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# If x, y, and z are consecutive integers and x<y<z, is y an even number

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5271
GMAT 1: 800 Q59 V59
GPA: 3.82
If x, y, and z are consecutive integers and x<y<z, is y an even number [#permalink]

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28 Dec 2017, 23:02
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25% (medium)

Question Stats:

68% (00:59) correct 32% (00:59) wrong based on 53 sessions

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[GMAT math practice question]

If $$x$$, $$y$$, and $$z$$ are consecutive integers and $$x<y<z$$, is $$y$$ an even number?

1) $$xz$$ is an odd number
2) $$xyz$$ is a multiple of $$8$$
[Reveal] Spoiler: OA

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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 27 Dec 2017 Posts: 27 Re: If x, y, and z are consecutive integers and x<y<z, is y an even number [#permalink] ### Show Tags 28 Dec 2017, 23:31 1. Two possibilities a) XZ odd- 5,7,9- consecutive but y is odd b) XZ odd ,5,6,7- consecutive but y is even 2. Consider 4,,5,6- y is odd and xz multiple of 8. Another 4,6,8_ y is even still xz multiple of 8 Combine together- xz are off only when x is odd and z is odd but to make xyz multiple of y , y must be multiple of 8 i.e y is even So answer is C study mode Math Expert Joined: 02 Aug 2009 Posts: 5777 Re: If x, y, and z are consecutive integers and x<y<z, is y an even number [#permalink] ### Show Tags 29 Dec 2017, 01:30 Binggm14 wrote: 1. Two possibilities a) XZ odd- 5,7,9- consecutive but y is odd b) XZ odd ,5,6,7- consecutive but y is even 2. Consider 4,,5,6- y is odd and xz multiple of 8. Another 4,6,8_ y is even still xz multiple of 8 Combine together- xz are off only when x is odd and z is odd but to make xyz multiple of y , y must be multiple of 8 i.e y is even So answer is C study mode consecutive means one after another 5,6,7 5,7,9 would be consecutive ODD integers.. Quote: If x, y, and z are consecutive integers and x<y<z, is y an even number? 1) xz is an odd number ONLY possible when both x and z are odd.. y is between x and z, so it has to be even Suff 2) xyz is a multiple of 8 many ways possible 7,8,9 ...YES 2,3,4 or 8,9,10...NO insuff A _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Manager Joined: 24 Nov 2016 Posts: 148 Re: If x, y, and z are consecutive integers and x<y<z, is y an even number [#permalink] ### Show Tags 29 Dec 2017, 03:30 MathRevolution wrote: [GMAT math practice question] If $$x$$, $$y$$, and $$z$$ are consecutive integers and $$x<y<z$$, is $$y$$ an even number? 1) $$xz$$ is an odd number 2) $$xyz$$ is a multiple of $$8$$ Consecutive integers are integers that follow one another from a given starting point without skipping any integers {-4,-3,-2,-1,0,1,2...}. Any three consecutive integers will have one term that is a multiple of three. Two terms are consecutive integers if their difference is equal to 1 (d = 1). 1) $$xz$$ is an odd number. Then, $$x=odd$$ and $$z=odd$$ because only $$odd*odd=odd$$; So, {x=odd,y=even,z=odd} because they are consecutive; sufficient. 2) $$xyz$$ is a multiple of $$8$$. Then, $$xyz=8*something$$, but could be anything, eg. {x,y,z=2,3,4; 8,9,10; 24,25,26; etc...}; insufficient. (A) is the answer. Intern Joined: 27 Dec 2017 Posts: 27 Re: If x, y, and z are consecutive integers and x[#permalink] ### Show Tags 29 Dec 2017, 19:54 chetan2u wrote: Binggm14 wrote: 1. Two possibilities a) XZ odd- 5,7,9- consecutive but y is odd b) XZ odd ,5,6,7- consecutive but y is even 2. Consider 4,,5,6- y is odd and xz multiple of 8. Another 4,6,8_ y is even still xz multiple of 8 Combine together- xz are off only when x is odd and z is odd but to make xyz multiple of y , y must be multiple of 8 i.e y is even So answer is C study mode consecutive means one after another 5,6,7 5,7,9 would be consecutive ODD integers.. Quote: If x, y, and z are consecutive integers and x<y<z, is y an even number? 1) xz is an odd number ONLY possible when both x and z are odd.. y is between x and z, so it has to be even Suff 2) xyz is a multiple of 8 many ways possible 7,8,9 ...YES 2,3,4 or 8,9,10...NO insuff A Thanks for pointing study mode Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5271 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If x, y, and z are consecutive integers and x<y<z, is y an even number [#permalink] ### Show Tags 01 Jan 2018, 02:16 => 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 3 variables (x,y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. Conditions 1) and 2) Since xz is an odd number, both x and z are odd integers. Since xz is an odd number, it follows from condition 2) that y is a multiple of 8. Therefore, y is an even number. Conditions 1) and 2) are sufficient when taken together. Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A). Condition 1) Since xz is an odd integer, x and z are odd integers. As the three integers are consecutive, y must be even. Thus, condition 1) is sufficient. Condition 2) If x = 7, y = 8, z = 9, the answer is ‘yes’. If x = 2, y = 3, z = 4, the answer is ‘no’. Since we do not have a unique answer, condition 2) is NOT sufficient. Therefore, A is the answer. Normally, in problems which require 2 additional 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. Answer: A _________________ 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 3 month Online Course"
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Re: If x, y, and z are consecutive integers and x<y<z, is y an even number   [#permalink] 01 Jan 2018, 02:16
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