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A function * is defined for all even positive integers n as

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A function * is defined for all even positive integers n as [#permalink] New post 18 Apr 2018, 12:11
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A function \(*\) is defined for all even positive integers n as the number of even factors of n other than n itself.

Quantity A
Quantity B
*(48)
*(122)


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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Re: A function * is defined for all even positive integers n as [#permalink] New post 19 Apr 2018, 03:17
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The question states
*n = Number of even factors of n other than n

Let's look at the definition of the given function here with a simple example:

For example to find *4, we need to find the number of even factors of 4 other than 4 itself.
What is the number of even factors of 4 ?
4 has following factors: 1,2 and 4
2 is the only even factor of 4 apart from 4 itself. That is "number of even factors" of 4 apart from 4 itself is 1

So *4 = 1

Now coming to the question:
Qty A = *48
Factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Number of even factors other than 48 = 7 (2,4,6,8,12,16,24)

Qty A = *122
Factors of 122 are: 1, 2, 61, 122
Number of even factors other than 122 = 1 (2)

Qty A is 7 and Qty B is 1
Correct Answer: Option A
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Re: A function * is defined for all even positive integers n as   [#permalink] 19 Apr 2018, 03:17
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