GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 04:29

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The integers x, y, and z are consecutive positive even integers and x

Author Message
TAGS:

### Hide Tags

Director
Joined: 08 Jun 2013
Posts: 543
Location: France
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Consulting (Other)
The integers x, y, and z are consecutive positive even integers and x  [#permalink]

### Show Tags

23 Sep 2018, 04:17
1
3
00:00

Difficulty:

65% (hard)

Question Stats:

57% (02:04) correct 43% (01:46) wrong based on 72 sessions

### HideShow timer Statistics

The integers x, y, and z are consecutive positive even integers and x < y < z. Which of the following statements must be true?

I) x + y + z is a multiple of 9.

II) 2Z = x + y + 6

III) xyz is a multiple of 48.

A) I only
B) II only
C) III only
D) II and III only
E) I, II, and III

_________________
Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
It will all make sense.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: The integers x, y, and z are consecutive positive even integers and x  [#permalink]

### Show Tags

23 Sep 2018, 07:44
Harshgmat wrote:
The integers x, y, and z are consecutive positive even integers and x < y < z. Which of the following statements must be true?

I) x + y + z is a multiple of 9.

II) 2Z = x + y + 6

III) xyz is a multiple of 48.

A) I only
B) II only
C) III only
D) II and III only
E) I, II, and III

$$\left. \matrix{ x = 2M \hfill \cr y = 2\left( {M + 1} \right)\,\,\, \hfill \cr z = 2\left( {M + 2} \right) \hfill \cr} \right\}\,\,\,\,\,\,M \ge 1\,\,\,{\mathop{\rm int}}$$

$$?\,\,\,:\,\,\,{\rm{true}}$$

$${\rm{I}}.\,\,\,\,{\rm{Take }}\left( {x,y,z} \right) = \left( {2,4,6} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\, \Rightarrow \,\,\,\,{\rm{Refute}}\,\,\left( A \right)\,\,{\rm{and}}\,\,\left( E \right)$$

$${\rm{II}}.\,\,\,\,\,\left\{ {\matrix{ {2z = 4\left( {M + 2} \right) = 4M + 8} \cr {x + y + 6 = 4M + 2 + 6} \cr } } \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\, \Rightarrow \,\,\,\,{\rm{Refute}}\,\,\left( C \right)$$

$${\rm{III}}.\,\,\,xyz = {2^3} \cdot M\left( {M + 1} \right)\left( {M + 2} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( D \right)$$

$$\left( * \right)\,\,\,\,M\left( {M + 1} \right)\left( {M + 2} \right)\,\,\,{\rm{is}}\,\,\,\left\{ \matrix{ \,{\rm{even}} \hfill \cr {\rm{multiple}}\,\,{\rm{of}}\,\,3 \hfill \cr} \right.\,\,$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Director
Joined: 08 Jun 2013
Posts: 543
Location: France
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Consulting (Other)
Re: The integers x, y, and z are consecutive positive even integers and x  [#permalink]

### Show Tags

03 Oct 2018, 09:06
Kaplan OE :

Statement I: If , , and , then . Since 12 is not a multiple of 9, statement I does not have to be true. Eliminate choices (A) and (E).

Statement II: If , , and , then . If , , and , then . If we test any other set of 3 consecutive even integers, we will find that . So statement II will be part of the correct answer. Eliminate choice (C).

Statement III: If x = 2, y = 4, and z = 6, then xyz = (2)(4)(6) = 48, which is a multiple of 48. If x = 4, y = 6, and z = 8, then xyz = (4)(6)(8) = 192, which is also a multiple of 48. If we test any other set of 3 consecutive even integers, we will find that xyz is a multiple of 48. So statement III must be part of the correct answer. Choice (D), II and III only, is correct.
_________________
Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
It will all make sense.
Non-Human User
Joined: 09 Sep 2013
Posts: 13316
Re: The integers x, y, and z are consecutive positive even integers and x  [#permalink]

### Show Tags

13 Oct 2019, 18:21
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.
_________________
Re: The integers x, y, and z are consecutive positive even integers and x   [#permalink] 13 Oct 2019, 18:21
Display posts from previous: Sort by