NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 01:33 It is currently 26 Apr 2024, 01:33
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92922
Own Kudos [?]: 619090 [1]
Given Kudos: 81596
Send PM
CAT Tests Forum Quiz Mode
If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 02:01
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

84% (01:17) correct 16% (01:13) wrong based on 79 sessions
Hide Show timer Statistics

Competition Mode Question



If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
(2) z^3 is even.
ShowHide Answer
Official Answer
D
User avatar
L
firas92
Current Student
Joined: 16 Jan 2019
Posts: 631
Own Kudos [?]: 1444 [2]
Given Kudos: 144
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Send PM
Reviews Badge
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 02:17
1
Kudos
1
Bookmarks
(1) (z + 7)/3 = 2m + 1, where m is an integer.

z+7=3(2m+1)

(2m+1) is always odd and so 3(2m+1) is odd

z+7=odd
z=odd-7=even

1 is sufficient

(2) z^3 is even.

Since we are given that z is an integer, if z^3 is even then z is even since raising an integer to an integer power does not change the odd-even nature

2 is sufficient

Answer is D

Posted from my mobile device
User avatar
L
Leadership
Retired Moderator
Joined: 17 Dec 2018
Status:WHU MBA 2022 candidate
Posts: 932
Own Kudos [?]: 512 [1]
Given Kudos: 73
Location: Germany
Concentration: Leadership, Operations
GMAT 1: 650 Q49 V29
WE:Engineering (Manufacturing)
Send PM
Reviews Badge
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 03:05
1
Kudos
If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
Re-writing: Z + 7 = 3 (2m + 1) ... Z = 3 (2m + 1) - 7
We know 2m will always be EVEN irrespective of what 'm' is.
2m + 1 = Will be always odd (even + odd = odd)
3 (2m + 1) = Will be always odd (odd * odd = odd)
3 (2m + 1) - 7 = will be always even (odd - odd = even)

Sufficient

A D / B C E

(2) z^3 is even.
From the number properties we know that even^3 = even and odd^3 = odd.
Hence, Z will be always Even. Sufficient

'D' is the winner
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8020
Own Kudos [?]: 4098 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 03:40
#1
(z + 7)/3 = 2m + 1, where m is an integer.
LHS ; 2m+1 will be odd ; so now to get LHS as odd value of z has to be even ; sufficient
#2
z^3 is even
z has to even integer; sufficient
IMO D


If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
(2) z^3 is even.
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13388 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 03:48
1
Kudos
Expert Reply
Quote:
If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
(2) z^3 is even


Question: Is integer z even?

Statement 1: (z + 7)/3 = 2m + 1
since, m is an integer, (z + 7)/3 = 2m + 1 = odd

i.e. (z + 7) =3* Odd
i.e. z = 3* odd - 7 = Odd - Odd = Even

SUFFICIENT

Statement 2: z^3 is even
since, z is an integer therefore, z^3 also will be an integer
and since z^3 is even so z also must be even

SUFFICIENT

Answer: Option D



P.S. The question would have been far more trickier if the question had not mentioned that z is an Integer because 2nd statement then would have been Insufficient
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [1]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 05:17
1
Kudos
(1) (z+7)/3= odd --> z+7= 3*odd= odd --> z is even
SUFFICIENT

(2) z^3 is even.
If z^3 is even, then z is even
SUFFICIENT

FINAL ANSWER IS (D)

Posted from my mobile device
User avatar
L
unraveled
CEO
CEO
Joined: 07 Mar 2019
Posts: 2554
Own Kudos [?]: 1813 [1]
Given Kudos: 763
Location: India
WE:Sales (Energy and Utilities)
Send PM
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 11:51
1
Kudos
If z is an integer, is z even?

(1) \(\frac{(z + 7)}{3} = 2m + 1\), where m is an integer.
2m + 1 = odd since m is an integer.
\(\frac{(z + 7)}{3} = 2m + 1\) = \(\frac{e + o}{o} = o\)

z is even.

