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# If r, s, and t are positive integers, is r + s + t even? (1)

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Senior Manager
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If r, s, and t are positive integers, is r + s + t even? (1) [#permalink]

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15 Sep 2007, 15:46
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If r, s, and t are positive integers, is r + s + t even?

(1) r + s is even.

(2) s +t is even.
VP
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Re: DS - Set 6, Q26 - odd + even [#permalink]

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15 Sep 2007, 15:55
gluon wrote:
If r, s, and t are positive integers, is r + s + t even?

(1) r + s is even.

(2) s +t is even.

r+s+t even?

1. r+s doesnt say anything we do not know if t is even or odd

2. s+t as well alone doesnt say anything

combined. even +even=even r+s+s+t=even so r+t is even 2s is even.
but r can be odd and t can be odd as well. or all of three integers can be odd
so cannot say yes or no

would go with E.
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15 Sep 2007, 22:09
Agreed, I think the answer is E.

(1) r + s is even (therefore r & s are either both even or both odd), t could be odd or even, therefore not enough info

(2) same analysis, s + t is even (therefore s & t are either both even or both odd), r could be odd or even, therefore not enough info

Combine (1) & (2): if we start by assuming that r & s are both even (from statement (1)), then we know that s & t will also both be even (from statement (2)), therefore r + s + t would be even.

BUT

if we then assume that r & s are both odd (also from statement (1)), then we know that s & t will also both be odd (from statement (2)), therefore r + s + t would be odd

therefore answer must be E
CEO
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Re: DS - Set 6, Q26 - odd + even [#permalink]

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15 Sep 2007, 22:38
gluon wrote:
If r, s, and t are positive integers, is r + s + t even?

(1) r + s is even.

(2) s +t is even.

I say E.

lets look at the ways for R+S+T NOT to be even. i.e. ODD

E+E+O or any order = odd

O+O+O = odd.

S1: insuff. R+S could be O+O or E+E

S2: insuff. same as S1.

S1and S2:

R+S+T could each be even--> E+E+E= E. So YES it is even

R+S+T could each be odd and still satisfy the statements: O+O+O= odd

So NO it is not even.

Ans E.
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16 Sep 2007, 03:16
e = even
o = odd

r+s = e ---> o+o=e or e+e=e

insufficient

s+t = e ---> o+o=e or e+e=e

insufficient

hence:

r+s+t = ? ---> o+o+o=o or e+e+e=e

insufficient

the answer is (E)

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Re: DS - Set 6, Q26 - odd + even [#permalink]

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16 Sep 2007, 10:50
gluon wrote:
If r, s, and t are positive integers, is r + s + t even?

(1) r + s is even.

(2) s +t is even.

yup a clear E

1) doesn't tell us anything about t
r and s could be two even or two odd ints

2) doesn't tell us about r
s and t could be two even or two odd ints

putting 1) and 2) together

all three can either be all even, which would make r + s + t even OR
all three could be odd, which would make r + s + t odd
Re: DS - Set 6, Q26 - odd + even   [#permalink] 16 Sep 2007, 10:50
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# If r, s, and t are positive integers, is r + s + t even? (1)

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