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For positive integers x, y, and z, the function x * y * z means that

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For positive integers x, y, and z, the function x * y * z means that  [#permalink]

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New post 10 Feb 2019, 04:38
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For positive integers x, y, and z, the function x * y * z means that \(\frac{z}{x^y}\) is an integer, but z/x ^(y+1) is not. If x * 2 * 144, then which of the following is NOT a possible value of x ?

A. 2
B. 3
C. 4
D. 6
E. 12

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Re: For positive integers x, y, and z, the function x * y * z means that  [#permalink]

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New post 10 Feb 2019, 04:54
SajjadAhmad wrote:
For positive integers x, y, and z, the function x * y * z means that \(\frac{z}{x^y}\) is an integer, but z/x ^(y+1) is not. If x * 2 * 144, then which of the following is NOT a possible value of x ?

A. 2
B. 3
C. 4
D. 6
E. 12



144= 2^4*3^2

so only at x = 2
z/x ^(y+1) this would be an integer
IMO A
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Re: For positive integers x, y, and z, the function x * y * z means that  [#permalink]

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New post 10 Feb 2019, 06:57
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SajjadAhmad wrote:
For positive integers x, y, and z, the function x * y * z means that \(\frac{z}{x^y}\) is an integer, but z/x ^(y+1) is not. If x * 2 * 144, then which of the following is NOT a possible value of x ?

A. 2
B. 3
C. 4
D. 6
E. 12


IMO A

144 = \(2^4 * 3^2\)

\(2^4 * 3^2\)/ x^2 is an Integer --------------(a)

\(2^4 * 3^2\) / x^3 is not an Integer --------------------(b)

x*2*144, To find not a possible value of x

So start from C and substitute for x , (a) Satisfied, (b) not satisfied

A (a) is Satisfied and even (b) is satisfied

Goes against the case (b)
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Re: For positive integers x, y, and z, the function x * y * z means that   [#permalink] 10 Feb 2019, 06:57
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