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# Is z an odd number?

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Re: Is z an odd number? [#permalink]
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CrackVerbalGMAT
Hi Ashikaverma13,

The best way to approach inequality questions of this type is to plug in values. There are two things you need to keep in mind while plugging in values on a Yes/No DS question

1. Plug in values to satisfy the statement first and then answer a Yes or No to the main question.
2. Plug in values to disprove the statement i.e. if you plug in a value which gives you a YES, try to plug in a value to get a NO instead of trying to get a definite YES or No and prove it sufficient

Also in questions where you are not given any constraint, you need to be doubly careful. Here we have not been given any information about the type of number z is. So z can be any real number. The trap here would be to assume that z has to be a positive integer.

Is z an odd number?

Keep in mind that only positive and negative numbers can be odd or even. We cannot have fractions or irrational numbers to be odd or even.

Statement 1 : 3z is an odd number

Plug in z = 1. This gives us a YES.
Plug in z =1/3. This gives us a NO. Insufficient.

Statement 2 : z/3 is an odd number

z/3 = odd -----> z = odd * 3 -----> z = odd. Sufficient.

OA : B

Can you please explain statement 1 again. As far as I know Odd*odd =odd.. now it is mentioned 3z=odd
so 3 is odd so for 3z to be odd z has to be odd
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Re: Is z an odd number? [#permalink]
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AmritaSarkar89
CrackVerbalGMAT
Hi Ashikaverma13,

The best way to approach inequality questions of this type is to plug in values. There are two things you need to keep in mind while plugging in values on a Yes/No DS question

1. Plug in values to satisfy the statement first and then answer a Yes or No to the main question.
2. Plug in values to disprove the statement i.e. if you plug in a value which gives you a YES, try to plug in a value to get a NO instead of trying to get a definite YES or No and prove it sufficient

Also in questions where you are not given any constraint, you need to be doubly careful. Here we have not been given any information about the type of number z is. So z can be any real number. The trap here would be to assume that z has to be a positive integer.

Is z an odd number?

Keep in mind that only positive and negative numbers can be odd or even. We cannot have fractions or irrational numbers to be odd or even.

Statement 1 : 3z is an odd number

Plug in z = 1. This gives us a YES.
Plug in z =1/3. This gives us a NO. Insufficient.

Statement 2 : z/3 is an odd number

z/3 = odd -----> z = odd * 3 -----> z = odd. Sufficient.

OA : B

Can you please explain statement 1 again. As far as I know Odd*odd =odd.. now it is mentioned 3z=odd
so 3 is odd so for 3z to be odd z has to be odd

Yes, odd*odd = odd but we don't know whether z is an integer thus from 3z = odd it follows that z = odd/3. So, z can be 1/3, 3/3=1, 5/3, 7/3, 9/3=3, ..., -1/3, ...
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Re: Is z an odd number? [#permalink]
If a question asks us to check whether a certain variable is odd, a test taker will only think of substituting integer values to check. Because a fractional value is neither even nor odd and hence, it will not lead to any answer.
I do not understand why are we considering fractional values?
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Re: Is z an odd number? [#permalink]
sukoon9334
Is z an odd number?

(1) 3z is an odd number.
(2) z/3 is an odd number.

If a question asks us to check whether a certain variable is odd, a test taker will only think of substituting integer values to check. Because a fractional value is neither even nor odd and hence, it will not lead to any answer.
I do not understand why are we considering fractional values?

The question asks: is z an odd number?

We don't know whether z is odd, even, or a non-integer. If z is odd, then the answer to the question would be 'YES'. If z is even, the answer would be 'NO'. It is important to note, however, that we are not given that z must be an integer; therefore, considering non-integer values for z is perfectly valid. Thus, z could also be a fraction, in which case the answer to whether z is an odd number would still be 'NO'.
Re: Is z an odd number? [#permalink]
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