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

Redeem

odds and evens - WOW.

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1077
Joined: Mon Dec 13, 2010 1:44 am
Thanked: 118 times
Followed by:33 members
GMAT Score:710

odds and evens - WOW.

by bblast » Sun Jul 10, 2011 7:10 am
If a,b,c ,d and are integers such that a-c + b is even and d+b-a is odd, which of the following expressions is always odd?


a+d
b+d
c+d
a+b
a+c

C
Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Top
Source: — Problem Solving |
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 am
Location: India
Thanked: 375 times
Followed by:53 members

by Frankenstein » Sun Jul 10, 2011 9:05 am
Hi,
a-c+b is even. So, there are 2 possibilities
1)a,b,c are all even (or)
2)2 of them are odd, 1 is even

d+b-a is odd. So, there are 2 possibilities
3)a,b,d are all odd (or)
4)2 of them are even and 1 is odd

Combining the above cases, we get the following cases.
i)1 and 3 cannot be true at the same time.
ii)if 1 and 4 are true, we get a,b,c even and d is odd
iii)if 2 and 3 are true, we get a,b,d odd and c is even
iv)if 2 and 4 are true, we get c is odd, one of a,b is odd, d is even
Now, consider the options:
A) a+d is even in case (iii)
B) b+d is even in case (iii)
C) c+d is odd in all cases
D) a+b is even in case(ii) and case(iii)
E) a+c is even in case(ii) and case(iii)

Hence, C
Cheers!

Things are not what they appear to be... nor are they otherwise
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

by Ian Stewart » Sun Jul 10, 2011 9:32 am
bblast wrote:If a,b,c ,d and are integers such that a-c + b is even and d+b-a is odd, which of the following expressions is always odd?


a+d
b+d
c+d
a+b
a+c

C
a - c + b is even, and d + b - a is odd, so if we subtract the first expression from the second expression, the result must be odd:

d + b - a - (a - c + b) = d + b - a - a + c - b = c + d - 2a

So c + d - 2a is odd. Since 2a is even, c + d must therefore be odd.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
User avatar
Legendary Member
Posts: 1077
Joined: Mon Dec 13, 2010 1:44 am
Thanked: 118 times
Followed by:33 members
GMAT Score:710

by bblast » Sun Jul 10, 2011 9:54 am
Ian's solution is as good as the question. Frank- I went by the method that you have nicely described in the post above, took me 3 min and 27 secs, :/
Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Top
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 am
Location: India
Thanked: 375 times
Followed by:53 members

by Frankenstein » Sun Jul 10, 2011 10:08 am
bblast wrote:Ian's solution is as good as the question. Frank- I went by the method that you have nicely described in the post above, took me 3 min and 27 secs, :/
Haha.. Good that you can save 3 mins now :)
Cheers!

Things are not what they appear to be... nor are they otherwise
Top
User avatar
Legendary Member
Posts: 1255
Joined: Fri Nov 07, 2008 2:08 pm
Location: St. Louis
Thanked: 312 times
Followed by:90 members

by Tani » Sun Jul 10, 2011 10:39 am
I did this much more quickly. If a-c + b is even and d+b-a is odd then their sum is odd.

adding those two quantities you get d-c+2b. We know 2b is even, so d-c must be odd, which means d+c must be odd. 30 seconds!
Tani Wolff
Top
User avatar
Legendary Member
Posts: 1077
Joined: Mon Dec 13, 2010 1:44 am
Thanked: 118 times
Followed by:33 members
GMAT Score:710

by bblast » Sun Jul 10, 2011 8:31 pm
Tani Wolff - Kaplan wrote:I did this much more quickly. If a-c + b is even and d+b-a is odd then their sum is odd.

adding those two quantities you get d-c+2b. We know 2b is even, so d-c must be odd, which means d+c must be odd. 30 seconds!
Good 1 Tani !!
Yet, another subtle way to approach the problem.

Takeaway >> always try to manipulate given equations by addition/subtraction before diving into the answer choices for odds and evens.


i cant recall but there is a gmat prep question also which is on similar lines- rs+r = something
Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 461
Joined: Tue May 10, 2011 9:09 am
Location: pune
Thanked: 36 times
Followed by:3 members

by amit2k9 » Mon Jul 11, 2011 9:24 pm
a-c+b-[b-a+d]= odd
thus
2a-(c+d)=odd
meaning c+d = odd
For Understanding Sustainability,Green Businesses and Social Entrepreneurship visit -https://aamthoughts.blocked/
(Featured Best Green Site Worldwide-https://bloggers.com/green/popular/page2)
Top
Post new topic Post Reply
• Page 1 of 1