If m is a positive integer, is \(\sqrt{m}>25\) ?

Question: If m is a positive integer, is \(\sqrt{m}>25\)?

1. m is divisible by 50
2. m is divisible by 52

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.

“If m is a positive integer, is \(\sqrt{m}>25\) ?" is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

Approach 1

Firstly, consider the statement (1), we have m is divisible by 50.
m can be 50 so less than 625 as well as 5,000 so more than 625.
Hence, this statement is not sufficient.

Now considering statement (2), we have m is divisible by 52
M can be 52 so less than 625 as well as 5,200 so more than 625.
Hence, this statement is not sufficient.

Combining statement (1) and (2),
Since m is a multiple of both 50 and 52 then it’s a multiple of the least common multiple (LCM) of those two numbers, so a multiple of 1300.
Since, given that m s a positive integer then the least value of m is 1300, so m > 625.

Hence, it is sufficient statement.

Correct option: C

Approach 2

As m is a positive integer, we need to check if value of m is greater than 625
Taking statement (1): m is divisible by 50. So, m can be 50 or 5000
So, this statement is not sufficient.

Taking statement (2), m is divisible by 52. So, m can be 52 or 5200.
So, this statement is not sufficient.

Now, combining both the statements, we will get:
M is divisible by both 50 = 25*2 and 52 = 4*13.
So, we have at least 25*13*2 as the value of m.
That is 650.
This means the square root of m is surely greater than 25.

Correct option: C

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