Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 May 2016, 00:20

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# M16#18

Author Message
Senior Manager
Joined: 29 Sep 2009
Posts: 396
GMAT 1: 690 Q47 V38
Followers: 2

Kudos [?]: 29 [0], given: 5

### Show Tags

13 Nov 2010, 11:12
Is the product $$2*x*5*y$$ an even integer?

1. $$2 + x + 5 + y$$ is an even integer
2. $$x - y$$ is an odd integer

(C) 2008 GMAT Club - m16#18

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

I did get the right answer, but I overshot on time. I have a fundamental question that I want to ask you guys:
if x + y = Odd and
x - y = Odd , then can we conclude that x and y will always be integers? In the question solution we did prove it algebraically and thus I am inclined to "remember" this fact rather than solve it, if encountered again in a problem.
Extrapolating from the official explanation:
x+y=n ....1
x-y=m.....2
1: x=n-y , subst in 2
2 can be re-written as 2y=(n-m)
LHS is always Even - this implies y is an Integer
Examine RHS : n-m , now difference of 2 Integers is Even when both are odd or both are even. Thus we can conclude the following:
if x+y = Odd and x-y = Odd then both x, and y are integers.
if x+y = Even and x-y = Even then both x, and y are integers.

FYI - O.A. is C
Math Expert
Joined: 02 Sep 2009
Posts: 32965
Followers: 5748

Kudos [?]: 70415 [0], given: 9844

### Show Tags

13 Nov 2010, 11:30
Expert's post
vicksikand wrote:
Is the product $$2*x*5*y$$ an even integer?

1. $$2 + x + 5 + y$$ is an even integer
2. $$x - y$$ is an odd integer

(C) 2008 GMAT Club - m16#18

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

I did get the right answer, but I overshot on time. I have a fundamental question that I want to ask you guys:
if x + y = Odd and
x - y = Odd , then can we conclude that x and y will always be integers? In the question solution we did prove it algebraically and thus I am inclined to "remember" this fact rather than solve it, if encountered again in a problem.

O.A. is C

Question: is $$2*x*5*y=even$$? As there is 2 as a multiple, then this expression will be even if $$5xy=integer$$. Basically we are asked is $$5xy=integer$$ true?

Note that $$x$$ and $$y$$ may not be integers for $$2*x*5*y$$ to be even (example $$x=\frac{7}{9}$$ and $$y=\frac{9}{7}$$) BUT if they are integers then $$2*x*5*y$$ is even.

(1) $$2+x+5+y=even$$ --> $$7+x+y=even$$ --> $$x+y=odd$$. Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=1.7 answer NO)

(2) $$x-y=odd$$. Not sufficient. (x=1 and y=2 answer YES BUT x=1.3 and y=0.3 answer NO)

(1)+(2) Sum (1) and (2) $$(x+y)+(x-y)=odd_1+odd_2$$ --> $$2x=even$$ --> $$x=integer$$ --> $$y=integer$$ --> Both $$x$$ and $$y$$ are integers. Hence sufficient.

As for your question: if $$x+y=odd_1$$ and $$x-y=odd_2$$ then $$x$$ and $$y$$ must be integers (see proof above).

Hope it helps.
_________________
Senior Manager
Joined: 29 Sep 2009
Posts: 396
GMAT 1: 690 Q47 V38
Followers: 2

Kudos [?]: 29 [0], given: 5

### Show Tags

13 Nov 2010, 11:48
Bunuel
I didn't have a problem understanding the explanation ,however what i am saying is that shouldn't the following always hold true:
if x+y=odd and
x-y=odd
then both x and y are always integers
similarly
if x+y=even and
x-y=even then both x and y are always integers.
This result may come in handy to save time solving some complex number prop problems.
Math Expert
Joined: 02 Sep 2009
Posts: 32965
Followers: 5748

Kudos [?]: 70415 [0], given: 9844

### Show Tags

13 Nov 2010, 11:54
Expert's post
vicksikand wrote:
Bunuel
I didn't have a problem understanding the explanation ,however what i am saying is that shouldn't the following always hold true:
if x+y=odd and
x-y=odd
then both x and y are always integers
similarly
if x+y=even and
x-y=even then both x and y are always integers.
This result may come in handy to save time solving some complex number prop problems.

I thought I answered this question.

If $$x+y=odd_1$$ and $$x-y=odd_2$$ then $$x$$ and $$y$$ must be integers: add them up $$(x+y)+(x-y)=odd_1+odd_2$$ --> $$2x=even$$ --> $$x=integer$$ --> $$y=integer$$ --> Both $$x$$ and $$y$$ are integers.

If $$x+y=even_1$$ and $$x-y=even_2$$ then $$x$$ and $$y$$ must be integers: add them up $$(x+y)+(x-y)=even_1+even_2$$ --> $$2x=even$$ --> $$x=integer$$ --> $$y=integer$$ --> Both $$x$$ and $$y$$ are integers.

Hope it's clear.
_________________
Re: M16#18   [#permalink] 13 Nov 2010, 11:54
Display posts from previous: Sort by

# M16#18

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.