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

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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!
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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.

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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
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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.
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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
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Could this be a 700 level? Does not seem like the regular 700 questions
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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.
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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.
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Re: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) [#permalink]
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 ?
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Re: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) [#permalink]
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Re: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) [#permalink]
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