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How many factors does y have?

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Source: — Data Sufficiency |

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by [email protected] » Fri Nov 24, 2017 10:54 am
Hi lheiannie07,

We're asked for the number of factors that Y has.

1) Y is the CUBE of an integer.

IF....
Y = 1, then Y has 1 factor (1)
Y = 8, then Y has 4 factors (1, 2, 4 and 8)
Fact 1 is INSUFFICIENT

2) Y is the product of 2 distinct positive digits.

IF...
Y = 2, then Y has 2 factors (1 and 2)
Y = 8, then Y has 4 factors (1, 2, 4 and 8)
Fact 2 is INSUFFICIENT

Combined, we know...
Y is a CUBE
Y is limited by Fact 2 to the product of 2 SINGLE-DIGIT integers. (for example: 8 is possible, since 8 = 2 x 4; 100 is NOT possible since you cannot get to 100 by multiplying two 1-digit numbers).

The number of possible cubes worth considering is limited: 1, 8, 27, 64, 125

1, 64 and 125 do NOT fit the 'restrictions' given by the two Facts - so we're left with just 8 and 27
IF....
Y = 8, then Y has 4 factors (1, 2, 4 and 8)
Y = 27, then Y has 4 factors (1, 3, 9 and 27)
The answer is ALWAYS 4.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by BTGmoderatorDC » Wed Jan 17, 2018 9:33 pm
[email protected] wrote:Hi lheiannie07,

We're asked for the number of factors that Y has.

1) Y is the CUBE of an integer.

IF....
Y = 1, then Y has 1 factor (1)
Y = 8, then Y has 4 factors (1, 2, 4 and 8)
Fact 1 is INSUFFICIENT

2) Y is the product of 2 distinct positive digits.

IF...
Y = 2, then Y has 2 factors (1 and 2)
Y = 8, then Y has 4 factors (1, 2, 4 and 8)
Fact 2 is INSUFFICIENT

Combined, we know...
Y is a CUBE
Y is limited by Fact 2 to the product of 2 SINGLE-DIGIT integers. (for example: 8 is possible, since 8 = 2 x 4; 100 is NOT possible since you cannot get to 100 by multiplying two 1-digit numbers).

The number of possible cubes worth considering is limited: 1, 8, 27, 64, 125

1, 64 and 125 do NOT fit the 'restrictions' given by the two Facts - so we're left with just 8 and 27
IF....
Y = 8, then Y has 4 factors (1, 2, 4 and 8)
Y = 27, then Y has 4 factors (1, 3, 9 and 27)
The answer is ALWAYS 4.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Thanks a lot!
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