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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # If x and y are integers, what is the least possible positive value of  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6504 GMAT 1: 760 Q51 V42 GPA: 3.82 If x and y are integers, what is the least possible positive value of [#permalink] ### Show Tags 03 Sep 2018, 23:27 00:00 Difficulty: 15% (low) Question Stats: 80% (01:14) correct 20% (01:07) wrong based on 55 sessions ### HideShow timer Statistics [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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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03 Sep 2018, 23:41
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)

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

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04 Sep 2018, 12:55
1
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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Re: If x and y are integers, what is the least possible positive value of  [#permalink]

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04 Sep 2018, 13:04
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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06 Sep 2018, 00:34
=>

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

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

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07 Sep 2018, 16:20
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.

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Re: If x and y are integers, what is the least possible positive value of &nbs [#permalink] 07 Sep 2018, 16:20
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