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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
15% (02:14) correct
85%
(02:03)
wrong
based on 496
sessions
History
Date
Time
Result
Not Attempted Yet
21 Dec 2009, 14:49
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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.
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.
General Discussion
21 Dec 2009, 13:51
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chetan2u
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
