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# Can the total number of integers that divide x be express

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Re: Can the total number of integers that divide x be express [#permalink]
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D.
Question asked if the x has odd number total of factors.
S1: Plug in x = 3 & x = 27 --> both get √12x integer and both 3, 27 have even number total of factors. Sufficient
S2: y/3 has odd number total of factors --> y = 3A (with A is prime factorize of Y/3) --> y has even number total of factors.
In order for √xy integer, x must have odd exponent --> x has even number total of factors. Sufficient
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Re: Can the total number of integers that divide x be express [#permalink]
dunghoang110 wrote:
D.
Question asked if the x has odd number total of factors.
S1: Plug in x = 3 & x = 27 --> both get √12x integer and both 3, 27 have even number total of factors. Sufficient
S2: y/3 has odd number total of factors --> y = 3A (with A is prime factorize of Y/3) --> y has even number total of factors.
In order for √xy integer, x must have odd exponent --> x has even number total of factors. Sufficient

Good solution.

Just exploring possible s1 without testing numbers:
Another way to think of S1 is sqrt(12x)=sqrt(2².3.x), which means x has to have an odd number of 3 factors. (3^1, 3^3, 3^5, ...), which means no x will have an odd total number of factors.
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Re: Can the total number of integers that divide x be express [#permalink]
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Re: Can the total number of integers that divide x be express [#permalink]
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