SUFFICIENT.

(2) \(z^3\) is even.
\(even^3\) = even

z is even.

SUFFICIENT.

Answer D.
User avatar
D
lacktutor
Director
Director
Joined: 25 Jul 2018
Posts: 668
Own Kudos [?]: 1119 [1]
Given Kudos: 69
Send PM
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 14:48
1
Kudos
If z is an integer, is z even?

(Statement1): \(\frac{(z + 7)}{3}= 2m + 1\), where m is an integer.
—> z+7 = 6m+ 3
z= 6m —4 = 2( 3m—2)
Z—even
Sufficient

(Statement2): \(z^{3}\) is even.
Since \(z^{3}\) is even, z must be even
(Even if z is equal to zero)
Sufficient

The answer is D

Posted from my mobile device
User avatar
D
exc4libur
SVP
SVP
Joined: 24 Nov 2016
Posts: 1720
Own Kudos [?]: 1344 [1]
Given Kudos: 607
Location: United States
Send PM
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 18:17
1
Kudos
Quote:
If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
(2) z^3 is even.


z is integer

(1) sufic
z+7/3=2m+1
z+7/odd=even+odd=odd
z+7=odd*odd=odd
z+odd=odd
z=odd-odd=even

(2) sufic
z^3=even then z=even, because if z=odd then an odd^3=odd

Ans (D)
User avatar
P
ostrick5465
Manager
Manager
Joined: 30 Jul 2019
Posts: 205
Own Kudos [?]: 185 [0]
Given Kudos: 68
Location: Viet Nam
WE:Education (Education)
Send PM
Reviews Badge
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 21:49
If z is an integer, is z even?

(1) \(\frac{z + 7}{3} = 2m + 1\), where m is an integer.
=> z+7 = 6m+3
=> z = 6m - 4
=> z is even
=> Suff

(2) \(z^3\) is even.
For example z^3 = 8 => z=2 => z is even
but \(z^3 = 6 => z = \sqrt[3]6\) => z is not an integer.
=> Not suff

=> Choice A
User avatar
S
Jawad001
Manager
Manager
Joined: 14 Sep 2019
Posts: 223
Own Kudos [?]: 138 [1]
Given Kudos: 31
Send PM
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 23:07
1
Kudos
If z is an integer, is z even?

(1) (z + 7)/3 = 2m + 1, where m is an integer.
(2) Z^3 is even.

From statement (1), (z + 7)/3 = 2m + 1, where m is an integer.
Or, (z + 7) = 3(2m + 1)
Or, z = 3(2m + 1) – 7
Or, z = 3( 2 *even/Odd + 1) -7
Or, z = 3(even + 1) – 7
Or, z = Odd *Odd -7
Or z = Odd –odd = Even, Sufficient.

From statement (2),
(2) Z^3 is even.
Z is even. Sufficient.

Answer: D
avatar
B
vthatha
Intern
Intern
Joined: 13 Dec 2018
Posts: 10
Own Kudos [?]: 9 [1]
Given Kudos: 460
Send PM
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink] New post   17 Feb 2020, 23:12
1
Kudos
(1) (z + 7)/3 = 2m + 1, where m is an integer.

z = 2(3m) + 3 - 7
z = 2(3m) -4
z = even - even
z is even --> sufficient

(2) z^3 is even.
z^3 = Z * Z * Z

if z is odd, then Z^3 --> (( Z * Z ) * Z) is ((odd) * odd) = odd
if z is even, then Z^3 --> (( Z * Z ) * Z) is ((even) * even) = even --> Sufficient
GMAT Club Bot
gmatclubot
Re: If z is an integer, is z even? (1) (z + 7)/3 = 2m + 1, where m is an [#permalink]
17 Feb 2020, 23:12
Moderator:
Bunuel
Math Expert
92922 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions