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Re: If a and b are positive integers [#permalink]
Nomad wrote:
The answers are D and E.

Since a-b = even and a/b = even, then both a and b are positive even integers.

We can rewrite D as a/2 + 2/2. a/2 will always be even, 2/2 = 1. Even+1 = Odd.

The same for E


Yeah, I too got same doubt,Just posted the question with same answer as in material.
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Re: If a and b are positive integers [#permalink]
AchyuthReddy wrote:
Nomad wrote:
The answers are D and E.

Since a-b = even and a/b = even, then both a and b are positive even integers.

We can rewrite D as a/2 + 2/2. a/2 will always be even, 2/2 = 1. Even+1 = Odd.

The same for E


Yeah, I too got same doubt,Just posted the question with same answer as in material.


Actually, @Carcass solution is the correct one. I did not consider if b=2. That is a mistake
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Re: If a and b are positive integers [#permalink]
How is E wrong?
if a = 4, b = 2

then b--> 2+2/2 = 2 which is even?
Please explain what is wrong here?
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Re: If a and b are positive integers [#permalink]
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a must be greater than 2 in a way a/b is even.
b can be 2 also in which case b+2/2 is NOT odd
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Re: If a and b are positive integers [#permalink]
Carcass wrote:
\(a-b\) even --> either both even or both odd

\(\frac{a}{b}\) even --> either both even or \(a\) is even and \(b\) is odd.

As both statements are true --> \(a\) and \(b\) must be even.

As \(\frac{a}{b}\) is an even integer --> \(a\) must be multiple of 4.


Options A is always even.

Options B can be even or odd.

Options C can be even or odd.

Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd.

Options E can be even, odd.


Answer: D.

Hope this helps. The answer is one and only.

Regards


what if a=12 and b=4?
then a/b will not be even. plz explain. thanks in advance
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Re: If a and b are positive integers [#permalink]
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Triti wrote:
Carcass wrote:
\(a-b\) even --> either both even or both odd

\(\frac{a}{b}\) even --> either both even or \(a\) is even and \(b\) is odd.

As both statements are true --> \(a\) and \(b\) must be even.

As \(\frac{a}{b}\) is an even integer --> \(a\) must be multiple of 4.


Options A is always even.

Options B can be even or odd.

Options C can be even or odd.

Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd.

Options E can be even, odd.


Answer: D.

Hope this helps. The answer is one and only.

Regards


what if a=12 and b=4?
then a/b will not be even. plz explain. thanks in advance


Here in the question it is give a/b is even and a-b is even.
So both a and b should be even and also 'a' can be only multiple of 4.
'b' can be only those numbers where the ratio remains even.
so if you consider a=12, b can be = 2, 6 only.
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Re: If a and b are positive integers [#permalink]
What are some number properties that I have to keep in mind for the division?
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Re: If a and b are positive integers [#permalink]
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Greprep911 wrote:
What are some number properties that I have to keep in mind for the division?


Sir what do you mean ? for the division ??
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Re: If a and b are positive integers [#permalink]
There are certain properties for addition, subtraction and multiplication like: If you add even + even = result is even and if 2 is multiple of anything, the result is an even number. Are there any such properties for division too?
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Re: If a and b are positive integers [#permalink]
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Greprep911 wrote:
There are certain properties for addition, subtraction and multiplication like: If you add even + even = result is even and if 2 is multiple of anything, the result is an even number. Are there any such properties for division too?


Here read please

Basic number properties https://gre.myprepclub.com/forum/gre-math- ... 24947.html
Advanced https://gre.myprepclub.com/forum/gre-quant ... tml#p51913

Please also take a look at the sticky and announcements posts under every section here on the board. All the notions for the GRE are listed in evidence

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Re: If a and b are positive integers [#permalink]
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Greprep911 wrote:
There are certain properties for addition, subtraction and multiplication like: If you add even + even = result is even and if 2 is multiple of anything, the result is an even number. Are there any such properties for division too?


I like to write this out whenever I do a number properties problem of this nature:

(e = even & o = odd)

e + e = e
e + o = o
o + o = e

e x e = e
e x o = e
o x o = o

The signs are interchangeable, so for this problem, you could instead write:

e - e = e
e - o = o
o - o = e

e ÷ e = e
e ÷ o = e
o ÷ o = o

This is only a shortcut. Please see the number properties lessons provided above to get a full understanding of the subject. Thanks.
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Re: If a and b are positive integers [#permalink]
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