If m and n are positive integers...

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BTGmoderatorLU: Moderator; Posts: 2550; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Oct 17, 2017 6:28 pm

If m and n are positive integers, is$$\sqrt{n-m}$$an integer?

(1) n>m+15
(2) n=m(m+1)

The OA is B.

Can any expert explain this PS question please? I don't understand. Thanks.

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Source: Beat The GMAT — Data Sufficiency | Tue Oct 17, 2017 6:28 pm

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Wed Oct 18, 2017 7:51 am

LUANDATO wrote:If m and n are positive integers, is$$\sqrt{n-m}$$an integer?

(1) n>m+15
(2) n=m(m+1)

The OA is B.

Can any expert explain this PS question please? I don't understand. Thanks.

S1: Pick some easy numbers
If m = 1, then n > 16
Case 1: m =1 and n = 17. âˆš (17-1) = âˆš 16 = 4; YES, we have an integer
Case 2: m =1 and n = 18. âˆš (18-1) = âˆš 17, NO, we don't have an integer. S1 alone is not sufficient.

S2: n = m^2 + m. so âˆš (n - m) = âˆš( m^2 + m - m) = âˆš (m^2) = m; because we're told that m is an integer, we know that the answer to the question is YES, so S2 alone is sufficient. The answer is B

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