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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
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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03 Sep 2018, 23:27
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15% (low)

Question Stats:

82% (01:32) correct 18% (01:50) wrong based on 109 sessions

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 07 Oct 2017 Posts: 249 Re: If x and y are integers, what is the least possible positive value of [#permalink] ### Show Tags 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 Answer is D ( NOTE : 0 is neither positive nor negative integer. It is just even integer) Thank you = Kudos GMAT Club Legend Joined: 11 Sep 2015 Posts: 4873 Location: Canada GMAT 1: 770 Q49 V46 Re: If x and y are integers, what is the least possible positive value of [#permalink] ### Show Tags 04 Sep 2018, 12:55 4 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 _________________ Test confidently with gmatprepnow.com GMAT Club Legend Joined: 11 Sep 2015 Posts: 4873 Location: Canada GMAT 1: 770 Q49 V46 Re: If x and y are integers, what is the least possible positive value of [#permalink] ### Show Tags 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 _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8987 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers, what is the least possible positive value of [#permalink] ### Show Tags 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. Therefore, the answer is D. Answer: D _________________ 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$79 for 1 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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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  [#permalink]

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02 Feb 2020, 22:02
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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