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DS - odd/even problem (m04q06) [#permalink]
 16 Nov 2007, 18:10
Question Stats:
80% (01:37) correct
19% (00:15) wrong based on 2 sessions
Is integer R even? 1. R^3 + R^2 is even 2. 3R is divisible by 6Source: GMAT Club Tests - hardest GMAT questions
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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.
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Re: DS - odd/even problem [#permalink]
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.
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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
answer is B
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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
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Re: DS - odd/even problem [#permalink]
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
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Re: DS - odd/even problem (m04q06) [#permalink]
10 Nov 2010, 07:44
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yuefei wrote: Is integer R even? 1. R^3 + R^2 is even 2. 3R is divisible by 6Source: 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.
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Re: DS - odd/even problem (m04q06) [#permalink]
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
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Re: DS - odd/even problem (m04q06) [#permalink]
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....
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Re: DS - odd/even problem (m04q06) [#permalink]
11 Nov 2010, 08:52
cnrnld wrote: yuefei wrote: Is integer R even?
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. hey, nice explanation, +1!
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Re: DS - odd/even problem (m04q06) [#permalink]
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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Re: DS - odd/even problem (m04q06) [#permalink]
13 Nov 2010, 00:48
yuefei wrote: Is integer R even? 1. R^3 + R^2 is even 2. 3R is divisible by 6Source: 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.
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Re: DS - odd/even problem (m04q06) [#permalink]
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!? 
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Re: DS - odd/even problem (m04q06) [#permalink]
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.
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Re: DS - odd/even problem (m04q06) [#permalink]
14 Nov 2011, 08:45
snbury wrote: 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!? I got that same mistake this morning!.. hehehe.. someone from the gmatclub should correct it... 
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Re: DS - odd/even problem (m04q06) [#permalink]
14 Nov 2011, 11:21
ya the email didnt come clear.
i just plugged in an even number to see if it would work and it did so i would assume it is an even number.
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Re: DS - odd/even problem (m04q06) [#permalink]
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.
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Re: DS - odd/even problem (m04q06) [#permalink]
14 Nov 2012, 06:57
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Re: DS - odd/even problem (m04q06) [#permalink]
14 Nov 2012, 07:35
Question of the day posted incorrectly. In case it helps track down a bug, the email contained the following for statement 2: "2s is divisible by 6"
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Re: DS - odd/even problem (m04q06) [#permalink]
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.
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Re: DS - odd/even problem (m04q06)
[#permalink]
14 Nov 2012, 09:08
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