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02 Mar 2023, 06:42
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:21) correct
24%
(00:49)
wrong
based on 34
sessions
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Not Attempted Yet
02 Mar 2023, 10:57
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GMATinsight
Statements 1 and 2 are individually not sufficient.
Both statements provide us with the identical information that a and b have the same even-odd nature. That is both the numbers are either even or both are odd.
If both numbers are even, \(\frac{a }{ b}\) can be even or it can be odd. However, when both numbers are odd, \(\frac{a }{ b}\) is always odd.
As the statements are not individually sufficient, we can eliminate A, B and D.
Combined
a-b = even
a+b = even
Adding both the statements
2a = even
a can be even or odd.
Case 1
- a - b = 2
- a + b = 4
2a = 6
a = 3; b = 1
a/b = 3 = odd
Case 2
- a - b = -4
- a + b = 4
2a = 0
a = 0 ; b = 4
a / b = 0 = even
Hence we still can have multiple answers.
Option E
02 Mar 2023, 11:50
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The given condition is pretty strange.
Is a/b = odd?
1) a-b = even
2) a+b = even
Consider a = 0 and b = 0, which is not restricted.
1) 0 - 0 = 0 insuff becuase 0/0 = not possible
2) 0 + 0 = 0 insuff becuase 0/0 = not possible
If we were given parameters, for example, a and b does not = 0 then
is a/b = odd? there is only one way for a/b to be definitely odd and that's if both a and b are odd.
consider the following properties:
even - even = even
even - odd = odd
odd - odd = even
odd - even = odd
even + even = even
even + odd = odd
odd + odd = even
odd + even = odd
1) a - b = even
a - b can be even - even or odd - odd, insufficient
2) a + b = even
a + b can be even + even or odd + odd, insufficient
combined, a and b can be both even or both odd, still insufficient.
because a/b = odd can only be answered if we know both a or b are definitely both odd. (one more condition should be added here and that is a/b = integer, for example, if a = 7, b = 5, even if both numbers fit properties 1 and 2, 7/5 is neither even nor odd. It's not an integer)
if they are both even, they can possibly be odd (6/2 = 3) or even (8/4 = 2).
So combined they are insufficient.
E
Is a/b = odd?
1) a-b = even
2) a+b = even
Consider a = 0 and b = 0, which is not restricted.
1) 0 - 0 = 0 insuff becuase 0/0 = not possible
2) 0 + 0 = 0 insuff becuase 0/0 = not possible
If we were given parameters, for example, a and b does not = 0 then
is a/b = odd? there is only one way for a/b to be definitely odd and that's if both a and b are odd.
consider the following properties:
even - even = even
even - odd = odd
odd - odd = even
odd - even = odd
even + even = even
even + odd = odd
odd + odd = even
odd + even = odd
1) a - b = even
a - b can be even - even or odd - odd, insufficient
2) a + b = even
a + b can be even + even or odd + odd, insufficient
combined, a and b can be both even or both odd, still insufficient.
because a/b = odd can only be answered if we know both a or b are definitely both odd. (one more condition should be added here and that is a/b = integer, for example, if a = 7, b = 5, even if both numbers fit properties 1 and 2, 7/5 is neither even nor odd. It's not an integer)
if they are both even, they can possibly be odd (6/2 = 3) or even (8/4 = 2).
So combined they are insufficient.
E
