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Is b even?

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SVP
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Is b even?  [#permalink]

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New post 26 Dec 2018, 14:02
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:28) correct 36% (01:47) wrong based on 17 sessions

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Is b even?

1) 3a + 4b = even

2) 3a + 5b = even
Senior Manager
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Concentration: Strategy, International Business
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Re: Is b even?  [#permalink]

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New post 26 Dec 2018, 14:59
Mo2men wrote:
Is b even?

1) 3a + 4b = even

2) 3a + 5b = even


statement 1: concludes that 'a' must be even, but no clue about 'b'.

statement 2: concludes that 'a' and 'b' can both be even or both be odd. however, it can't give certain answer.

by combining (1) and (2): if 'a' must be even according to (1), then 'b' must be even as well according to (2).

so IMO "C"
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Re: Is b even?  [#permalink]

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New post 26 Dec 2018, 15:05
Mo2men wrote:
Is b even?

1) 3a + 4b = even

2) 3a + 5b = even


statement 1: 3a + 4b = even. 4b = even. it's not possible to determine whether b is even or odd. NOT sufficient.

Statement 2: 3a + 5b = even. In this case, both a and b can take both odd and even integers. NOT sufficient.

Combining :

deduct statement 1 from statement 2:

3a + 5b =even
3a + 4b = even
.............................
b = even -even
b = even.

C is our answer.
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Re: Is b even?  [#permalink]

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New post 26 Dec 2018, 15:12
1) 3a + 4b = even
Even + Even = Even OR Odd + Odd = Even. 4b will always be even regardless of b's value. So, 3a is even--Thus, a is even. b can be odd or even. Example: a = 2, b =2 OR a=2, b =3. More than one possibility = NS.

2) 3a + 5b = even
This tells us that a and b are BOTH even OR a and b are BOTH odd. NS

Combined: a is even (from 1) and a and b are BOTH even (from 2). Thus, b must be even. Sufficient "yes" to the prompt question.

Final answer: C
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Re: Is b even?   [#permalink] 26 Dec 2018, 15:12
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