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If m and n are positive integers, what is the greatest commo

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by Max@Math Revolution » Thu Nov 29, 2018 1:34 am

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[Math Revolution GMAT math practice question]

If m and n are positive integers, what is the greatest common divisor of m and n?

1) m=n+1
2) m*n is divisible by 2
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by fskilnik@GMATH » Thu Nov 29, 2018 7:20 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If m and n are positive integers, what is the greatest common divisor of m and n?

1) m=n+1
2) m*n is divisible by 2
$$m,n\,\, \geqslant 1\,\,{\text{ints}}$$
$${\text{?}}\,\,{\text{ = }}\,\,{\text{GCD}}\left( {m,n} \right)$$

$$\left( 1 \right)\,\,\,m = n + 1\,\,\,\,\, \Rightarrow \,\,\,\,? = 1\,\,\,\,\,\left( {{\rm{consecutive}}\,\,{\rm{positive}}\,\,{\rm{integers}}\,\,{\rm{are}}\,\,{\rm{always}}\,\,{\rm{relatively}}\,\,{\rm{prime}}} \right)$$

$$\left( 2 \right)\,\,\,{{m \cdot n} \over 2} = {\mathop{\rm int}} \,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {1,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 1\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 2\,\, \hfill \cr} \right.\,\,$$

The correct answer is therefore (A).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by fskilnik@GMATH » Thu Nov 29, 2018 7:20 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If m and n are positive integers, what is the greatest common divisor of m and n?

1) m=n+1
2) m*n is divisible by 2
$$m,n\,\, \geqslant 1\,\,{\text{ints}}$$
$${\text{?}}\,\,{\text{ = }}\,\,{\text{GCD}}\left( {m,n} \right)$$

$$\left( 1 \right)\,\,\,m = n + 1\,\,\,\,\, \Rightarrow \,\,\,\,? = 1\,\,\,\,\,\left( {{\rm{consecutive}}\,\,{\rm{positive}}\,\,{\rm{integers}}\,\,{\rm{are}}\,\,{\rm{always}}\,\,{\rm{relatively}}\,\,{\rm{prime}}} \right)$$

$$\left( 2 \right)\,\,\,{{m \cdot n} \over 2} = {\mathop{\rm int}} \,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {1,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 1\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 2\,\, \hfill \cr} \right.\,\,$$

The correct answer is therefore (A).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Sun Dec 02, 2018 5:39 pm
=>

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.

Since two consecutive integers are always relatively prime, the greatest common divisor of m and n is 1. Thus, condition 1) is sufficient.

Condition 2)
If m = 2 and n = 3, then the greatest common divisor of m and n is 1.
If m = 2 and n = 4, then the greatest common divisor of m and n is 2.
Thus, condition 2) is not sufficient since it does not yield a unique solution.

Therefore, the correct answer is A.
Answer: A
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