Is x<5 ? (1)x^2 > 5  (2)x^2 + x < 5 GMAT Data Sufficiency

Question: Is x < 5?

1. x^2 > 5
2.  x^2 + x < 5

1. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
2. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

‘Is x<5 Is x<5 ? (1)x^2 > 5 (2)x^2 + x < 5’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for GMAT Reviews”. 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.

Solution and Explanation:

Approach Solution 1:

It is asked in the question if x < 5 or not. This is a data sufficiency problem. We are given two statements and we have to check if these statements are sufficient to solve the problem or not.

The given statements are :

(1) x^2 > 5
(2) x^2 + x < 5

Coming to the first statement
Given that,
x^2 > 5
Here if we take the value of x = 3 then x < 5 and also x^2 > 5
But if we take the value of x = 6 then x > 5 and x^2 > 5
Therefore this statement alone is not sufficient to say whether x < 5 or not.

In statement 2,
x^2 + x < 5
Taking x^2 to right,
X < 5 - x^2
x^2 cannot be negative.
Therefore
5 - x^2 <= 5
We get,
X < 5
This statement is sufficient to get the answer.So option B is the correct answer.

Correct Answer: B

Approach Solution 2:

It is asked in the question if x < 5 or not. This is a data sufficiency problem. We are given two statements and we have to check if these statements are sufficient to solve the problem or not.

Given statements are :

(1) x^2 > 5
(2) x^2 + x < 5
Coming to the first statement
x^2 > 5
X >\(\sqrt{5}\)

Or x < - \(\sqrt{5}\)

\(\sqrt{5}\) \(\approx\) 2.2
X > 2.2 or x < -2.2
X may be smaller than 5 but x can also be larger than 5. Hence this is not sufficient to get the answer.
In option 2,
x^2 + x < 5
x(x+1) < 5
Let x = 2
2(2+1) = 6 > 5
So,
the values of x for which this equation satisfies is x < 2 and x > -2
Hence we get -2 < x < 2
This range is less than 5, so the answer to the given question is yes.
The correct answer will be option B.

Correct Answer: B

Approach Solution 3:

We need to find whether x < 5.
Statement (1) Alone: x^2 > 5
So, if x = 3, then x< 5. Furthermore, if x = 6, then x is not less than 5. Statement one alone is not sufficient to answer the question.

Statement (2) Alone:
x^2 + x < 5
So, we have x < 5 - x^2. Since x^2 is not negative, we have 5 - x^2< 5. Since x < 5 - x^2 and 5 - x^2> 5, we have x < 5.

Correct Answer: B

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