It is currently 17 Oct 2017, 23:18

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If y is the average of x odd consecutive integers and |z - 6/4| = 1/2,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 07 Sep 2014
Posts: 16

Kudos [?]: 36 [0], given: 132

Location: United States
GMAT Date: 03-14-2015
GMAT ToolKit User
If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 08 Mar 2015, 10:01
20
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

70% (02:34) correct 30% (02:43) wrong based on 472 sessions

HideShow timer Statistics

If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, which of the following MUST be true?

I. xy(z + 1) is even.

II. x(z + y) is even.

III. (x^2 - x)yz is even.

(A) I only
(B) III only
(C) I and II
(D) II and III
(E) I, II, and III
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Mar 2015, 10:54, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 36 [0], given: 132

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128641 [2], given: 12181

Re: If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 08 Mar 2015, 11:07
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
vinyasgupta wrote:
If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, which of the following MUST be true?

I. xy(z + 1) is even.

II. x(z + y) is even.

III. (x^2 - x)yz is even.

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


If x is even, then the average of even number of odd consecutive integers (y), will be even. For example, the average of {1, 3} is 2.
If x is odd, then the average of odd number of odd consecutive integers (y), will be odd. For example, the average of {1, 3, 5} is 3.

Thus:
If x = even, then y = even;
If x = odd, then y = odd.

Next, |z - 6/4| = 1/2:
z - 6/4 = 1/2 --> z = 2;
-(z - 6/4) = 1/2 --> z = 1.
Since, z can be even as well as odd, then it takes no part in deciding whether the options are even or odd. So, we can ignore it.


I. xy(z + 1) is even: xy can be odd if both are odd and even if both are even. So, this option is not necessarily even. Discard.

II. x(z + y) is even: if x and y are odd, and z is even, then x(z + y) = odd(odd + even) = odd but if if x and y are odd, and z is odd too, then x(z + y) = odd(odd + odd) = even. So, this option is not necessarily even. Discard.

III. (x^2 - x)yz is even: (x^2 - x)yz = x(x - 1)yz. Since either x or x - 1 is even, then the whole expression must be even irrespective of the values of x, y, and z.

Answer: B.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128641 [2], given: 12181

Senior Manager
Senior Manager
User avatar
B
Joined: 01 Nov 2013
Posts: 344

Kudos [?]: 226 [0], given: 403

GMAT 1: 690 Q45 V39
WE: General Management (Energy and Utilities)
Reviews Badge
Re: If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 08 Mar 2015, 11:46
1
This post was
BOOKMARKED
Notice that the average of x no. of first odd consecutive integers = x

e.g.
average of 1,3,5 is 3 ; x=3 ( first three odd numbers)

average of 1,3,5,7 is 4; x =4 ( first four odd numbers )

average of 1, 3, 5, 7,9 is 5 ; x=5 ( first five odd numbers )


:shock: :shock:
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.

I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.-Mohammad Ali

Kudos [?]: 226 [0], given: 403

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16732

Kudos [?]: 273 [0], given: 0

Premium Member
Re: If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 04 Jun 2016, 02:38
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Intern
Intern
avatar
S
Joined: 29 Jul 2015
Posts: 12

Kudos [?]: 6 [0], given: 232

Location: India
Concentration: Marketing, Strategy
WE: Information Technology (Retail Banking)
If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 17 May 2017, 23:54
Bunuel wrote:
vinyasgupta wrote:
If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, which of the following MUST be true?

I. xy(z + 1) is even.

II. x(z + y) is even.

III. (x^2 - x)yz is even.

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


If x is even, then the average of even number of odd consecutive integers (y), will be even. For example, the average of {1, 3} is 2.
If x is odd, then the average of odd number of odd consecutive integers (y), will be odd. For example, the average of {1, 3, 5} is 3.

Thus:
If x = even, then y = even;
If x = odd, then y = odd.

Next, |z - 6/4| = 1/2:
z - 6/4 = 1/2 --> z = 2;
-(z - 6/4) = 1/2 --> z = 1.
Since, z can be even as well as odd, then it takes no part in deciding whether the options are even or odd. So, we can ignore it.


I. xy(z + 1) is even: xy can be odd if both are odd and even if both are even. So, this option is not necessarily even. Discard.

II. x(z + y) is even: if x and y are odd, and z is even, then x(z + y) = odd(odd + even) = odd but if if x and y are odd, and z is odd too, then x(z + y) = odd(odd + odd) = even. So, this option is not necessarily even. Discard.

III. (x^2 - x)yz is even: (x^2 - x)yz = x(x - 1)yz. Since either x or x - 1 is even, then the whole expression must be even irrespective of the values of x, y, and z.

Answer: B.

Hope it's clear.



Sir,

Just out of curiosity, in how many minutes can we solve this problem?

As we need to first find out the values of z and then check it with the z equation.

Then we take all the values and check all the options. so total 6 cases.

Kudos [?]: 6 [0], given: 232

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41872

Kudos [?]: 128641 [0], given: 12181

Re: If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 18 May 2017, 00:04
Animatzer wrote:
Bunuel wrote:
vinyasgupta wrote:
If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, which of the following MUST be true?

I. xy(z + 1) is even.

II. x(z + y) is even.

III. (x^2 - x)yz is even.

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


If x is even, then the average of even number of odd consecutive integers (y), will be even. For example, the average of {1, 3} is 2.
If x is odd, then the average of odd number of odd consecutive integers (y), will be odd. For example, the average of {1, 3, 5} is 3.

Thus:
If x = even, then y = even;
If x = odd, then y = odd.

