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# If x and y are integers, is x a multiple of 5?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42
GPA: 3.82
If x and y are integers, is x a multiple of 5?  [#permalink]

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07 Mar 2018, 03:38
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Difficulty:

55% (hard)

Question Stats:

58% (01:55) correct 42% (01:13) wrong based on 54 sessions

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[GMAT math practice question]

If $$x$$ and $$y$$ are integers, is $$x$$ a multiple of $$5$$?

1) $$x+y$$ is a multiple of $$5$$
2) $$x+2y$$ is a multiple of $$5$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 23 May 2017 Posts: 236 Concentration: Finance, Accounting WE: Programming (Energy and Utilities) Re: If x and y are integers, is x a multiple of 5? [#permalink] ### Show Tags 07 Mar 2018, 04:10 1 [1] x + y = 5k (x = 0 ; y = 5 ) Answer = yes (x = 1 ; y = 4 ) Answer = No Hence [1] alone is not sufficient [2] x + 2y = 5m ( x = 0 ; y = 5 ) Answer = yes ( x = 4 ; y = 3) Answer = No Hence [2] alone is not sufficient [1] + [2] x + y + y = 5m 5k + y = 5m so y is a multiple of 5 so from statement 1 : x + y = 5k ; if y is a multiple of 5 , then x must also be multiple of 5 _________________ If you like the post, please award me Kudos!! It motivates me Math Expert Joined: 02 Aug 2009 Posts: 7757 Re: If x and y are integers, is x a multiple of 5? [#permalink] ### Show Tags 07 Mar 2018, 04:50 MathRevolution wrote: [GMAT math practice question] If $$x$$ and $$y$$ are integers, is $$x$$ a multiple of $$5$$? 1) $$x+y$$ is a multiple of $$5$$ 2) $$x+2y$$ is a multiple of $$5$$ Clearly statement 1 and II are insufficient... 1) x+y is a multiple of 5.. Both x and y are multiple of 5.. 5+15 is MULTIPLE of 5.. Both x and y are not a multiple of 5 Insufficient 2) x+2y is a multiple of 5.. Same as above.. Insuff Combined.. Multiple of 5-multiple of 5 has to be a MULTIPLE of 5.. So x+2y-(x+y) should be a MULTIPLE of 5.. x+2y-x-y=y is a multiple of 5.. So x also has to be a MULTIPLE of 5 as seen above.. Sufficient C _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7465 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers, is x a multiple of 5? [#permalink] ### Show Tags 09 Mar 2018, 00:19 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 2 variables ($$x$$ and $$y$$) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables with the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2): $$x = 2(x+y) – (x+2y)$$ is a multiple of $$5$$ since $$2(x+y)$$ and $$(x+2y)$$ are multiples of $$5$$. Thus, both conditions 1) & 2) together are sufficient. Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B. Condition 1) If $$x = 5$$ and $$y = 5$$, $$x$$ is a multiple of $$5$$, and the answer is ‘yes’. If $$x = 2$$ and $$y = 3$$, $$x$$ is not a multiple of $$5$$, and the answer is ‘no’. Thus condition 1) is not sufficient. Condition 2) If $$x = 5$$ and $$y = 5$$, $$x$$ is a multiple of $$5$$, and the answer is ‘yes’. If $$x = 1$$ and $$y = 2$$, $$x$$ is not a multiple of $$5$$, and the answer is ‘no’. Thus condition 2) is not sufficient. Therefore, the answer is C. Answer: C Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E. _________________ 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$149 for 3 month Online Course"
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Re: If x and y are integers, is x a multiple of 5?   [#permalink] 09 Mar 2018, 00:19
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