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# If c and d are integers, is c even? 1. c(d+1) is even 2.

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If c and d are integers, is c even? 1. c(d+1) is even 2. [#permalink]  30 Jan 2010, 13:15
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If c and d are integers, is c even?

1. c(d+1) is even
2. (c+2)(d+4) is even

What's the fastest way to solve this?
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Re: GMATprep DS (Number properties) [#permalink]  30 Jan 2010, 15:23
zaarathelab wrote:
If c and d are integers, is c even?

1. c(d+1) is even
2. (c+2)(d+4) is even

What's the fastest way to solve this?

Statement 1:

C(d+1) is even : Insufficient
3 cases: Case 1: C is even, d+1 is even => C is even, D is Odd.
Case 2: C is even, d+1 is Odd => C is even, D is Even.
Case 3: C is Odd, d+1 is even => C is Odd, D is Odd.

Statement 2:
(C+2)(D+4) is even: Insufficient
3 Cases: Case 1:(C+2)is even, (D+4) is even => C and D : Both even
Case 2: (C+2) is even, (D+4) is Odd => C is even, D is Odd
Case 3: (C+2) is Odd, (D+4) is even => C is Odd, D is Odd.

Together: Insufficient: As multiple cases exist for both the statements.
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Re: GMATprep DS (Number properties) [#permalink]  30 Jan 2010, 15:39
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(1) c*(d+1) is even, C can be even or D+1 can be even, or both for product to be even. Hence not necessary C to be even. Not sufficient.

(2) (c+2)(d+4) is even. Again C+2 can be even (which is the same as C to be even) or D+4 can be even, or both for product to be even. Hence not necessary C to be even. Not sufficient.

(1)+(2) If D+1 is even then D+4 can not be even and that means C+2 must be even (which is the same as C to be even). If D+4 is even then D+1 can not be even and that means C must be even. Sufficient.

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Re: GMATprep DS (Number properties) [#permalink]  31 Jan 2010, 10:49
Thanks Bunuel

OA is C

But i got lost in this number property question (was consuming too much time) and hence picked E on the test.

Is there any faster way to solve this?
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Re: GMATprep DS (Number properties) [#permalink]  31 Jan 2010, 11:43
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zaarathelab wrote:
Thanks Bunuel

OA is C

But i got lost in this number property question (was consuming too much time) and hence picked E on the test.

Is there any faster way to solve this?

We have c(d+1)=even and c(d+4)=even (I say c as it's the same as to write c+2 in this case).

Now if c is not even than d+1 and d+4 must be even, but they can not be even together, hence c is even.

Sorry no other faster way.
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Re: GMATprep DS (Number properties) [#permalink]  01 Feb 2010, 14:46
obviously, 1 or 2 separatly is not sufficient.

Both:

(c+2)(d+4)=cd +4c+2d+8=even => cd is even

now statement one says :

c(d+1)=cd+c is even. From statement 2, cd is even => for stament 2 to be true c has to be even.

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Re: GMATprep DS (Number properties) [#permalink]  02 Feb 2010, 05:29
alexBLR has applied good strategy.

Intially I went to do it all in head. But it works better if you do it on the paper--substitution with number.

C even?

1. say NO and check: 5 *(7+1) = even,
say YES and check: 8*(7+1) 0 even -> not sufficient, clearly not A

2. say NO and check: (5+2)*(2+4) = even
say YES and check: (6+2)*(2+4) = even -> not sufficient, clearly not B

3. say No and check: 5*(7+1) = even; (5+2)*(7+4) = odd -> restricted
5*(8+1) = odd; (5+2)*(8+4) = even ->restricted
say YES and check: just one look and you know (1) and (2) both are satisfied

Maybe it is not that faster. With numbers there are too many things to assume if I do it in head.
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Re: GMATprep DS (Number properties) [#permalink]  02 Feb 2010, 13:15
zaarathelab wrote:
If c and d are integers, is c even?

1. c(d+1) is even
2. (c+2)(d+4) is even

What's the fastest way to solve this?

S1:
c(d+1) is even means either c is even or d+1 is even..... not suff

S2:
(c+2)(d+4) is even means either (c+2) is even or (d+4) is even... not suff

Both together:
c(c+2)(d+1+3) = c(d+1) + 3c + 2(d+1+3) which implies Even + __ + Even = Even

Therefore 3c is even... Hence c is even...

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Re: GMATprep DS (Number properties) [#permalink]  14 Mar 2010, 02:58
zaarathelab wrote:
If c and d are integers, is c even?

