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# If x, y, and z are consecutive integers such that x > y > z

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Senior Manager
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If x, y, and z are consecutive integers such that x > y > z [#permalink]

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21 Jul 2013, 08:55
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Difficulty:

65% (hard)

Question Stats:

51% (02:41) correct 49% (01:11) wrong based on 193 sessions

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If x, y, and z are consecutive integers such that x > y > z and the sum of x, y, and z is a multiple of 10, which of the following could be the value of x?

A. 0
B. 1
C. 9
D. 10
E. 12

[Reveal] Spoiler:
Guys I think 2 answers are correct. What do you come up with?
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Jul 2013, 09:19, edited 1 time in total.
Edited the question.
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Kudos [?]: 106471 [0], given: 11626

Re: If x, y, and z are consecutive integers such that x > y > z [#permalink]

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21 Jul 2013, 09:19
vibhav wrote:
If x, y, and z are consecutive integers such that x > y > z and the sum of x, y, and z is a multiple of 10, which of the following could be the value of x?

A. 0
B. 1
C. 9
D. 10
E. 12

[Reveal] Spoiler:
Guys I think 2 answers are correct. What do you come up with?

Given that $$z + y +x = (y-1) + y + (y+1) = 3y = 10k$$ --> $$y$$ is a multiple of 10 --> $$x = y+1$$, so x is a multiple of 10 plus 1. Only answer choices B fits: $$z=-1$$, $$y=0$$, and $$z=1$$ --> $$z+y+x=0$$.

Else you could simply plug-in values for x in (x-2) + (x-1) + x and see which one yields a multiple of 10.
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Kudos [?]: 230 [0], given: 33

Re: If x, y, and z are consecutive integers such that x > y > z [#permalink]

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21 Jul 2013, 09:53
Bunuel why can't it be 11,10,9 totals to 30 which is divisible by 10?
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Kudos [?]: 106471 [0], given: 11626

Re: If x, y, and z are consecutive integers such that x > y > z [#permalink]

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21 Jul 2013, 09:54
vibhav wrote:
Bunuel why can't it be 11,10,9 totals to 30 which is divisible by 10?

Yes, x could be 11, but 11 is not among the options.
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Re: If x, y, and z are consecutive integers such that x > y > z [#permalink]

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15 Dec 2014, 05:01
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Re: If x, y, and z are consecutive integers such that x > y > z [#permalink]

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23 Dec 2014, 11:20
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Expert's post
Hi All,

This question can be easily beaten by a bit of "brute force" and TESTing THE ANSWERS.

We're given a very specific set of restrictions in this prompt:
1) X, Y and Z are CONSECUTIVE INTEGERS
2) X > Y > Z
3) X+Y+Z = a multiple of 10

We're asked which of the 5 answer COULD be the value of X given these restrictions. Rather than staring at the screen or doing layered math, we can "brute force" the answers until we find one that fits these restrictions..

In this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.

In this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.

[Reveal] Spoiler:
B

For the sake of argument, if you did not immediately realize that 0 is a multiple of 10, then you could quickly TEST the remaining 3 options and quickly disprove them.

GMAT assassins aren't born, they're made,
Rich
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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Senior Manager Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 441 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Followers: 2 Kudos [?]: 123 [0], given: 169 Re: If x, y, and z are consecutive integers such that x > y > z [#permalink] ### Show Tags 25 Dec 2014, 09:20 I did it this way, which might be a bit similar in a way: 1) Since they are consecutive integers, these could be: x, x-1, x-2 (x>y>z) 2) I added them to give 0 (the 1st multiple of 10, if we say that they add up to 0*Unckown value): x+x-1+x-2=0 3x-3=0 3x=3 x=3/3 x=1, Answer is B EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9125 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 445 Kudos [?]: 2876 [0], given: 169 Re: If x, y, and z are consecutive integers such that x > y > z [#permalink] ### Show Tags 25 Dec 2014, 10:42 Hi pacifist85, Your approach works here, but ONLY because 0 is the multiple of 10 that is involved in the correct answer. If it was any other multiple of 10, then you would have only gotten the solution by "brute forcing" your equation into every possible multiple of 10. eg. 3x - 3 = 10 3x - 3 = 20 3x - 3 = 30 Etc. Since these answer choices in this question are all relatively small, even if you did have to brute force multiple possibilities, you would have gotten to the answer relatively quickly, so I think that your approach is fine. In the end, I measure any approach by 2 things: 1) Did it get you the correct answer. 2) Were you able to complete the question relatively quickly (for that prompt). If the answer to both questions is YES, then you did well. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: If x, y, and z are consecutive integers such that x > y > z [#permalink]

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05 Apr 2016, 11:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If x, y, and z are consecutive integers such that x > y > z   [#permalink] 05 Apr 2016, 11:21
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