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What is the greatest common divisor of positive integers m a

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by Max@Math Revolution » Fri Jun 21, 2019 12:54 am

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D

E

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[GMAT math practice question]

What is the greatest common divisor of positive integers m and n?

1) m and n are different prime numbers
2) m and n are consecutive integers
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Jun 23, 2019 5:14 pm
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify the conditions if necessary.

Condition 1)
m and n have a unique common divisor since 1 and m are the only factors of m and, 1 and n are the only factors of n. This tells us that gcd(m,n)=1 and condition 1) is sufficient.

Condition 2)
Since the greatest common divisor of consecutive integers is 1, condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
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by deloitte247 » Sat Jun 29, 2019 10:34 am
Statement 1
m and n are different prime numbers
If m = 3 and n = 5 ; h.c.f = 1
If m = 5 and n =7 ; h.c.f = 1
The h.c.f of m and n = 1
Statement 1 is SUFFICIENT.

Statement 2
m and n are consecutive integers
Any two consecutive numbers will be a pair of ODD and EVEN numbers and their H. C. F is always 1

If m = 3 and n = 4 H. C. F = 1
If m = 4 and n = 5 H. C. F = 1
The H. C. F of m and n = 1
Statement 2 is SUFFICIENT.

Each statement alone is SUFFICIENT.
$$Answer\ is\ Option\ D$$
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