questioner wrote:

From 8*x* = 16 + 2*x* we have *x* = 8/3.

From (1) *x* ≤ 3

From (2) *x* ≥ 3

then, answer A is correct.

Apparently, you confused given information and what the question was asking. Look at these two different statements to feel the difference:

"If

*x* = 8/3 then

*x* ≤ 3" is TRUE.

"If

*x* ≤ 3 then

*x* = 8/3" is NOT TRUE.

In this particular problem

the question asks: "Is *x* = 8/3 ?". The given information is:

1) Statement (1) alone:

*x* ≤ 3

2) Statement (2) alone:

*x* ≥ 3

3) The both statements combined:

*x* = 3

1) If we know that

*x* ≤ 3 then

*x* **can** be 8/3. But it also can be 3, or any other value less than 3. So we can not give a

**definite** answer to the question. Statement (1) by itself is NOT sufficient.

Question: Does 8

*x* = 16 + 2

*x* IF -3

*x* ≥ -9?

Answer: It can be, but not necessarily.

2) If we know that

*x* ≥ 3 then

*x* definitely

**cannot** be 8/3. So we can give the

**definite** answer to the question. This

**definite** answer is "NO".

Question: Does 8

*x* = 16 + 2

*x* IF 2

*x* ≥ 6?

Answer: NO.

The information in Statement (2) is sufficient to answer the question, while the information in Statement (1) is NOT sufficient to answer the question.