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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
Question Stats:
25% (03:03) correct
75% (01:15) wrong based on 1 sessions
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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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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Re: GMATprep DS (Number properties) [#permalink]
01 Feb 2010, 14:46
obviously, 1 or 2 separatly is not sufficient.
Both:
start with a second statement:
(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.
Answer C
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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... Answer C...
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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? Answer is C. 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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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. Hence combining both statements would answer the question. Answer C.
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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
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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.
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Re: GMATprep DS (Number properties)
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24 Feb 2011, 23:38
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