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If x^2 is divisible by 160, what is the minimum possible value of

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If x^2 is divisible by 160, what is the minimum possible value of [#permalink]

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Re: If x^2 is divisible by 160, what is the minimum possible value of [#permalink]

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New post 07 Dec 2017, 21:41
X is an integer greater than 0 and X^2 is divisible by 160 .. we can write X^2 as X^2=160*K k is an integer

let us solve this X^2-160K=0 which leads to X=4*Sq.root(10*k)

For x to be integer 10*K must be a perfect square for that to happen minimum possible value of k has to be 10 leading sq.root (10*k) =10

so answer is 4*10=40 i.e C
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Re: If x^2 is divisible by 160, what is the minimum possible value of [#permalink]

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New post 10 Dec 2017, 01:41
Bunuel wrote:
If x^2 is divisible by 160, what is the minimum possible value of integer x?

A. 10
B. 20
C. 40
D. 80
E. 160

These problems make me feel as if I am trying (unsuccessfully) to think in reverse. I used answer choices.

\(x^2\) is divisible by 160.
We need a number, x, that, when squared, is divisible by 160. And we need the smallest x for which that is true. Minimum possible value of \(x\)?

Because we need smallest x, start with smallest answer.

A.10
\(x = 10\)
\(x^2 = 10^2 = 100\)
100 is not divisible by 160. REJECT

B. 20
\(x = 20\). \(x^2 = 20^2 = 400\)
400 is not divisible by 160. REJECT

C. 40
\(x = 40\). \(x^2 = 40^2 = 1,600\)
1,600 IS divisible by 160
\(x = 40\) works.

And \(x = 40\) is smaller than the next two answers' numbers (D = 80 and E = 160), so REJECT Answers D and E.

From these answer choices, the minimum possible integer that x could be is 40.

Answer C

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Re: If x^2 is divisible by 160, what is the minimum possible value of [#permalink]

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New post 10 Dec 2017, 01:51
Bunuel wrote:
If x^2 is divisible by 160, what is the minimum possible value of integer x?

A. 10
B. 20
C. 40
D. 80
E. 160




Get 160 into prime factor with each factor squared if possible as x^2 is being used and x should then be product of these prime factors..
160=\(2^2*2^2*2*5\)..
So x=2*2*2*5=40

Other simpler way would be make use of choices..
10^2=100, not div by 160
20^2=400, again no
40^2=1600, YES

C
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Re: If x^2 is divisible by 160, what is the minimum possible value of   [#permalink] 10 Dec 2017, 01:51
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