Next, |z - 6/4| = 1/2:
z - 6/4 = 1/2 --> z = 2;
-(z - 6/4) = 1/2 --> z = 1.
Since, z can be even as well as odd, then it takes no part in deciding whether the options are even or odd. So, we can ignore it.


I. xy(z + 1) is even: xy can be odd if both are odd and even if both are even. So, this option is not necessarily even. Discard.

II. x(z + y) is even: if x and y are odd, and z is even, then x(z + y) = odd(odd + even) = odd but if if x and y are odd, and z is odd too, then x(z + y) = odd(odd + odd) = even. So, this option is not necessarily even. Discard.

III. (x^2 - x)yz is even: (x^2 - x)yz = x(x - 1)yz. Since either x or x - 1 is even, then the whole expression must be even irrespective of the values of x, y, and z.

Answer: B.

Hope it's clear.



Sir,

Just out of curiosity, in how many minutes can we solve this problem?

As we need to first find out the values of z and then check it with the z equation.

Then we take all the values and check all the options. so total 6 cases.


As you can see in the stats, average time of correct answer is 03:36 minutes, which means that it's possible to solve in about 2-3 minutes.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128641 [0], given: 12181

Manager
Manager
avatar
S
Joined: 12 Feb 2017
Posts: 64

Kudos [?]: 46 [0], given: 31

Re: If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 02 Sep 2017, 13:29
2
This post was
BOOKMARKED
y is the average of x odd consecutive integers
lets consider (1+3+5)/ 3 =3 and (1+3+5+7)/4 = 4.
Hence when x is even,y is even and when x is odd,y is odd as well.

now |z - 6/4| = 1/2
case 1) z - 6/4=1/2
z=2
case 2) z - 6/4= -1/2
z=1
that means z can take even value as well as odd value.

I. xy(z + 1) is even.
case 1) even*even (even+1)
even*even*odd= even.
case 2) odd*odd*(even+1)
odd*odd*odd= odd
hence I is false. Note: I have not considered each and every possible case

II. x(z + y) is even.
odd* (odd + even)= odd
hence II is false.

III. (x^2 - x)yz is even.

x can be even as well as odd
case 1) (even^2 - even) = even
case 2) (odd^2 - odd)= even
In both cases X turns out to be even.

as even * anything is even, given statement is true.

Hence answer is III only, option B

Kudos if it helps

Kudos [?]: 46 [0], given: 31

Director
Director
avatar
S
Joined: 12 Dec 2016
Posts: 892

Kudos [?]: 11 [0], given: 859

Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User Premium Member CAT Tests
Re: If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 16 Sep 2017, 09:07
there are only 2 possible cases of z, same to y and x.
Now, just check each I, II, III
=> B is the only answer

Kudos [?]: 11 [0], given: 859

Intern
Intern
avatar
B
Joined: 23 Sep 2017
Posts: 2

Kudos [?]: 0 [0], given: 12

If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 10 Oct 2017, 01:36
vinyasgupta wrote:
If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, which of the following MUST be true?

I. xy(z + 1) is even.

II. x(z + y) is even.

III. (x^2 - x)yz is even.

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


Let consider the odd consecutive set with the first term is 1.
Is x is even assume x = 2n, => the last term is 4n-1 => y = 2n, even
If x is odd assume x = 2n+1 => last term is 4n+1 => y = 2n+1, odd
From that, we can come to conclude that y even(odd) if x eve (odd)
z could be calculated easily, so odd or even what ever.
=> Answer B

Kudos [?]: 0 [0], given: 12

Director
Director
avatar
P
Joined: 22 May 2016
Posts: 802

Kudos [?]: 254 [0], given: 544

If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, [#permalink]

Show Tags

New post 10 Oct 2017, 15:16
vinyasgupta wrote:
If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, which of the following MUST be true?

I. xy(z + 1) is even.

II. x(z + y) is even.

III. (x^2 - x)yz is even.

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

The answer choices shortened my time usage.

If neither Option I nor Option II is correct, from the answer choices, only (B) is left.

I did not even test III.

With a lot of moving pieces, I almost always plug in.

1) Find z

\(|z - \frac{6}{4}| = \frac{1}{2}\)

\((z - \frac{3}{2} = \frac{1}{2})\) OR \((z -\frac{3}{2} = -\frac{1}{2}\))

\(z = 2\) OR
\(z = 1\)

2) Assign x, derive y
Let x = 3 numbers: (1,3,5)
y = average = 3

Let x = 4 numbers: (1,3,5,7)
y = 4

3) Possibilities
\(x = 3, y = 3\)
\(x = 4, y = 4\)
\(z = 1\) OR
\(z\) = 2

4) Assess

I. xy(z + 1) is even

To disprove, need all odds: O*O(*O) = O

We must pick x = 3, y = 3.

Make (z + 1) odd. Choose z = 2

xy(z + 1)

x = 3, y = 3, z = 2:
(3*3)(2+1) = 9. Not even. NO

II. x(z + y) is even

We need 2 odds.
Must pick x = 3, y = 3

Make (z + 3) odd; choose z = 2

x(z + y)
3(2 + 3) = 15. Not even. NO

From the answer choices, only III is possible.

All the others have I and/or II, neither of which is correct. I did not test Option III, but it must be the answer.

Answer B

Kudos [?]: 254 [0], given: 544

If y is the average of x odd consecutive integers and |z - 6/4| = 1/2,   [#permalink] 10 Oct 2017, 15:16
Display posts from previous: Sort by

If y is the average of x odd consecutive integers and |z - 6/4| = 1/2,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.