When 120 is Divided by Positive Single-Digit Integer M the Remainder GMAT Data Sufficiency

Question: When 120 is divided by positive single-digit integer m the remainder is positive. When 120 is divided by positive integer n the remainder is also positive. If m ≠ n what is the remainder when 120 is divided by |n − m|?

1) When 120 divided by integer n the remainder equal to √n
2) n is a single-digit integer

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

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:

When 120 is divided by positive single-digit integer m the remainder is positive.
When 120 is divided by positive integer n the remainder is also positive.

Asked:

If m ≠ n what is the remainder when 120 is divided by |n − m|?

Statement 1: When 120 divided by integer n the remainder equal to √n
From this statement, we know that the value n is 9.
However, 9 cannot be the only value possible.

There may be another second value that can be derived from the question.
Any value of n >120 will leave a remainder of 120.
Therefore, 120^2 will also leave a remainder of 120.
Hence, the second value of n is 120^2.
At least two possible values of n are 9 and 120^2.
Hence, statement one alone is Insufficient.

Statement 2: n is a single-digit integer.
When we divide 120 by a single-digit positive integer only two numbers give the remainder: 9 and 7
We know that m≠n
Therefore, we can conclude that there are two possible cases
1) m=7 and n=9
2) m=9 and n=7
Therefore, |9−7|=2
And |7−9|=2

Hence, by dividing 120 by 2 we get:
120/2 = 60 i.e the Remainder is 0

Hence, statement two alone is Sufficient.

Approach Solution 2:

The problem statement states that:
Given:

When 120 is divided by positive single-digit integer m the remainder is positive.
When 120 is divided by positive integer n the remainder is also positive.

Asked:

If m ≠ n what is the remainder when 120 is divided by |n − m|?

According to the original condition, it is given that there are 2 variables (m and n) and 1 equation. Since 120 can be derived as 2^3*3*5, so only m = 7 and 9 are possible.
In order to match the number of variables to the number of equations we require 1 equation.
Since statement (1) and statement (2) each have 1 equation, there is a high chance that D is the correct answer choice.

In the case of the statement (1) alone: When 120 divided by integer n the remainder equal to √n
Since the value of n = 9 and 120^2, the answers are not unique.
Hence, statement one alone is not sufficient.

In the case of the statement (2) alone: n is a single-digit integer
Since m can be 9 and n can be 7 or m can be 7 and n can be 9, only |n-m| = 2 is possible.
Hence, the remainder becomes 0 and the answer becomes unique.
Therefore, statement two alone is sufficient.

“When 120 is divided by positive single-digit integer m the remainder”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide 2021”. The GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions include a problem statement that is followed by two factual statements. GMAT data sufficiency constitutes a set of 15 questions which are two-fifths of the total 31 GMAT quant questions.

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When 120 is Divided by Positive Single-Digit Integer M the Remainder GMAT Data Sufficiency

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