1. c(d+1) is even
2. (c+2)(d+4) is even

What's the fastest way to solve this?

1. c can be odd then d can be odd
c can be even then d can be odd or even
alone insufficient.

2. c can be odd then d is even
c can be even then d is even
alone insufficient.

combining both common is c has to even d can be odd or even.
So sufficient.
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Re: GMAT PREP DS [#permalink]  22 Aug 2010, 19:27
uzzy12 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 is insufficient since c could be even or odd and (d+1) could also be even or odd and still c * (d+1) could be even.

Refer the below table.

c ***** d+1 ***** c (d+1)
E ***** E ***** E
E ***** O ***** E
O ***** E ***** E

Statement 2 is insufficient.
(c+2) (d+4) = cd + 2d + 4c + 8. (Here 2d, 4c and 8 are even).
Hence c * d should even, however we cannot say whether c is even.

Refer the below table.

c ***** d ***** c * d
E ***** E ***** E
E ***** O ***** E
O ***** E ***** E

Combining two statements.

c(d+1) and cd is even. Also if d is even then (d+1) is odd and vice versa.

Now set up a table.

c ***** d ***** (d+1) **** cd *********** c(d+1)
O ***** E ***** O **** Even *********** Odd --- This combination does not work
E ***** O ***** E **** Even *********** Even --- This works and hence c is even.

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If c and d are integers, is c even? [#permalink]  22 Feb 2011, 01:42
What is the best way of tackling problems like this one?

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Re: If c and d are integers, is c even? [#permalink]  22 Feb 2011, 01:58
I don't know the best way; but here's how I would solve it;

1.
c(d+1) is even
c even and d+1 even i.e. d odd
OR
c odd and d+1 even i.e. d odd
OR
c even and d+1 odd i.e. d even

We can see that c can be even or odd.
Not sufficient.

2.
(c+2)(d+4) is even

c+2 even and d+4 even i.e. c even and d even
OR
c+2 odd and d+4 even i.e. c odd and d even
OR
c+2 even and d+4 odd i.e. c even and d odd

C can be even or odd.
Not sufficient.

If you see the odd case for c in both statements;
c odd and d+1 even i.e. d odd
c+2 odd and d+4 even i.e. c odd and d even
You see that for c=odd; 1 statement says d=odd; 2nd statement says d=even; Conflict; D can't be odd and even at the same time.

If you consider c=even;
c even and d+1 even i.e. d odd
c+2 even and d+4 odd i.e. c even and d odd
Both statements match.

c even and d+1 odd i.e. d even
c+2 even and d+4 even i.e. c even and d even
Both statements match.

Ans: "C"
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Re: If c and d are integers, is c even? [#permalink]  22 Feb 2011, 02:00
I tried this approach:

Statement 1:

c(d+1) is even

Therefore, we have three possibilities.
a) c - E & (d+1) - E => c is even and d is odd
b) c - E & (d+1) - O => c is even and d is even
c) c - O & (d+1) - E => c is odd and d is odd

So c and be even or odd!

Thus statement is not sufficient.

Statment 2:
(c+2) (d+4) is even
Therefore, there are three possibilities.
a) (c+2) is even and (d+4) is even => c is even and d is even
b) (c+2) is even and (d+4) is odd => c is even and d is odd
c) (c+2) is odd and (d+4) is even => c is odd and d is even
So c can be even or odd!
Thus statement is not sufficient.

Both Statements together:
For the cases c even and d odd or even, both the statements will always be true!
Thus c is even!
Ans: 'C'
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Re: If c and d are integers, is c even? [#permalink]  22 Feb 2011, 02:01
Looks like we used the same approach! Does anyone have a better way?
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Re: If c and d are integers, is c even? [#permalink]  22 Feb 2011, 02:09
Subtracting 2 from 1;

c(d+1)-(c+2)(d+4) = even-even=even
cd+c-cd-4c-2d-8=even
c-4c-2d-8=even
4c;2d;8 are all even
c should be even.
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Re: If c and d are integers, is c even? [#permalink]  22 Feb 2011, 02:13
Merging similar topics.
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Re: GMATprep DS (Number properties) [#permalink]  24 Feb 2011, 23:38
zaarathelab wrote:
Thanks Bunuel

OA is C

But i got lost in this number property question (was consuming too much time) and hence picked E on the test.

Is there any faster way to solve this?

No easy way to do this but you can jump to c quickly ruling out a,d and b.

Once you see which statements remain valid while taking into consideration 1 and 2, we can see that c is even.
Re: GMATprep DS (Number properties)   [#permalink] 24 Feb 2011, 23:38
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