [#permalink]

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New post 30 Jul 2017, 21:40
1
GMATinsight wrote:
DH99 wrote:
If x and y are integers such that -12≤ x ≤ 1 and -4≤ y ≤10, what is the sum of the minimum and the maximum possible values of x/y?

A. -8
B. -4
C. 0
D. 4
E. 8


Mistake in Question The question must mention that y is NOT equal to zero for the x/y to be defined


Corrected the Questions.Thank you.
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Re: If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10,  [#permalink]

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New post 01 Aug 2017, 17:20
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2
DH99 wrote:
If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10, what is the sum of the minimum and the maximum possible values of x/y?

A. -8
B. -4
C. 0
D. 4
E. 8


Since both x and y can be positive or negative, we see that the maximum possible value of x/y is one such that x and y have the same sign (so that x/y is positive) and the minimum possible value of x/y is one such that x and y have opposite signs (so that x/y is negative). With that in mind, let’s determine the maximum possible value of x/y.

If we want x/y to be maximum, and both x and y are positive, we want both x and y to be equal to 1, so that x/y = 1. If both x and y are negative, we want x to be -12 and y to be -1, so that x/y = 12. Thus, the maximum value of x/y is 12.

Now let’s determine the minimum possible value of x/y.

If we want x/y to be a minimum, and x is positive and y is negative, we want x to be 1 and y to be -1, so that x/y = -1. If x is negative and y is positive, we want x to be -12 and y to be 1, so that x/y = -12. Thus, the minimum value of x/y is -12.

We see that the sum of the minimum and the maximum possible values of x/y is -12 + 12 = 0.

Answer: C
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Re: If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10,  [#permalink]

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New post 15 Oct 2018, 04:02
DHAR wrote:
If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10, what is the sum of the minimum and the maximum possible values of x/y?

A. -8
B. -4
C. 0
D. 4
E. 8


Minimum x/y
Since x and y can take negative values, minimum will be a negative number so make it go as left as possible on the number line. For this, make the absolute value of x/y as large as possible and then give it a negative sign. For |x/y| to be large, |x| should take the maximum value and |y| should take the minimum value.
x can be -12 and y can be 1.
x/y = -12

Maximum x/y
x/y must be positive with |x/y| as large as possible. So again x could bee -12 and y could be -1 (to make x/y positive)
x/y = 12

Adding them, we get 0

Answer (C)
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Re: If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10,   [#permalink] 15 Oct 2018, 04:02
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