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

1. 2 < x < 16
2. 2 <= x < 4
3. 2 < x <= 8
4. 4 < x <= 8
5. 4 <= x <= 16

“Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x – 3 < = 5?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

x + 6 > 10 --- x > 4

x – 3 <= 5 --- x <= 8

Therefore 4 < x <= 8

Correct Option: D

Approach Solution (2):

x > 4 and x <= 8

OR

4 < x and x <= 8

4 < x <= 8

Correct Option: D

Approach Solution (3):

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

x + 6 > 10

x > 4

5 < = Next we isolate x in the inequality x – 5

x – 3 <= 5

x <= 8

Bringing these two inequalities together, we know:

4 < x <= 8

Correct Option: D

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