OG 12 Diagnostic #44 is:
If m and n are positive integers, is [sqrt(m)]^n an integer?
(1) sqrt(m) is an integer
(2) sqrt(n) is an integer
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hi Venmic,
The 1st statement is sufficient because it tells us that the base of the question stem is an integer, so [sqrt(m)]^n is an integer^n. The result will always be an integer (because n is an integer).
The 2nd statement is not sufficient because although it guarantees that n itself is an integer (a perfect square), the base of the question stem could be an integer (which would make the whole expression an integer) or a weird decimal.
The answer is A. A fuller explanation is attached along with take-away lesson from the OG 12 Companion. Those who cannot see the attachment can
read it here.
If you have trouble with this type of problems, practice similar questions by setting topic='Number Properties & Exponents & Roots' and difficulty='500-600' in the Drill Generator
-Patrick
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Attachments
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- OG12 Companion-T044.pdf
- (70.76 KiB) Downloaded 85 times
