For a positive integer p, the index-3 of p is defined as the greatest

Question

For a positive integer p, the index-3 of p is defined as the greatest integer n such that 3^n is factor of p. For example, the index-3 of 54 is 3 as 3 is the greatest exponent of 3 and is a factor of 54. If q and r are positive integers, is the index-3 of q greater than the index-3 of r ?

(1) q − r > 0
(2) q/r is a multiple of 3

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Official Answer

B

(1) q − r > 0
(2) q/r is a multiple of 3

Are You Up For the Challenge: 700 Level Questions

JerryAtDreamScore · Answer

Breaking Down the Info:

We may interpret index-3 as how many multiples of 3 a number contains. Thus in order to know the index-3 of q and r, we might need something like the prime factorization of each number.

Statement 1 Alone:

This doesn't tell us anything about the factors. Insufficient.

Statement 2 Alone:

Assume r has an index-3 of  x . Then since  \frac{q}{r}  is exactly 3, q has exactly one more multiple of 3 compared to r, and q will have an index-3 of  x + 1 . Then q must have a greater index-3. Sufficient.

Answer: B

nikitamishra25 · Answer

statement 1: q could be greater than r , yet not have an extra 3 as its factor. NS
statement 2: q is at least 3 times of r. sufficient
so b

For a positive integer p, the index-3 of p is defined as the greatest

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For a positive integer p, the index-3 of p is defined as the greatest

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