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If x < 12, then it must be true that

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If x < 12, then it must be true that

by VJesus12 » Tue Jul 17, 2018 1:04 am

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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

The OA is the option E.

I've got confused here. Could someone clarify this PS question to me? Please. <i class="em em-worried"></i>
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by GMATGuruNY » Tue Jul 17, 2018 2:02 am
VJesus12 wrote: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
If x=-100, then A, B and C are not true.
If x=11, then D is not true.

The correct answer is E.

E: x-2 < 11
x < 13.
Since the prompt indicates that x<12, x must be less than 13.
Thus, E must be true.
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by Brent@GMATPrepNow » Tue Jul 17, 2018 6:03 am
VJesus12 wrote: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
NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

E) x - 2 < 11
Take the given inequality: x < 12
Subtract 2 from both sides to get: x - 2 < 10
If x-2 is less than 10, we can be certain that x-2 is less than 11
So, answer choice E is TRUE

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Thu Jul 19, 2018 4:21 pm
VJesus12 wrote: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
Let's analyze each choice.

A) -x < -12

If we multiply both sides of x < 12 by -1, we will have -x > -12 (notice that we have to switch the inequality sign since we've multiplied by a negative number). So A is not correct.

B) -x - 2 < 14

Starting with x < 12, we have:

x < 12

-x > -12

-x - 2 > -14

We see that B is not correct either.

C) -x + 2 < -10

x < 12

-x > -12

-x + 2 > -10

We see that C is not correct either.

D) x + 2 < 10

x < 12

x + 2 < 14

We see that D is not correct either. So the correct answer must be E. But let's verify it anyway.

E) x - 2 < 11

x < 12

x - 2 < 10

If x - 2 < 10, then x - 2 is less than 11 also. So E is correct.

Answer: E

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