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.")