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If x and y are integers, what is the least possible positive value of

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Math Revolution GMAT Instructor
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If x and y are integers, what is the least possible positive value of  [#permalink]

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New post 04 Sep 2018, 00:27
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[Math Revolution GMAT math practice question]

If x and y are integers, what is the least possible positive value of 21x+35y?

A. 1
B. 3
C. 5
D. 7
E. 9
Spoiler: OA

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Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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New post 04 Sep 2018, 00:41
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If x and y are integers, what is the least possible positive value of 21x+35y?

A. 1
B. 3
C. 5
D. 7
E. 9
We need least positive value. That means 35y is greater than 21x
Y will be positive and x will be negative.

Possible values of y= 35,70,105,140,175
Possible values of x= - 21, - 42, - 63, - 84, - 105, - 126, - 147

Least possible POSITIVE value = 70 - 63 = 7

Answer is D
( NOTE : 0 is neither positive nor negative integer. It is just even integer)

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Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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New post 04 Sep 2018, 13:55
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Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If x and y are integers, what is the least possible positive value of 21x+35y?

A. 1
B. 3
C. 5
D. 7
E. 9


21x + 35y = 7(3x + 5y)

Since x and y are INTEGERS, we know that 3x and 5y are each INTEGERS, which means 3x + 5y equals some integer
So, we can write: 21x + 35y = 7(some integer)
In other words, 21x + 35y is a multiple of 7

Check the answer choices.....only D is a multiple of 7

Answer: D

Cheers,
Brent
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Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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New post 04 Sep 2018, 14:04
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If x and y are integers, what is the least possible positive value of 21x+35y?

A. 1
B. 3
C. 5
D. 7
E. 9


Another approach:

There's a nice rule that says:
If j, k and d are integers, and j is a multiple of d, and k is a multiple of d, then (j+k) must be a multiple of d

21x is a multiple of 7, since 21x = 7(3x)
35y is a multiple of 7, since 35y = 7(5y)

Since 21x and 35y are multiples of 7, the sum 21x + 35y must be a multiple of 7.
Since only 1 answer choice (D) is a multiple of 7, D must be the correct answer.

Cheers,
Brent
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Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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New post 06 Sep 2018, 01:34
=>

\(21x + 35y = 7*3x + 7*5y = 7(3x+5y)\) is a multiple of \(7\). The smallest positive multiple of \(7\) is \(7\). So, we look for \(x\) and \(y\) such that \(21x + 35y = 7\). This will occur when \(3x + 5y = 1\).
When \(x = 2\) and \(y = -1, 3x + 5y = 3*2 + 5*(-1) = 6 – 5 = 1\), and \(21x + 35y = 7(3x+5y) = 7(1) = 7.\)
Thus, \(7\) is the answer.

Therefore, the answer is D.
Answer: D
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Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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New post 07 Sep 2018, 17:20
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If x and y are integers, what is the least possible positive value of 21x+35y?

A. 1
B. 3
C. 5
D. 7
E. 9


Since x and y are integers and 21x + 35y = 7(3x + 5y), we see that the answer must be a multiple of 7. Therefore, D is the correct answer.

Answer: D
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