If c and d are integers, is c even?
1. c(d+1) is even
2. (c+2)(d+4) is even
[spoiler]OA: C[/spoiler]
DS: even/odd
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 65
- Joined: Tue Nov 23, 2010 9:44 am
- Thanked: 16 times
- Followed by:6 members
- GMAT Score:780
Do you need an explanation, or are you just sharing the problem?
If you'd like help with the question, please let us know what about it is causing you trouble -- what answer you thought it was and why. That'll help us know what you need to know.
If you'd like help with the question, please let us know what about it is causing you trouble -- what answer you thought it was and why. That'll help us know what you need to know.
hello Laura, Thanks for your reply. I needed an explanation for this. I thought it was E. I found c could be both even or odd combining both 1 & 2. Can you help?
Laura GMAT Tutor wrote:Do you need an explanation, or are you just sharing the problem?
If you'd like help with the question, please let us know what about it is causing you trouble -- what answer you thought it was and why. That'll help us know what you need to know.
- rishab1988
- Master | Next Rank: 500 Posts
- Posts: 332
- Joined: Tue Feb 09, 2010 3:50 pm
- Thanked: 41 times
- Followed by:7 members
- GMAT Score:720
The answer is C.
Let us assume c=1 and d+1 =1.
I have marked y where the expression satisfies the statement
1) The last 3 rows produce the result c(d+1) even
c could be odd or even.
2) the first and the last 2 rows produce (c+2)(d+4) even. c could odd or even.Insufficient
Combining 1 and 2.
Only last 2 rows satisfy and in each case c is even.Hence sufficient
Let us assume c=1 and d+1 =1.
I have marked y where the expression satisfies the statement
1) The last 3 rows produce the result c(d+1) even
c could be odd or even.
2) the first and the last 2 rows produce (c+2)(d+4) even. c could odd or even.Insufficient
Combining 1 and 2.
Only last 2 rows satisfy and in each case c is even.Hence sufficient
-
- Senior | Next Rank: 100 Posts
- Posts: 65
- Joined: Tue Nov 23, 2010 9:44 am
- Thanked: 16 times
- Followed by:6 members
- GMAT Score:780
If c and d are integers, is c even?
1. c(d+1) is even
2. (c+2)(d+4) is even
Focus on what must be true and can be deduced. Keep in mind that (even)(any integer) = even, and (odd)(odd) = odd.
From statement (1), if c(d+1) is even, then it must be true that either c = even or (d+1)=even, or possibly both.
d+1=even means that d would be odd.
So from statement 1, there are two possibilities, which aren't mutually exclusive (meaning they could both be happening at the same time):
either c= even (and it doesn't matter what d is) or d=odd (and it doesn't matter what c is).
It's possible that c is even. It's possible that c is odd. That's insufficient to answer the original question.
From statement (2), it must be true that (c+2) is even or (d+4) is even.
If (c+2) = even, then c= even. If (d+4) = even, then d= even.
From statement (2), either c=even (with d being even or odd), or d=even (with c being even or odd), or both. It's possible that c is even, it's possible that c=odd. That's insufficient to answer the original question.
Together, it may be a big confusing to think through all of this. Let's organize it this way.
Either d=odd or d=even. That's for sure.
If d=odd, then according to statement (2), c would HAVE to be even. That's because according to statement (2), at least one of the two variables HAS to be even. [Note that d=odd and c=even also satisfies statement (1).]
If d=even, the according to statement (1), c would HAVE to be even. That's because according to statement (1), if d=even, then c would have be even in order for statement (1) to hold true. [Note that d=even and c=even also satisfies statement (2).]
Therefore in both scenarios, c has to be even.
Hope that helps.
1. c(d+1) is even
2. (c+2)(d+4) is even
Focus on what must be true and can be deduced. Keep in mind that (even)(any integer) = even, and (odd)(odd) = odd.
From statement (1), if c(d+1) is even, then it must be true that either c = even or (d+1)=even, or possibly both.
d+1=even means that d would be odd.
So from statement 1, there are two possibilities, which aren't mutually exclusive (meaning they could both be happening at the same time):
either c= even (and it doesn't matter what d is) or d=odd (and it doesn't matter what c is).
It's possible that c is even. It's possible that c is odd. That's insufficient to answer the original question.
From statement (2), it must be true that (c+2) is even or (d+4) is even.
If (c+2) = even, then c= even. If (d+4) = even, then d= even.
From statement (2), either c=even (with d being even or odd), or d=even (with c being even or odd), or both. It's possible that c is even, it's possible that c=odd. That's insufficient to answer the original question.
Together, it may be a big confusing to think through all of this. Let's organize it this way.
Either d=odd or d=even. That's for sure.
If d=odd, then according to statement (2), c would HAVE to be even. That's because according to statement (2), at least one of the two variables HAS to be even. [Note that d=odd and c=even also satisfies statement (1).]
If d=even, the according to statement (1), c would HAVE to be even. That's because according to statement (1), if d=even, then c would have be even in order for statement (1) to hold true. [Note that d=even and c=even also satisfies statement (2).]
Therefore in both scenarios, c has to be even.
Hope that helps.