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14 Sep 2020, 00:15
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If a is an integer, is a/2 an even integer?
(1) 3a is even.
(2) 4a is even.
Are You Up For the Challenge: 700 Level Questions
(1) 3a is even.
(2) 4a is even.
Are You Up For the Challenge: 700 Level Questions
yashikaaggarwal
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14 Sep 2020, 00:46
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Given: If a is an integer,
To find: is a/2 an even integer?
(1) 3a is even.
Odd*even = even
So a = even
Case 1: A = 2
Then A/2 = 2/2 = 1 (Not an even integer)
Case 2: A = 4
Then A/2 = 4/2 = 2 (An even integer)
(Insufficient)
(2) 4a is even.
Even*odd = even
Even*even= even
A can be odd or even
Case 1: A is odd, let say 3
A/2 = 3/2 = 1.5 (not an even integer)
Case 2: A is even , let say 2
A/2 = 2/2 = 1(not an even integer)
Case 3: A = 4
A/2 = 4/2 = 2(even integer)
(Insufficient)
Combining both A can be 2 or 4
(Insufficient again)
Answer is E
Posted from my mobile device
To find: is a/2 an even integer?
(1) 3a is even.
Odd*even = even
So a = even
Case 1: A = 2
Then A/2 = 2/2 = 1 (Not an even integer)
Case 2: A = 4
Then A/2 = 4/2 = 2 (An even integer)
(Insufficient)
(2) 4a is even.
Even*odd = even
Even*even= even
A can be odd or even
Case 1: A is odd, let say 3
A/2 = 3/2 = 1.5 (not an even integer)
Case 2: A is even , let say 2
A/2 = 2/2 = 1(not an even integer)
Case 3: A = 4
A/2 = 4/2 = 2(even integer)
(Insufficient)
Combining both A can be 2 or 4
(Insufficient again)
Answer is E
Posted from my mobile device
14 Sep 2020, 00:55
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This is a YES/No type of DS question. Substituting values would be the best way to solve.
Constraint: a is an integer. So a can range from -\(\infty\) to +\(\infty\)
Question: Is \(\frac{a}{2}\) even.
This here might suggest that a has to be 0 or even, but that is not correct if a = 2, 6, 10 as \(\frac{a}{2}\), will be odd for these numbers.
So, we need to know if a is a multiple of 4 or if a is 0.
Statement 1: 3a is even
Since 3a is even and we know that Odd * Even given an even number, so a is even (0,2,4...)
If a = 2, then \(\frac{a}{2} = 1\) which is odd
If a = 4, then \(\frac{a}{2} = 2\) which is even
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E
Statement 2: 4a is even.
This indicates that a can be even or odd as Even * Even = Even and Even * Odd = Even.
a = 1, \(\frac{a}{2} = \frac{1}{2}\) which is neither even nor odd
a = 2, \(\frac{a}{2} = 1\) which is odd
Therefore Statement 2 Alone is Insufficient.
Combining Both Statements: We get that a is definitely even, but we cannot say that it is a multiple of 4.
Therefore Both Statements together are Insufficient.
Option E
Arun Kumar
Constraint: a is an integer. So a can range from -\(\infty\) to +\(\infty\)
Question: Is \(\frac{a}{2}\) even.
This here might suggest that a has to be 0 or even, but that is not correct if a = 2, 6, 10 as \(\frac{a}{2}\), will be odd for these numbers.
So, we need to know if a is a multiple of 4 or if a is 0.
Statement 1: 3a is even
Since 3a is even and we know that Odd * Even given an even number, so a is even (0,2,4...)
If a = 2, then \(\frac{a}{2} = 1\) which is odd
If a = 4, then \(\frac{a}{2} = 2\) which is even
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E
Statement 2: 4a is even.
This indicates that a can be even or odd as Even * Even = Even and Even * Odd = Even.
a = 1, \(\frac{a}{2} = \frac{1}{2}\) which is neither even nor odd
a = 2, \(\frac{a}{2} = 1\) which is odd
Therefore Statement 2 Alone is Insufficient.
Combining Both Statements: We get that a is definitely even, but we cannot say that it is a multiple of 4.
Therefore Both Statements together are Insufficient.
Option E
Arun Kumar
