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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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If x and y are integers, what is the least possible positive value of  [#permalink]

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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

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Manager  S
Joined: 07 Oct 2017
Posts: 249
Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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1
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

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

Thank you = Kudos
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4873
GMAT 1: 770 Q49 V46
Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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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

Cheers,
Brent
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GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4873
GMAT 1: 770 Q49 V46
Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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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

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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Math Revolution GMAT Instructor V
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Posts: 8987
GMAT 1: 760 Q51 V42
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Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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=>

$$21x + 35y = 7*3x + 7*5y = 7(3x+5y)$$ 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.

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

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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

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.

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_________________ Re: If x and y are integers, what is the least possible positive value of   [#permalink] 02 Feb 2020, 22:02

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