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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

(1) Two cases: (i) If x = odd => z = odd (ii) If x = even => z = even

(2) Two cases: (i) if y = odd => z = even (and vice versa) (ii) if y = even => Z = odd (and vice versa)

(1) & (2) combined, again two cases: (i) If x = odd => y = even (ii) If x = even => y = odd

As subtracting an odd number from an even number and subtracting an even number from an odd number always results in an odd number it follows that C is the correct solution.

If x, y and z are positive integers, is x - y odd? (1) x=z^2 (2) y=(z-1)^2

Can this problem be solve by plunging number?

Yes, you can plug in numbers. Generally, in even odd questions, plugging numbers works. (mind you, generally, not always)

Break it down in the following way:

If x, y and z are positive integers, is x - y odd? Question: Is one of x and y even and one odd? (because x - y will be odd only if one of them is even and one is odd) (1) x=z^2 If z is even, x is even. If z is odd, x is odd. No info about y. or if z = 2, x is 4. If z = 1, x is 1.

(2) y=(z-1)^2 If z is even, y is odd. If z is odd, y is even. No info about x. or If z = 2, y = 1. If z = 1, y is 0 (even number).

Together: If z is even, x is even and y is odd. If z is odd, x is odd and y is even. One is always odd, other is always even. or If z is 2, x = 4 and y = 1 If z = 1, x = 1 and y = 0

Re: If x, y and z are positive integers, is x - y odd? [#permalink]

Show Tags

07 Jan 2014, 05:31

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 x, y and z are positive integers, is x - y odd? [#permalink]

Show Tags

22 Feb 2015, 07:42

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. _________________

If x, y and z are positive integers, is x - y odd? [#permalink]

Show Tags

08 Mar 2015, 12:51

Another approach might be the following which doesn't involve calculating:

(1) x = z^2 Not suff. (as explained) (2) y = (z-1)^2 Not suff. (as explained)

(1) & (2) x = z^2 states that x is some number, which for instance could be even. An even number to any power stays even. So if z^2 is even, x is even.

Now (2) states that (z-1)^2. Hence, as z^2 is even, (z-1)^2 has to be odd. Again, an odd number to any power stays odd. Therefore, x has to be even (in the example) and y has to be odd.

If x, y and z are positive integers, is x - y odd? [#permalink]

Show Tags

05 Dec 2015, 11:21

I think most of the gmat problems could have elegant solutions like the one given below. Though this one is not a very difficult question, i think it has implications. Test writers could make it into a difficult question by changing the answer choices as follows:

1) x=z^p & 2)y=(z-1)^q...where p and q are pos int

or 1) x=z^p & 2)y=(z-3)^q...where p and q are pos int

or 1) x=z^p & 2)y=(z-m)^q...where m=odd integer

What do math experts think about it?

gmat1220 wrote:

Rephrasing the question - Is x odd and y even or x even and y odd? Or Is x and y squares of consecutive integers respectively?

1. Insufficient. y is unknown 2. Insufficient. x is unknown

combine 1) + 2) z and z-1 are consecutive integers. Hence sufficient.

_________________

Please consider giving 'kudos' if you like my post and want to thank

Re: If x, y and z are positive integers, is x - y odd? [#permalink]

Show Tags

06 Dec 2015, 11:29

Expert's post

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x, y and z are positive integers, is x - y odd?

(1) x=z^2 (2) y=(z-1)^2

There are 3 variables (x,y,z) but only 2 equations are given by the 2 conditions, so there is high chance (E) will become the answer. Looking at the conditions together, x=z^2, y=(z-1)^2, and as x=odd and y=even or x=even and y=odd, the answer to the question always becomes 'yes' and the answer seems like (C) However, this is a question with commonly made mistakes, so just to make sure, if the conditions are examined separately, we cannot know the value of y from condition 1, and condition 2 is not sufficient as well, so the answer becomes (C).

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D. _________________

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

Cal Newport is a computer science professor at GeorgeTown University, author, blogger and is obsessed with productivity. He writes on this topic in his popular Study Hacks blog. I was...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...