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
Og Inequality Q
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We have two inequalities: x + 6 > 10 and x - 3 ≤ 5;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
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
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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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.
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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Another approach is to eliminate 4 of the answer choicesAbeNeedsAnswers 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
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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We are given two inequalities: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
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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