Which of the following is equivalent to the pair of

Question

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

Bunuel · Answer

x + 6 > 10 --> x > 4; x - 3 <= 5 --> x<=8; Therefore 4 < x <=8. Answer: D.

luckyme17187 · Answer

x + 6 > 10 and x - 3 <= 5 x>4 and x<=8 combining 4

PareshGmat · Answer

x > 4 & x< = 8

OR

4 < x & x < = 8

4 < x < = 8

Answer = D

mcelroytutoring · Answer

Attached is a visual that should help.

JeffTargetTestPrep · Answer

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 The answer is D.

BrentGMATPrepNow · Answer

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

RELATED VIDEO
 https://www.youtube.com/watch?v=S_fjYmCtvy0

SeregaP · Answer

x>4
x<=8
hence answer is D

BrentGMATPrepNow · Answer

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

audentes · Answer

Simplify

x + 6 > 10

\Rightarrow x > 4

x - 3 \le 5

\Rightarrow x \le 8

Combine

4< x \le8

Answer D

hiranmay · Answer

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

TheUltimateWinner · Answer

Adding one thing with your explanation...
The highlighted part also says that x is greater than 4 (not equal to 4). So, we can also cancel E by this way.

BrentGMATPrepNow · Answer

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

Cheers,
Brent

TheUltimateWinner · Answer

And thanks for the nice explanation.

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=4IO8TsHbpC8

palaknayyar · Answer

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.

curiouscanary13 · Answer

Solving the equations will get us the answer: x + 6 > 10 x> 4 x - 3 <= 5 x <= 8 So, 4

totaltestprepNick · Answer

D https://www.youtube.com/watch?v=S7Y4COBsqJI Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

Which of the following is equivalent to the pair of

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Which of the following is equivalent to the pair of

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