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If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where

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Bunuel
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If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where [#permalink] New post  28 Apr 2016, 01:08
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If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?

A. 198
B. 288
C. 363
D. 396
E. 484
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Re: If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where [#permalink] New post  28 Apr 2016, 02:44
Bunuel wrote:
If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?

A. 198
B. 288
C. 363
D. 396
E. 484


I will go with D (pending elements to match is 2^2*3^2*11^1 = 396
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Re: If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where [#permalink] New post  13 Apr 2020, 05:59
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Bunuel wrote:
If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?

A. 198
B. 288
C. 363
D. 396
E. 484


    \(\frac{1452*w}{2^4*3^3*11^3}\) = integer
    \(1452 = 2^2*3*11^2\)
      \(\frac{1452*w}{2^4*3^3*11^3} = \frac{2^2*3*11^2*w}{2^4*3^3*11^3}\)
      \(\frac{w}{2^2*3^2*11} = integer\)
    The minimum possible positive value of w is when, the value of integer is minimum positive value i.e., 1
      \(\frac{w}{2^2*3^2*11} = 1\)
      \(w =2^2*3*11 = 4*9*11=396\)
Answer: Option D.
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Re: If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where [#permalink] New post  15 Apr 2020, 11:27
1452=2^2∗3∗11^2
2^4, 3^3, and 11^3 are factors of the product of 1,452 and w,
so, 2^4 ∗ 3^3 ∗ 11^3 = 2^2 ∗ 3 ∗ 11^2 ∗ w
or, w= 2^2 ∗ 3^2 ∗ 11 = 4 ∗ 9 ∗ 11 =396

correct answer D
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Re: If 2^4, 3^3, and 11^3 are factors of the product of 1,452 and w, where [#permalink]
15 Apr 2020, 11:27
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