Problem Solving

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

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