If x < 12

[fighting_cax]

If x < 12, then it must be true that

(a) -x < -12
(b) -x - 2 < 14
(c) -x + 2 < -10
(d) x + 2 < 10
(e) x - 2 < 11

OA is E but can't understand why.

Please explain.

[DanaJ]

Let's take each inequality at a time:
A. -x < -12 - multiply by (-1) on each side to eliminate the minuses and you get:
x > 12 - "<" gets reversed when you multiply by a negative number. So the initial inequality is equivalent to x > 12, which is not consistent with x < 12.

B. -x - 2 < 14 - add 2 on each side to get;
-x < 16 - multiply by (-1)
x > - 16. While it is true that for some numbers that are smaller than 12 this is correct, it isn't for everything. Just consider x = 20:
20 > -16, but 20 is not greater than 12.

C. -x + 2 < -10 - subtract 2 from each side
-x < - 12 - takes us back to A

D. x + 2 < 10 means that x < 8. Again, take x = 10. While it is true that x < 12, 10 is not smaller than 8.

E is our answer: x - 2 < 11 means that x < 13. Now, this is consistent with x < 12, since any number smaller than 12 will also be smaller than 13.

[fighting_cax]

But if x< 13, x can be equal to 12. And if x = 12, x cannot be less than 12.

For answer D, however, where it can be derived that x < 8, x can be any number less than 8 (i.e. 7, 6, 5, etc). And if this is the case, then this statement MUST be true?

[kamu]

Read the question slowly and then DanaJ's answer. You'll get it.

D. x + 2 < 10 means that x < 8. Again, take x = 10.
While it is true that x < 12, 10 is not smaller than 8.

A number smaller than 12 will be smaller than 13.

[Brent@GMATPrepNow]

If x < 12, then it must be true that

(a) -x < -12
(b) -x - 2 < 14
(c) -x + 2 < -10
(d) x + 2 < 10
(e) x - 2 < 11

OA is E but can't understand why.

Please explain.

STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test values that satisfy the given inequality.
From here, I'll give myself 15-20 seconds to identify a faster approach.....
We can also solve the question by analyzing each answer choice to see if it adheres to the given inequality algebraically, but since I'm less likely to make mistakes testing values, I'll go that route

Let's start by testing an "extreme" possible value of x.
For example, x = -20 is an obvious solution to the given inequality, x < 12

So, let's plug x = -20 into each answer choice to see if it's a solution.
(a) -(-20) < -12, which simplifies to 20 < -12. Doesn't work. Eliminate A.
(b) -(-20) - 2 < 14, which simplifies to 20 - 2 < 14. Doesn't work. Eliminate B.
(c) -(-20) + 2 < -10, which simplifies to 20 + 2 < -10. Doesn't work. Eliminate C.
(d) -20 + 2 < 10. Works. KEEP.
(e) -20 - 2 < 11. Works. KEEP.

We're already down to answer choices D, and E

Now let's test an " extreme" upper value that's close to 12
x = 11.5 is another solution to the given inequality, x < 12.
So we'll plug x = 11.5 into the remaining two answer choices....
(d) 11.5 + 2 < 10. Doesn't work. Eliminate D
(e) 11.5 - 2 < 11. Works. KEEP.

Answer: E