Even or not

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humblescarabee: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Wed Apr 30, 2008 8:08 pm

by humblescarabee » Sun Aug 03, 2008 2:24 pm

Hi all.

Couple of weeks before the exam. I am aiming 750. Currently, I am scoring 710 on GMAT prep 1 Q43, V45.

Can you help me solve this one?

If c and d are integers, is c even?
1/ c(d+1) is even
2/ (c+2)(d+4) is even

Thans for your help.

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Source: Beat The GMAT — Data Sufficiency | Sun Aug 03, 2008 2:24 pm

kshin78: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Tue Jun 17, 2008 1:18 pm; Thanked: 2 times

by kshin78 » Sun Aug 03, 2008 10:38 pm

If c and d are integers, is c even?
1/ c(d+1) is even
2/ (c+2)(d+4) is even

OK, here's my crack at the problem.

but first ground rules:

odd x odd = odd
odd x even = even
even x even = even

Let's look at stem 1.

c(d+1) is even: it's telling us that when c is even d+1 is either even or odd. OR if c is odd, d+1 is even. Hence, c can be either even or odd. NOT SUFFICIENT.

Stem 2. Similar to stem 1, c+2 or d+4 can be either even or odd to make the statement work. hence, it's NOT SUFFICIENT.

Combined: Stem 1 & 2 tell us that c and c+2 are the same but d+1 and d+4 are different, meaning it's either even or odd. Since stem 1 & 2 results are even, C would have to be EVEN to satisfy stem 1 & 2.

The answer: C

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Thouraya: Master | Next Rank: 500 Posts; Posts: 112; Joined: Wed Jan 20, 2010 5:46 am; Thanked: 1 times

by Thouraya » Sun May 29, 2011 6:01 am

@kshin78,

Thanks for your post.I understand up until that statement 1 alone is sufficient, neither is statement B alone; however, I still don't understand why combined, they are sufficient.

From my solving, both c and d can each be either even or odd, then? Thank you

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun May 29, 2011 7:10 am

humblescarabee wrote: If c and d are integers, is c even?
1/ c(d+1) is even
2/ (c+2)(d+4) is even

Statement 1: If c(d+1) is even then there are 3 possible cases:
case a) c is even and d is even
case b) c is even and d is odd
case c) c is odd and d is odd

Since c can be even or odd, statement 1 is INSUFFICIENT

Statement 2: If (c+2)(d+4) is even then there are 3 possible cases:
case x) c is even and d is even
case y) c is even and d is odd
case z) c is odd and d is even

Since c can be even or odd, statement 2 is INSUFFICIENT

Statements 1 and 2 combined:
Now we need to find the cases that the two statements share.
They share the case where c is even and d is even (cases a and x)
And they share the case where c is even and d is odd (cases b and y)
In both cases, c is even, so c must be even.
This means the statements combined are sufficient and the answer is C

Brent Hanneson - Creator of GMATPrepNow.com

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