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# DS - odd/even problem (m04q06)

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Manager
Joined: 02 Aug 2007
Posts: 145
DS - odd/even problem (m04q06) [#permalink]

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16 Nov 2007, 18:10
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Is integer $$R$$ even?

1. $$R^3 + R^2$$ is even
2. $$3R$$ is divisible by $$6$$

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions
Manager
Joined: 02 Aug 2007
Posts: 145

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16 Nov 2007, 18:20
1) INSUFF
odd^2 or odd^3 = odd
even^2 or even^3 = even
So could be either even or odd.

2) SUFFICIENT B.
If 3R is divisible by 6, then 3R contains a prime number 2. An even* anything is even. This is sufficient.
CEO
Joined: 29 Mar 2007
Posts: 2559
Re: DS - odd/even problem [#permalink]

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17 Nov 2007, 00:05
yuefei wrote:
Is integer R even?

1) R3 + R2 is even
2) 3R is divisible by 6

Im kinda confused about s1 is it 3R +2R??? or is it R^3 +R^2???

If so I get it as suff. Remember R is an integer as stated by the original stem.

1: 3R+2R. 2R will always be even. 3R can be odd or even. However,
we have O+E=E... not true. So 3R must also be even. E+E=E... true.

so R must be even or 3R will not be even.

2: obviously sufficient.

1: again. R^3+R^2 =E R can be both E or O.

E+E=E O+O=E insuff.

So its either D or B.
SVP
Joined: 05 Jul 2006
Posts: 1747

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17 Nov 2007, 00:48
Is integer R even?

1) R3 + R2 is even
2) 3R is divisible by 6

from one

r^2(r+1) = even , odd* even = even, even*even = even

insuff

from 2

suff

Manager
Joined: 02 Aug 2007
Posts: 145

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17 Nov 2007, 18:05
Sorry, to clarify:
1) should be R^2 + R^3

This is insufficient. If R is odd, then R^2 and R^3 will also be odd. Same goes if R is even.

OA B
Intern
Joined: 19 Nov 2007
Posts: 4
Re: DS - odd/even problem [#permalink]

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20 Nov 2007, 01:59
yuefei wrote:
Is integer R even?

1) R3 + R2 is even
2) 3R is divisible by 6

Since (R3+R2) is even(It is given in first condition)
now R2 is always is even(R*2)
for (R3+R2) to be Even, R3 must be even bcos only even + even = Even.
for this R must be even bcos EvenR * 3 = even.
therefore condition one alone is sufficient.
now from i condition 2 it is clear the R is even.
therfore 2 alone itself is sufficient.

Therfore Ans must be D
Intern
Joined: 25 Aug 2010
Posts: 41
Re: DS - odd/even problem (m04q06) [#permalink]

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10 Nov 2010, 07:44
2
KUDOS
yuefei wrote:
Is integer $$R$$ even?

1. $$R^3 + R^2$$ is even
2. $$3R$$ is divisible by $$6$$

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

my way proposed as follows.

1. $$R^3+R^2=R^2(R+1)$$
in $$R*R*(R+1)$$, there is at least one number even, so we don't know if R is odd or even when the result is even.

2. $$\frac{3R}{6}=\frac{3R}{2*3}=\frac{R}{2}$$
since $$\frac{R}{2}$$ is an integer (divisible by 6), R should be even.

thus B.
Intern
Joined: 28 Sep 2010
Posts: 1
Re: DS - odd/even problem (m04q06) [#permalink]

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10 Nov 2010, 09:03
In statement #2, what would happen if zero is considered? Zero is an integer, however it is neither odd nor even. Am I thinking too much for the purpose of GMAT?

Also if I encounter this question on GMAT exam, should I consider zero at all?

Thanks
Manager
Joined: 16 Feb 2010
Posts: 225
Re: DS - odd/even problem (m04q06) [#permalink]

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10 Nov 2010, 21:33
peterwang wrote:
In statement #2, what would happen if zero is considered? Zero is an integer, however it is neither odd nor even. Am I thinking too much for the purpose of GMAT?

Also if I encounter this question on GMAT exam, should I consider zero at all?

Thanks

zero is a non-negative and non-positive EVEN number for GMAT....
Intern
Joined: 26 Nov 2009
Posts: 44
Location: India
Re: DS - odd/even problem (m04q06) [#permalink]

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11 Nov 2010, 09:36
To check 1 apply basic rules:

Odd + Odd = Even
Even + Even = Even

and Odd/Even raise to anything remains Odd/Even.
Thus 1 takes us no where.

