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

 It is currently 15 Oct 2018, 11:22

### 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

# If y and z are integers, is y*(z + 1) odd? (1) y is odd (2)

Author Message
TAGS:

### Hide Tags

Intern
Joined: 15 Oct 2009
Posts: 11
If y and z are integers, is y*(z + 1) odd? (1) y is odd (2)  [#permalink]

### Show Tags

06 Sep 2010, 07:39
2
00:00

Difficulty:

5% (low)

Question Stats:

84% (00:22) correct 16% (00:41) wrong based on 230 sessions

### HideShow timer Statistics

If y and z are integers, is y*(z + 1) odd?

(1) y is odd
(2) z is even

OA: C

Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ?
Manager
Joined: 09 Jun 2010
Posts: 103

### Show Tags

06 Sep 2010, 07:47

Q: is XY(Z+1) odd??

(1) y is odd => value of XY(Z+1) depends on Y & (Z+1). Y may be even or (Z+1) may be even. Insufficient
(2) z is even => value of XY(Z+1) depends on Y & X either of them can be even. Insufficient

Combine: We don't know whether X is odd or even. If X = odd then product is odd & if X = even then product is even. Insufficient

Math Expert
Joined: 02 Sep 2009
Posts: 49858

### Show Tags

06 Sep 2010, 07:49
2
anticipation wrote:
If y and z are integers, is y*(z + 1) odd?

(1) y is odd
(2) z is even

OA: C

Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ?

Hi, and welcome to Gmat Club. Below is a solution for your problem.

The product of two integers (in our case $$y$$ and $$z+1$$) to be odd both of them must be odd.

Question: is $$y*(z + 1)=odd$$ --> so basically the question asks is $$y=odd$$ and $$z+1=odd$$, or $$z=even$$?

(1) $$y$$ is odd, we don't know whether $$z=even$$. Not sufficient.

(2) $$z$$ is even, we don't know whether $$y=odd$$. Not sufficient.

(1)+(2) $$y=odd$$ and $$z=even$$, so both necessary conditions are satisfied. Sufficient.

As for your question: first of all, $$y$$ can not be zero as $$y=odd$$ and zero is an even integer, next if $$z=0=even$$, then $$z+1=0+1=even+odd=odd$$ and as from (1) $$y=odd$$ we still have the product of two odd numbers which is odd.

For more on this issues please check Number Theory chapter of Math Book (link in my signature).

Hope it helps.
_________________
Manager
Joined: 14 Jun 2010
Posts: 213

### Show Tags

06 Sep 2010, 21:05
the Q asks if y(z+1) is odd , in other words it asks if Y is odd and Z is even ( Z+1) is odd ONLY when Z is even.
Thus we have C, points 1 and 2 give the info required!
Intern
Joined: 06 Sep 2010
Posts: 10

### Show Tags

06 Sep 2010, 22:08

For y*(z + 1) to be Odd..the product of y and (z+1) has to be odd..It could happen in only one way when both the terms are odd(like 3*3=9).
1.) When y is odd - This will only give us one part of the answer since nature of z is unknown.Hence,INSUFFICIENT
2.) When z is even - This is also INSUFFICIENT coz nature of y is unknown.

On combining both cases,we can conclude that that when z is added to 1,it will become an odd number and when multiplied by an odd number y,it will always give an odd value.

Manager
Joined: 04 Aug 2010
Posts: 108

### Show Tags

07 Sep 2010, 10:33
1
If y and z are integers, is y*(z + 1) odd?

(1) y is odd
(2) z is even

Basically there are two conditions where you can answer if a product is odd:
either (a) both terms are odd - THEN product would be odd
or (b) one of the terms are even - THEN product would be even

Evaluate (1) y is odd
- According to condition (a), we don't know if (z + 1) is odd too.
- INSUFFICIENT

Evaluate (2) z is even
- Which means term (z + 1) is odd
- According to condition (a), we don't know if y is odd too.
- INSUFFICIENT

Evaluate (1) + (2)
- (z + 1) is odd AND y is odd
- SUFFICIENT to conclude that the product of the 2 terms is odd

Ans C
Intern
Joined: 15 Oct 2009
Posts: 11

### Show Tags

07 Sep 2010, 22:07
anticipation wrote:
If y and z are integers, is y*(z + 1) odd?

(1) y is odd
(2) z is even

OA: C

Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ?

Thanks everyone for the solution. The key here is to know that zero is even.
Pays to know the parity of zero.
Manager
Joined: 17 Nov 2009
Posts: 219

### Show Tags

08 Sep 2010, 10:15
anticipation wrote:
If y and z are integers, is y*(z + 1) odd?

(1) y is odd
(2) z is even

OA: C

Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ?

Rephrase as:

Is Y odd and Z even?

Logic: O*O=Odd.
since z+1 should be odd Z should be even.

st 1: answers only 1 part of what is needed the Y part
st 2: answers only 1 part of what is needed the Z part

Together I have all I need on Y and Z
Manager
Joined: 17 Nov 2009
Posts: 219

### Show Tags

08 Sep 2010, 10:16
Could this be a 700 level? Does not seem like the regular 700 questions
Manager
Joined: 19 Sep 2010
Posts: 141

### Show Tags

15 Oct 2010, 10:01
No..even i don't rate it as a 700 level question . I gave few MGMAT tests . The 700 level there was pretty tough , more
calculation oriented and time consuming.
VP
Status: mission completed!
Joined: 02 Jul 2009
Posts: 1297
GPA: 3.77

### Show Tags

15 Oct 2010, 10:19
1
agnok wrote:
Could this be a 700 level? Does not seem like the regular 700 questions

no way. It is max of 600 level.

To solve just plug in even numbers including 0 {0;2} and few odd {-1;1;3} you will see that in any of cases the result will be odd.

No chances for us after Bunuel's excellent explanations.
_________________

Audaces fortuna juvat!

GMAT Club Premium Membership - big benefits and savings

Manager
Status: Please do not forget to give kudos if you like my post
Joined: 19 Sep 2008
Posts: 98
Location: United States (CA)
Re: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2)  [#permalink]

### Show Tags

29 Nov 2014, 23:20
With DS always spend 10 second stop and write down what is being asked.
Here we are asked y*(z + 1) odd?
Only way we can say this is by know whether y and z are odd/even.

1. NS - we don't know about z.
2. NS - we don't know about y.

1&2: S - have all the info to answer.

anticipation wrote:
If y and z are integers, is y*(z + 1) odd?

(1) y is odd
(2) z is even

OA: C

Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ?

_________________

Non-Human User
Joined: 09 Sep 2013
Posts: 8390
Re: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2)  [#permalink]

### Show Tags

30 Sep 2018, 09:57
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: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) &nbs [#permalink] 30 Sep 2018, 09:57
Display posts from previous: Sort by