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Which of the following is equivalent to the pair of

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Re: Which of the following is equivalent to the pair of [#permalink]
x > 4 & x< = 8

OR

4 < x & x < = 8

4 < x < = 8

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Re: Which of the following is equivalent to the pair of [#permalink]
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Attached is a visual that should help.
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Screen Shot 2016-05-25 at 9.43.26 PM.png [ 64.89 KiB | Viewed 53531 times ]

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Re: Which of the following is equivalent to the pair of [#permalink]
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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

Solution:

Let’s isolate x in both inequalities, starting with x + 6 > 10.

x + 6 > 10

x > 4

Next we isolate x in the inequality x – 3  5.

x – 3 <= 5

x <= 8

Bringing these two inequalities together we know:

4 < x <= 8

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Re: Which of the following is equivalent to the pair of [#permalink]
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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

The above solutions are great. I just want to add one more tip.
When it comes to multiple inequalities, I find that it helps to rearrange them so that the inequality signs are all facing the same direction (I prefer arranging them so that the values are in ascending order from left to right)

So, x + 6 > 10 and x - 3 < 5 first become 10 < x + 6 and x - 3 < 5
For 10 < x + 6, we subtract 6 from both sides to get: 4 < x
For x - 3 < 5, we add 3 to both sides to get: x < 8
With the two inequality signs facing the same direction, it's easy to combine them to get 4 < x < 8

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Re: Which of the following is equivalent to the pair of [#permalink]
x>4
x<=8
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Which of the following is equivalent to the pair of [#permalink]
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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 answer choice D

Cheers,
Brent
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Re: Which of the following is equivalent to the pair of [#permalink]
[1] Simplify

$$x + 6 > 10$$

$$\Rightarrow x > 4$$

$$x - 3 \le 5$$

$$\Rightarrow x \le 8$$

[2] Combine

$$4< x \le8$$

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Re: Which of the following is equivalent to the pair of [#permalink]
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 --> correct
(E) 4 <= x <= 16

Solution:
x + 6 > 10 and x - 3 <= 5
=> x > 4 and x <=8
=> 4 < x <=8
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Which of the following is equivalent to the pair of [#permalink]
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BrentGMATPrepNow 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 answer choice D

Cheers,
Brent

The highlighted part also says that x is greater than 4 (not equal to 4). So, we can also cancel E by this way.
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Re: Which of the following is equivalent to the pair of [#permalink]
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The highlighted part also says that x is greater than 4 (not equal to 4). So, we can also cancel E by this way.

Great point!
Kudos for you!!!!!!!

Cheers,
Brent
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Re: Which of the following is equivalent to the pair of [#permalink]
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BrentGMATPrepNow wrote:
The highlighted part also says that x is greater than 4 (not equal to 4). So, we can also cancel E by this way.

Great point!
Kudos for you!!!!!!!

Cheers,
Brent

And thanks for the nice explanation.
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Re: Which of the following is equivalent to the pair of [#permalink]
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Video solution from Quant Reasoning:
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Re: Which of the following is equivalent to the pair of [#permalink]
We can solve this question very simply by solving each individual inequality. We also need to pay close attention to which side of the final answer should have an inequality. so before we even start to solve, we can eliminate E, clearly, only 1 part of the final answer can have equality.

1) x+6>10
is x>10-6
is x> 4

2) x-3<= 5
is x<= 5+3
is x<=8

combining the two bold parts, clearly the answer is D.
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Re: Which of the following is equivalent to the pair of [#permalink]
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Re: Which of the following is equivalent to the pair of [#permalink]
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