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If x and y are positive integers and xy=36, what is the smallest possi

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Math Revolution GMAT Instructor
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If x and y are positive integers and xy=36, what is the smallest possi  [#permalink]

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New post 27 Aug 2018, 02:42
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[Math Revolution GMAT math practice question]

If \(x\) and \(y\) are positive integers and \(xy=36\), what is the smallest possible value of \(x+y\)?

\(A. 6\)
\(B. 8\)
\(C. 10\)
\(D. 12\)
\(E. 18\)

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Re: If x and y are positive integers and xy=36, what is the smallest possi  [#permalink]

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New post 27 Aug 2018, 02:53
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x\) and \(y\) are positive integers and \(xy=36\), what is the smallest possible value of \(x+y\)?

\(A. 6\)
\(B. 8\)
\(C. 10\)
\(D. 12\)
\(E. 18\)



Always remember that for any product xy, the minimum sum x+y is when x=y
So xy =36 and it X=y, x^2=36 or X=6 and thus y =6
x+y =6+6=12

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x and y are positive integers and xy=36, what is the smallest possi  [#permalink]

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New post 27 Aug 2018, 04:51
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x\) and \(y\) are positive integers and \(xy=36\), what is the smallest possible value of \(x+y\)?

\(A. 6\)
\(B. 8\)
\(C. 10\)
\(D. 12\)
\(E. 18\)


Possible options for x and y:
1 and 36
2 and 18
3 and 12
4 and 9
6 and 6

6 + 6 = 12

Answer: D
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Re: If x and y are positive integers and xy=36, what is the smallest possi  [#permalink]

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New post 29 Aug 2018, 01:55
=>

When we know the product of two numbers, the sum of those numbers is a minimum when the two numbers are equal.

Since \(xy = 36\), the minimum value of \(x + y\)occurs when \(x = y = 6\). It is \(6 + 6 = 12\).

Therefore, D is the answer.
Answer: D
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Re: If x and y are positive integers and xy=36, what is the smallest possi &nbs [#permalink] 29 Aug 2018, 01:55
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