Og Inequality Q

AbeNeedsAnswers wrote:Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

(A) 2 <= x < 16
(B) 2 <= x < 4
(C) 2 < x <= 8
(D) 4 < x <= 8
(E) 4 <= x < 16

D

We have two inequalities: x + 6 > 10 and x – 3 ≤ 5;

1. x + 6 > 10 => x > 4
2. x – 3 ≤ 5 => x ≤ 8

Together, we get

4 < x ≤ 8

We see that Option D is correct.

The correct answer: D

Hope this helps!

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Hi AbeNeedsAnswers,

When dealing with multiple inequalities, it can be helpful to simplify the inequalities one-at-a-time and use the results to help you 'narrow down' the possibilities.

Here, the first inequality is X + 6 > 10. Simplifying that, we get...

X + 6 > 10
X > 4

Looking at the answer choices, there's only ONE answer that includes X > 4.... Just to be sure though, let's see what happens with the second inequality....

X - 3 <= 5
X <= 8

That confirms the correct answer.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote:Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 <= 5 ?

(A) 2 ≤ x < 16
(B) 2 ≤ x < 4
(C) 2 < x ≤ 8
(D) 4 < x ≤ 8
(E) 4 ≤ x < 16

Another approach is to eliminate 4 of the answer choices

First, x + 6 > 10 can be rewritten as x > 4
This means that x CANNOT equal 3
When we check the answer choices, we see that A, B and C all say that x COULD equal 3
So, eliminate A, B and C

Second, x - 3 ≤ 5 can be rewritten as x ≤ 8
This means that x CANNOT equal 9
When we check the remaining answer choices, we see that E says that x COULD equal 9
So, eliminate E

We're left with D


Cheers,
Brent