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Re: If x is an integer and y = –2x – 8, what is the least value of x for
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21 Jun 2017, 04:57

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1

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

If x is an integer and y = –2x – 8, what is the least value of x for
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22 Jun 2017, 06:21

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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Re: If x is an integer and y = –2x – 8, what is the least value of x for
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22 Jun 2017, 06:59

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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.
_________________

Re: If x is an integer and y = –2x – 8, what is the least value of x for
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24 Jun 2017, 13:09

\(x\) 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 \(8\)

Hence, Answer is B _________________

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