BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Question regarding Number Properties

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Thu Aug 18, 2011 10:44 am

Question regarding Number Properties

by rog » Tue Sep 06, 2011 7:30 am
I had trouble with this question on my last practice exam. Any help on how to systematically approach this kind of question would be greatly appreciated.

If r and s are integers and rs + r is odd, which of the following must be even?

a) r
b) s
c) r + s
d) rs - r
e) r^2 + s
Top
Source: — Problem Solving |
User avatar
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Tue Jul 26, 2011 2:32 am
Thanked: 1 times

by rupamroy » Tue Sep 06, 2011 7:49 am
I would approach the problem as :

rs + r
=r(s+1)

In the problem it is mentioned that rs + r is odd. Now by number system properties we know that :

odd * odd = odd (i.e. 3*9=27)

From this we can deduce that r and s+1 both are odd numbers. So the answer would be - (b)

Now s and s+1 are consecutive integers. This makes s an even number as s+1 is an odd number.

Hope this helps...
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 158
Joined: Sat Sep 03, 2011 10:31 am
Thanked: 29 times
Followed by:2 members

by gmatclubmember » Tue Sep 06, 2011 7:50 am
rog wrote:I had trouble with this question on my last practice exam. Any help on how to systematically approach this kind of question would be greatly appreciated.

If r and s are integers and rs + r is odd, which of the following must be even?

a) r
b) s
c) r + s
d) rs - r
e) r^2 + s

------------
If r(s+1) is odd that means r and s+1 have to be odd, thereby meaning that s has to be even. (even+1 would make an odd). So r = odd and s = even.
1. Odd. Incorrect.
2. even. Correct.
3. Odd+Even = Odd so incorrect
4. r(s-1) = odd(even-1) = odd*odd = odd , so incorrect.
5. r^2+s=odd^2+even=odd+even=odd, so incorrect.

B(2) is the answer

Cheers
Ami/-
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Sep 06, 2011 8:12 am
rog wrote:I had trouble with this question on my last practice exam. Any help on how to systematically approach this kind of question would be greatly appreciated.

If r and s are integers and rs + r is odd, which of the following must be even?

a) r
b) s
c) r + s
d) rs - r
e) r^2 + s
Plug in values for r and s that satisfy the condition that rs+r is odd.
Plug these values for r and s into the answer choices.
Eliminate any answer choice that isn't even.

Let r=3 and s=2 so that rs+r = (3*2)+3 = 9, which is odd.

A: r=3. Not even. Eliminate A.
B: s=2. Even. Hold onto B.
C: r+s = 3+2 = 5. Not even. Eliminate C.
D: rs-r = (3*2)-3 = 3. Not even. Eliminate D.
E: r² + s = 3²+2 = 11. Not even. Eliminate E.

Only answer choice B remains.
The correct answer is B.

If more than one answer remained, we would:

Plug in different values for r and s that satisfy the condition that rs+r is odd.
Plug these new values for r and s into the remaining answer choices.
Eliminate any answer choice that isn't even.
Continue this process until only one answer choice is left, being sure to try different combinations of even and odd values.
.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1