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If m is a positive integer less than 200, what is the greate

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by Max@Math Revolution » Sun Jun 05, 2016 5:12 am
If m is a positive integer less than or equal to 200, what is the greatest prime factor of m?
1) 40 is a factor of m.
2) 50 is a factor of m.

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Last edited by Max@Math Revolution on Mon Jun 06, 2016 8:51 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Sun Jun 05, 2016 10:33 am
Max@Math Revolution wrote:If m is a positive integer less than 200, what is the greatest prime factor of m?
1) 40 is a factor of m.
2) 70 is a factor of m.

*An answer will be posted in 2 days.
I think this question is missing the mark.
There's no such positive integer m that's less than 200 AND has both 40 and 70 as factors.

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by Max@Math Revolution » Mon Jun 06, 2016 8:51 pm
If we modify the original condition and the question, we get 2*3*5=30, 2*3*5*7=210. There is one variable (m), hence, we need 1 equation. Hence, there is high chance that D is the correct answer.
In the case of the condition 1), from m=40(int)=(23)(5)(int), 5 is the greatest prime factor. This is because if we multiply 7, it becomes over 200. Hence, it is sufficient.
In the case of the condition 2), from m=50(int)=(2)(5)(7)(int), 7 is the greatest prime factor. This is because if we multiply 11, it becomes over 200. Hence, it is sufficient.
Therefore, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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by Brent@GMATPrepNow » Tue Jun 07, 2016 8:38 am
Max@Math Revolution wrote:If we modify the original condition and the question, we get 2*3*5=30, 2*3*5*7=210. There is one variable (m), hence, we need 1 equation. Hence, there is high chance that D is the correct answer.
In the case of the condition 1), from m=40(int)=(23)(5)(int), 5 is the greatest prime factor. This is because if we multiply 7, it becomes over 200. Hence, it is sufficient.
In the case of the condition 2), from m=50(int)=(2)(5)(7)(int), 7 is the greatest prime factor. This is because if we multiply 11, it becomes over 200. Hence, it is sufficient.
Therefore, the correct answer is D.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
I see that you changed statement 1 from 70 to 50. That's good, since the original statements contradicted each other.
If anyone wants to know what I mean by that, see this video titled "Useful Contradictions": https://www.gmatprepnow.com/module/gmat- ... cy?id=1104


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