Is a - 3b an even number?

Question

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

lagomez · Answer

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

lagomez · Answer

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

Bunuel · Answer

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.

adamsmith2010 · Answer

Debating between C and E. Testing decimals and C holds true a-3b is odd so I'll go with C.

DestinyChild · Answer

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

Bunuel ; because he's already helping us]

tuhinkanti · Answer

Can a fraction be even?
Is 1\2 even or odd?

Isn't the question stem ambiguos

Bunuel · Answer

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).

tuhinkanti · Answer

I got the solution thanks, I ignored the fact that to get an integer results the input could be any kind of number

tania · Answer

I went with option D, I completely ignored fraction values.

After going through the explanation I understand that it should be option C.

Bunuel · Answer

Think OA is wrong. Source? Any explanation given?

chetan2u · Answer

sorry i typed it wrong .. i have edited the oa, it is C

GMATinsight · Answer

Please find detailed solution as attached

lifetantrik · Answer

I fell for the oldest trick in the book :/

bumpbot · Answer

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Is a - 3b an even number?

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