If x is equal to one of the numbers 1/4, 3/8, or 2/5, what is the valu GMAT data sufficiency

Question: If x is equal to one of the numbers 1/4, 3/8, or 2/5, what is the value of x?

Statement (1) 1/4 < x < 1/2
Statement (2) ⅓ < x < 3/5

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.

Answer: E

Solution and Explanation:

Approach Solution 1:
The best strategy is to compare with 120*x rather than x. ( 120 is LCM of 3,4,5, and 8)
120x new questions is 30, 45, or 48
(1) 30 < 120x < 60, where x can have either a value of 45 or 48. Therefore, insufficient. Mark A and D (2) as unsatisfactory.
40 < 120x < 72... both 45 and 48 can be the values of x. Thus, this is also insufficient, Cross B.
1+2 is insufficient as well; cross C
Correct option: E

Approach Solution 2:
We can use the given information to determine the value of x as follows:
From the statement (1), we know that x is greater than 1/4 but less than 1/2. However, this information does not narrow down the possibilities of x to a single value since all three given numbers lie within this range.
Similarly, from statement (2), we know that x is greater than 1/3 but less than 3/5. Again, this information is not sufficient to determine the value of x since two of the given numbers lie within this range.
Therefore, we cannot determine the value of x based on the information provided in these statements. The answer is (E) - the two statements together are insufficient to answer the question.
Correct option: E

Approach Solution 3:
To calculate the value of x, we can do as follows using the information provided:
We can infer that x is higher than 1/4 but less than 1/2 from the assertion (1). Yet, because all three of the given numbers fall inside this range, this information does not reduce the possible values of x to a single one.
Therefore, we can infer from assertion (2) that x is higher than 1/3 but less than 3/5. Again, since two of the given values fall within this range, this information is insufficient to identify the value of x.
As a result, we are unable to calculate the value of x using the data in these sentences. The two assertions taken together are insufficient to answer the question, hence the answer is (E).
Correct option: E

“If x is equal to one of the numbers 1/4, 3/8, or 2/5, what is the valu GMAT data sufficiency" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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