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# Is a - 3b an even number?

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Math Expert
Joined: 02 Aug 2009
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Is a - 3b an even number?  [#permalink]

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Updated on: 04 Jul 2013, 22:45
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95% (hard)

Question Stats:

12% (02:13) correct 88% (02:04) wrong based on 322 sessions

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Is a - 3b an even number?

(1) b = 3a + 3
(2) b - a is an odd number

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Originally posted by chetan2u on 21 Dec 2009, 12:24.
Last edited by Bunuel on 04 Jul 2013, 22:45, edited 1 time in total.
Edited the question and added the OA.
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Math Expert
Joined: 02 Sep 2009
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Is a - 3b an even number?  [#permalink]

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21 Dec 2009, 13:49
5
5
Is a-3b an even number?

First note that we are not told that a and b are integers.

(1) $$b = 3a + 3$$ --> $$a - 3b = -8a - 9$$.

$$a = 1$$ --> $$-8a - 9 = -17 = odd$$.

$$a = \frac{3}{8}$$ --> $$-8a - 9 = -12 = even$$.

Not sufficient.

(2) $$b - a = odd$$ --> $$a = b - odd$$ --> $$a - 3b = b - odd - 3b = -2b - odd$$

$$b = odd$$ --> $$a - 3b = -2b - odd = odd$$

$$b = \frac{3}{2}$$ --> $$a - 3b = -2b - odd = even$$

Not sufficient.

(1)+(2) $$b=3a+3 and b=odd+a$$ --> $$b=odd+a=3a+3$$ --> $$odd=2a+3$$ --> $$2a=even$$ --> a is an integer --> b is an integer.

If a is even --> $$b=3a+3=odd$$ and $$a-3b=even-odd=odd$$;

If a is odd --> $$b=3a+3=even$$ and $$a-3b=odd-even=odd$$.

Sufficient.

Answer: C.
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VP
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Re: tricky ques  [#permalink]

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21 Dec 2009, 12:51
chetan2u wrote:
Is a-3b an even number?

1). b=3a+3
2). b-a is an odd number

for a -3b to equal even then a and b must be even or odd. One cannot be even and the other odd

Example:
if b = 3 to get an even a can be 11 but not 12
if b = 2 to get an even a must be even

1) b = 3a + 3
b = 3(a + 1)

if a = 2 then b = 9
if a = 3 then b = 12

none are both even or none are both odd so you can answer the question

2. b -a = odd

to get an odd b and a must be different

answer is D, each on its own that neither one will result in an even
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Re: tricky ques  [#permalink]

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21 Dec 2009, 12:54
Okay, having 2nd thoughts here because are not told that the numbers are integers. They can be fractions in which case the answer would be c
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Re: tricky ques  [#permalink]

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21 Dec 2009, 13:50
Debating between C and E. Testing decimals and C holds true a-3b is odd so I'll go with C.
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Re: tricky ques  [#permalink]

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21 Dec 2009, 14:43
if anyone did that in less than 2 mins; come on over and shovel some snow for me...!
you need a life and something to be busy with

[Except may be Bunuel; because he's already helping us]
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Re: tricky ques  [#permalink]

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21 Dec 2009, 15:05
Can a fraction be even?
Is 1\2 even or odd?

Isn't the question stem ambiguos
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Re: tricky ques  [#permalink]

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21 Dec 2009, 15:13
tuhinkanti wrote:
Can a fraction be even?
Is 1\2 even or odd?

Isn't the question stem ambiguos

An even number is an integer that is "evenly divisible" by 2 i.e., divisible by 2 without remainder, an integer of the form n = 2k, where k is an integer.

An odd number is an integer that is not evenly divisible by 2, an integer of the form n = 2k + 1, where k is an integer.

As for the question: D can not be the answer, see the solution above two different answers possible for (1) and (2).
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Re: tricky ques  [#permalink]

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21 Dec 2009, 15:47
I got the solution thanks, I ignored the fact that to get an integer results the input could be any kind of number
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Re: tricky ques  [#permalink]

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22 Dec 2009, 23:46
I went with option D, I completely ignored fraction values.

After going through the explanation I understand that it should be option C.
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Re: tricky ques  [#permalink]

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23 Dec 2009, 10:38
chetan2u wrote:
OA is E

Think OA is wrong. Source? Any explanation given?
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Re: tricky ques  [#permalink]

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26 Dec 2009, 10:50
sorry i typed it wrong .. i have edited the oa, it is C
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Re: Is a - 3b an even number?  [#permalink]

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25 Aug 2016, 20:35
1
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chetan2u wrote:
Is a - 3b an even number?

(1) b = 3a + 3
(2) b - a is an odd number

Please find detailed solution as attached
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Re: Is a - 3b an even number?  [#permalink]

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02 Sep 2016, 09:33
I fell for the oldest trick in the book :/
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Re: Is a-3b an even number? 1). b=3a+3 2). b-a is an odd number  [#permalink]

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05 Oct 2019, 00:58
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Re: Is a-3b an even number? 1). b=3a+3 2). b-a is an odd number   [#permalink] 05 Oct 2019, 00:58

# Is a - 3b an even number?

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