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Math Expert V
Joined: 02 Sep 2009
Posts: 61189
If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 72% (01:22) correct 28% (01:20) wrong based on 151 sessions

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If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

Source: Nova GMAT
Difficulty Level: 600

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Originally posted by Bunuel on 21 Jun 2017, 04:21.
Last edited by SajjadAhmad on 06 Jul 2019, 22:14, edited 1 time in total.
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4318
Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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Bunuel wrote:
If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

In other words, find the smallest INTEGER value of x such that -2x - 8 < 9
Take: -2x - 8 < 9
Add 8 to both sides to get: -2x < 17
Divide both sides by -2 to get: x > -8.5 [NOTE: since we divided by a NEGATIVE value, we reversed the inequality symbol]
The smallest INTEGER that's greater than -8.5 is -8

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Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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Bunuel wrote:
If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

Go through the options , here the options are arranged in descending order...

(A) y = –2x – 8

Or, y = 18 - 8

Or, y = 10

(B) y = –2x – 8

Or, y = 16 - 8

Or, y = 8 ( Maximum value < 9 )

(C) y = –2x – 8

Or, y = 14 - 8

Or, y = 6

(D) y = –2x – 8

Or, y = 12 - 8

Or, y = 4

(E) y = –2x – 8

Or, y = 10 - 8

Or, y = 2

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Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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Abhishek009 wrote:
Bunuel wrote:
If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

Go through the options , here the options are arranged in descending order...

(A) y = –2x – 8

Or, y = 18 - 8

Or, y = 10

(B) y = –2x – 8

Or, y = 16 - 8

Or, y = 8 ( Maximum value < 9 )

(C) y = –2x – 8

Or, y = 14 - 8

Or, y = 6

(D) y = –2x – 8

Or, y = 12 - 8

Or, y = 4

(E) y = –2x – 8

Or, y = 10 - 8

Or, y = 2

y = -2x-8 < 9
-> 2x+8 > -9
-> 2x > -17
-> x> -8.5
Since x is an integer. x =-8
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Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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Bunuel wrote:
If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

Bunuel, or GMATPrepNow, or any expert, I have a question about how to think about the end result. I solved as GMATPrepNow did:

-2x - 8 < 9
-2x < 17
x > -17/2, or x > -8.5

I couldn't decide, simply from that result and the number line, whether the integer equaling "least value for x" was -9 or -8.

So I plugged x = -9 into original equation. Incorrect. It yields y = 10, but y cannot be greater than 9. x = -8 yields y = 8, which satisfies y < 9.

I rarely have a hard time knowing whether to "round" up or round down.

Here it seemed tricky because x = -9 and x = -8 both satisfy the condition that x > - 8.5. "[L]east value of x" wasn't self-evident. Worse, -9 is smaller than -8, and we're looking for "least" integer.

I'm frustrated. This issue seems relatively simple. Because answer choice (A) is -9, I suspect that trap tempts others.

GMATPrepNow refers to "the smallest [integer] that's greater than -8.5 . . ." How do we know, intuitively or otherwise, to choose the value for x that's greater than -8.5? I'm missing something really obvious, I think. Sorry. (Then again, "Don't ask, don't know.")
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Joined: 02 Sep 2009
Posts: 61189
Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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1
genxer123 wrote:
Bunuel wrote:
If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

Bunuel, or GMATPrepNow, or any expert, I have a question about how to think about the end result. I solved as GMATPrepNow did:

-2x - 8 < 9
-2x < 17
x > -17/2, or x > -8.5

I couldn't decide, simply from that result and the number line, whether the integer equaling "least value for x" was -9 or -8.

So I plugged x = -9 into original equation. Incorrect. It yields y = 10, but y cannot be greater than 9. x = -8 yields y = 8, which satisfies y < 9.

I rarely have a hard time knowing whether to "round" up or round down.

Here it seemed tricky because x = -9 and x = -8 both satisfy the condition that x > - 8.5. "[L]east value of x" wasn't self-evident. Worse, -9 is smaller than -8, and we're looking for "least" integer.

I'm frustrated. This issue seems relatively simple. Because answer choice (A) is -9, I suspect that trap tempts others.

GMATPrepNow refers to "the smallest [integer] that's greater than -8.5 . . ." How do we know, intuitively or otherwise, to choose the value for x that's greater than -8.5? I'm missing something really obvious, I think. Sorry. (Then again, "Don't ask, don't know.")

After you get x > -8.5, think this way. You need the smallest x, which is greater than -8.5. -9 is not greater than -8.5 but -8 is.
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Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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Bunuel wrote:
If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

We need to determine the least value of x such that y < 9. Since y = -2x - 8, we have:

-2x - 8 < 9

-2x < 17

x > -17/2

x > -8.5

Since x must be an integer, its least value is when x = -8.

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Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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$$x$$ is an integer and

$$y = –2x – 8$$

Since we need to find least value of $$x$$ where $$y < 9$$

$$-2x - 8 < 9$$

$$-2x < 17$$

$$-x < 8.5$$

$$x > -8.5$$ (Sign Change)

Since, x is an integer and value of $$x > -8.5$$ and we have to find the least value of $$x$$ the answer will be $$8$$

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Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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Bunuel wrote:
If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

x is an I, can be +ive or -ive

y = -2x-8

A 18 -8 = 10 < 9 No

B 16 - 8 < 9 Yes

C 14 -8 = 6 < 9 Yes

D 12 - 8 = 4 < 9 Yes

E 10 - 8 = 2 < 9 Yes

Least is B
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Re: If x is an integer and y = –2x – 8, what is the least value of x for  [#permalink]

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Bunuel wrote:
If x is an integer and y = –2x – 8, what is the least value of x for which y is less than 9?

(A) –9
(B) –8
(C) –7
(D) –6
(E) –5

simply do plug in and check for values
we observe that at B its true
IMO B Re: If x is an integer and y = –2x – 8, what is the least value of x for   [#permalink] 24 Jan 2019, 10:11
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