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

 It is currently 15 Oct 2019, 05:18 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x, y and z are positive integers, is x - y odd?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Senior Manager  S
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 426
If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

6
22 00:00

Difficulty:   15% (low)

Question Stats: 79% (01:29) correct 21% (01:46) wrong based on 1085 sessions

HideShow timer Statistics

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

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

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 58333
Re: 172 OG DS  [#permalink]

Show Tags

7
8
Baten80 wrote:
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?

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

(1) x=z^2. No info about y. Not sufficient.

(2) y=(z-1)^2. No info about x. Not sufficient.

(1)+(2) Subtract (2) from (1): $$x-y=z^2-(z^2-2z+1)=2z-1=even-odd=odd$$. Sufficient.

_________________
General Discussion
Retired Moderator B
Joined: 16 Nov 2010
Posts: 1259
Location: United States (IN)
Concentration: Strategy, Technology
Re: 172 OG DS  [#permalink]

Show Tags

(1) and (2) are clearly not enough on their own.

So from (1) and (2) together:

z^2 - z^2 + 2z - 1 = 2z-1 which is odd, so answer is C.
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Manager  Joined: 02 Apr 2010
Posts: 94
Re: 172 OG DS  [#permalink]

Show Tags

Another way to solve this problem:

(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.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: 172 OG DS  [#permalink]

Show Tags

2
Baten80 wrote:
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

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 655
Re: 172 OG DS  [#permalink]

Show Tags

4
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.
Director  Joined: 01 Feb 2011
Posts: 551
Re: 172 OG DS  [#permalink]

Show Tags

1. Not sufficient.

x = z^2 , no information about y

x-y can be even or odd

lets say x y z are 16 3 4 respectively => x-y = 13 odd
x y z are 16 6 4 respectively => x-y = 12 even

2. Not sufficient

no x , similar to the above example , depending upon x , x-y can be odd or even . Not sufficient.

together

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

=> x-y = 2z-1 .i.e is odd.

Hence answer is C.
Intern  Joined: 19 Feb 2015
Posts: 4
If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

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.

Of course, it also works for odd x and even y.

Does that make sense?
Retired Moderator Joined: 29 Oct 2013
Posts: 252
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

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.

_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

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.
_________________
Intern  B
Joined: 16 Feb 2016
Posts: 10
GMAT 1: 630 Q48 V27 Re: If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

Question asks if either of x and y is even and other is odd.

Independently neither of two statements answer the question, so insufficient.

Together, if z is even: x:z^2 is even and y:(Z-1)^2 is odd
Same is the case, if z is odd, hence sufficient.

Ans: C
Director  G
Joined: 02 Sep 2016
Posts: 649
Re: If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

Baten80 wrote:
If x, y and z are positive integers, is x - y odd?

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

x,y,x>0 (They are positive and zero is neither positive nor negative)

x-y= Odd

Possible if one of the two integers is even.

(1) x=z^2
The even/odd nature of x depends on even/odd nature of z. And we have no idea about the even/odd nature of z.
Insufficient.

BCE

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

Even/odd nature of y depends on even/odd nature of z.

Insufficient.

Both the statements:
x=z^2 ..........eq.1
y=(z-1)^2 .........eq.2

Substitute eq. 1 in eq. 2

y=(x^2-1)^2

If x is odd, y is even.
If x is even, y is odd.

So one of the two is even and the other is odd.

C
VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

Bunuel wrote:
Baten80 wrote:
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?

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

(1) x=z^2. No info about y. Not sufficient.

(2) y=(z-1)^2. No info about x. Not sufficient.

(1)+(2) Subtract (2) from (1): $$x-y=z^2-(z^2-2z+1)=2z-1=even-odd=odd$$. Sufficient.

Bunuel how did you get this ---> $$(z^2-2z+1)$$ can you please explain ?
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1430
Location: India
Re: If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

1
dave13 wrote:
Bunuel wrote:
Baten80 wrote:
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?

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

(1) x=z^2. No info about y. Not sufficient.

(2) y=(z-1)^2. No info about x. Not sufficient.

(1)+(2) Subtract (2) from (1): $$x-y=z^2-(z^2-2z+1)=2z-1=even-odd=odd$$. Sufficient.

Bunuel how did you get this ---> $$(z^2-2z+1)$$ can you please explain ?

Hello

I think Bunuel has just squared (z-1). Since y = (z-1)^2 so it becomes = z^2 - 2z + 1
VP  D
Joined: 09 Mar 2016
Posts: 1230
Re: If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

amanvermagmat

many thanks for clarification just started practicing OG DS questions GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4000
Re: If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

Top Contributor
Baten80 wrote:
If x, y and z are positive integers, is x - y odd?

(1) x=z²
(2) y=(z - 1)²

Here's an algebraic approach:

Target question: Is x-y odd?

Given: x, y, and z are positive integers

Statement 1: x = z²
There's no information about y, so there's no way to determine whether or not x-y is odd.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = (z - 1)²
There's no information about x, so there's no way to determine whether or not x-y is odd.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: x = z²
Statement 2: y = (z-1)²
Subtract equations to get: x-y = z² - (z-1)²
Expand to get: x-y = z² - [z² - 2z + 1]
Simplify to get: x-y = 2z - 1
Since z is a positive integer, we know that 2z is EVEN, which means 2z-1 is ODD.
If 2z-1 is ODD, we can conclude that x-y is definitely ODD
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13160
Re: If x, y and z are positive integers, is x - y odd?  [#permalink]

Show Tags

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] 17 May 2019, 02:22
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  