To check 2 :

6 = 2*3
Thus if 3R is divisible by 6, 2 is a factor of R and thus R is even.
_________________

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Manager
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Re: DS - odd/even problem (m04q06) [#permalink]

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13 Nov 2010, 00:48
yuefei wrote:
Is integer $$R$$ even?

1. $$R^3 + R^2$$ is even
2. $$3R$$ is divisible by $$6$$

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

Stmnt 1: Holds true for both R=1 (odd) and R=2 (even). Insufficient.
Stmnt 2: R must be a multiple of 2 in order for 3R to be divisible 6. Sufficient.

B: 2 alone is sufficient.
_________________

Respect,
Vaibhav

PS: Correct me if I am wrong.

Manager
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Location: United States
Concentration: Strategy
GPA: 3.1
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Re: DS - odd/even problem (m04q06) [#permalink]

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14 Nov 2011, 07:34
What the...?

This is what I got in my email today as a question:

Is integer R even?

1. R^3+R^2 is even
2. 2S is divisible by 6

I was thinking what does 2S have to do with anything!?
Intern
Status: Stay Hungry, Stay Foolish.
Joined: 05 Sep 2011
Posts: 41
Location: India
Concentration: Marketing, Social Entrepreneurship
Re: DS - odd/even problem (m04q06) [#permalink]

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14 Nov 2011, 08:19
Statement 1)
R^2 (1 + R) is Even.

This can be Even*Even OR Odd*Even, which results in an Even number.
Hence insufficient.

Statement 2)
3R/ 6 is even.
3R will be multiple of 6.
R will take all those values that are even,and when multiplied by 3 will give a multiple of 6.
Therefore, R is even.
Sufficient.

Hence, B.
Manager
Joined: 21 Nov 2010
Posts: 128
Re: DS - odd/even problem (m04q06) [#permalink]

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16 Nov 2011, 18:08
B.

I got this as a question of the day and 2 was written as 2s is divisible by 6 and I was thinking this problem seems way too easy...makes sense now.
Math Expert
Joined: 02 Sep 2009
Posts: 39673
Re: DS - odd/even problem (m04q06) [#permalink]

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14 Nov 2012, 06:57
1
KUDOS
Expert's post
yuefei wrote:
Is integer $$R$$ even?

1. $$R^3 + R^2$$ is even
2. $$3R$$ is divisible by $$6$$

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

Is integer $$r$$ even?

(1) $$r^3+r^2$$ is even --> both even and odd values of $$r$$ satisfy this statement: $$odd^3+odd^2=odd+odd=even$$ and $$even^3+even^2=even+even=even$$. Not sufficient.

(2) $$3r$$ is divisible by 6 --> $$\frac{3r}{6}=integer$$ --> $$\frac{r}{2}=integer$$ --> $$r=2*integer$$ --> $$r=even$$. Sufficient.

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Manager
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Schools: Merage '15 (A)
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Re: DS - odd/even problem (m04q06) [#permalink]

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14 Nov 2012, 09:08
for 1:
R = 1 => R cube + R sqr = 2 (even)
R = 2 => R cube + R sqr = 12 (even)
R = 3 => R cube + R sqr = 36 (even)
R = 4 => R cube + R sqr = 82 (even)

so we get all values(even + odd) of R for which the eqn is even. NOT SUFFICIENT

for 2:
R = 1 => 3R = 3 => is div by 6 (no)
R = 2 => 3R = 6 => is div by 6 (yes)
R = 3 => 3R = 9 => is div by 6 (no)
R = 4 => 3R = 12 => is div by 6 (yes)

thus it gives us "is div by 6 -yes" of eqn for even values of R.
Hence B is SUFFICIENT.
Senior Manager
Joined: 08 Jun 2010
Posts: 392
Location: United States
Concentration: General Management, Finance
GMAT 1: 680 Q50 V32
Re: DS - odd/even problem (m04q06) [#permalink]

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15 Nov 2012, 17:53
Please correct the Arithmetic and Critical Reasoning question as of 14th Nov 2012.

Answer B is not phrased correctly.

The variable s is not mentioned in the question stem and hence cannot be the answer. The variable s should be variable R.
Re: DS - odd/even problem (m04q06)   [#permalink] 15 Nov 2012, 17:53
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# DS - odd/even problem (m04q06)

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