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Determine how many factors y has

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Determine how many factors y has  [#permalink]

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New post 03 Nov 2018, 15:38
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Which of the following statement(s) will support the ability to determine how many factors y has?

y is the cube of an integer.
y is the product of two distinct positive digits.


It says that C is the correct answer. Here is the explanation:

    No information is given about y in the question prompt so the statements must be analyzed for clues about the factors of y.

    Statement (1) indicates that y is an integer, but without knowing more, the number of factors cannot be determined.

    Statement (2) indicates that y is either 2, 3, 4, 5, 6, 7, 8, 9 (1 × any digit), or the product of any 2 distinct digits (such as 2 × 3, 3 × 5). The largest possible value is 8 × 9, which is equal to 72.

    Statements (1) and (2) together indicate that y is the product of 2 distinct digits that is also the cube of an integer, which means it could only be 8(2³ or 2 × 4) or 27(3³ or 3 × 9), both of which have 4 factors.


I don't understand how they've deducted that from statement two. There isn't anything saying that it is the product of two single digit numbers. Under the statements, wouldn't it be possible for y to be 4^3? That would be 64 which is still the product of two distinct digits (ex. 2 and 32).
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Re: Determine how many factors y has  [#permalink]

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New post 03 Nov 2018, 19:14
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You just have a terminology issue.
The digits are 0-9.
two distinct positive digits:
two distinct means two different
two distinct positive means two numbers that are different above 0
two distinct positive digits means 1 through to 9 (can't be 0)

11 is not a digit. it contains two digits

It can't be 64 as the only two digits that multiply to 64 are 8x8=64, but those are not distinct.
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Re: Determine how many factors y has  [#permalink]

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New post 04 Nov 2018, 09:45
Hi joejoe4868,

If you want to learn more about number properties, visit the following link:

Number theory

Hope this helps!
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Determine how many factors y has  [#permalink]

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New post 04 Nov 2018, 10:15
joejoe4868 wrote:
Which of the following statement(s) will support the ability to determine how many factors y has?

y is the cube of an integer.
y is the product of two distinct positive digits.


It says that C is the correct answer. Here is the explanation:

    No information is given about y in the question prompt so the statements must be analyzed for clues about the factors of y.

    Statement (1) indicates that y is an integer, but without knowing more, the number of factors cannot be determined.

    Statement (2) indicates that y is either 2, 3, 4, 5, 6, 7, 8, 9 (1 × any digit), or the product of any 2 distinct digits (such as 2 × 3, 3 × 5). The largest possible value is 8 × 9, which is equal to 72.

    Statements (1) and (2) together indicate that y is the product of 2 distinct digits that is also the cube of an integer, which means it could only be 8(2³ or 2 × 4) or 27(3³ or 3 × 9), both of which have 4 factors.


I don't understand how they've deducted that from statement two. There isn't anything saying that it is the product of two single digit numbers. Under the statements, wouldn't it be possible for y to be 4^3? That would be 64 which is still the product of two distinct digits (ex. 2 and 32).


joejoe4868
The ten digits of the decimal system are: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
64 is a 2 digit number,2 digits being 6 and 4.
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Re: Determine how many factors y has  [#permalink]

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New post 13 Nov 2018, 17:22
Thanks Phillip, that makes sense.
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Re: Determine how many factors y has &nbs [#permalink] 13 Nov 2018, 17:22
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