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Og Inequality Q

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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Og Inequality Q

Post Wed Jul 19, 2017 10:00 pm
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

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Post Wed Jul 19, 2017 10:22 pm
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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Post Thu Jul 20, 2017 12:02 pm
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

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Matt@VeritasPrep GMAT Instructor
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Post Sun Jul 23, 2017 3:24 pm
I'd simplify the inequalities then graft them together.

The first one: x + 6 > 10 => x > 4

The second one: 5 ≥ x - 3 => 8 ≥ x

Since x is the middle term, we use it to connect them: 8 ≥ x > 4.

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Post Mon Jul 24, 2017 11:52 am
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

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Post Tue Jul 25, 2017 11:00 am
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
We are given two inequalities:

x + 6 > 10

x > 4, which is equivalent to 4 < x

and

x - 3 ≤ 5

x ≤ 8

So we have:

4 < x ≤ 8

Answer: D

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