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16 Sep 2014, 00:28
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If \(m\) is a positive integer, is \(\sqrt{m} \gt 25\)?
(1) \(m\) is divisible by 50
(2) \(m\) is divisible by 52
(1) \(m\) is divisible by 50
(2) \(m\) is divisible by 52
16 Sep 2014, 00:28
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Official Solution:
If \(m\) is a positive integer, is \(\sqrt{m} \gt 25\)?
Square both sides: is \(m \gt 625\)?
(1) \(m\) is divisible by 50.
\(m\) can be 50, which is less than 625, as well as 5,000, which is more than 625. Not sufficient.
(2) \(m\) is divisible by 52.
\(m\) can be 52, which is less than 625, as well as 5,200, which is more than 625. Not sufficient.
(1)+(2) Since \(m\) is a multiple of both 50 and 52, it's a multiple of the least common multiple (LCM) of these two numbers, thus a multiple of 1,300. Given that \(m\) is a positive integer, the smallest value of \(m\) is 1,300, so \(m \gt 625\). Sufficient.
Answer: C
If \(m\) is a positive integer, is \(\sqrt{m} \gt 25\)?
Square both sides: is \(m \gt 625\)?
(1) \(m\) is divisible by 50.
\(m\) can be 50, which is less than 625, as well as 5,000, which is more than 625. Not sufficient.
(2) \(m\) is divisible by 52.
\(m\) can be 52, which is less than 625, as well as 5,200, which is more than 625. Not sufficient.
(1)+(2) Since \(m\) is a multiple of both 50 and 52, it's a multiple of the least common multiple (LCM) of these two numbers, thus a multiple of 1,300. Given that \(m\) is a positive integer, the smallest value of \(m\) is 1,300, so \(m \gt 625\). Sufficient.
Answer: C
General Discussion
13 Mar 2016, 03:14
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Small question here just to clarify.
If in the question stem were written only m is an integer (without positive), could we pick as a value for m: m=0? Because in principle 0 is divisible by 50 and 52...so in this case the answer would be E. Is this right?
Thanks
If in the question stem were written only m is an integer (without positive), could we pick as a value for m: m=0? Because in principle 0 is divisible by 50 and 52...so in this case the answer would be E. Is this right?
Thanks
