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07 Apr 2021, 04:00
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Difficulty:
45%
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Question Stats:
58% (01:29) correct
42%
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wrong
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If a and b are integers, is b even?
(1) 5a + 6b is even.
(2) 5a + 3b is even.
(1) 5a + 6b is even.
(2) 5a + 3b is even.
07 Apr 2021, 04:05
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If a and b are integers, is b even?
(1) 5a + 6b is even.
6b is surely even, so 5a must be even as the sum 5a+6b is even.
5a can be even only when a is even.
Nothing about b.
Insufficient
(2) 5a + 3b is even.
Both 5a and 3b can be even : Then a and b are even.
Both 5a and 3b can be odd: Then both a and b are odd.
Insufficient
Combined
Both a and b have same property. Thus b is even as a is even from statement I.
Sufficient
C
(1) 5a + 6b is even.
6b is surely even, so 5a must be even as the sum 5a+6b is even.
5a can be even only when a is even.
Nothing about b.
Insufficient
(2) 5a + 3b is even.
Both 5a and 3b can be even : Then a and b are even.
Both 5a and 3b can be odd: Then both a and b are odd.
Insufficient
Combined
Both a and b have same property. Thus b is even as a is even from statement I.
Sufficient
C
07 Apr 2021, 10:44
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If a and b are integers, is b even?
(1) 5a + 6b is even.
(2) 5a + 3b is even.
statement 1 : 5a + 6b = even
+6b must be even whether b even / odd
so, 5a must be even , a must be even
b even / odd, not sufficient
Statement 2 : 5a + 3b = even.
5a must be odd and 3b must be odd
or
5a must be even and 3b must be even
b can be even / odd, not sufficient
statement 1 + 2 : a must be even from statement 1
so, b must be even
sufficient
Answer C
(1) 5a + 6b is even.
(2) 5a + 3b is even.
statement 1 : 5a + 6b = even
+6b must be even whether b even / odd
so, 5a must be even , a must be even
b even / odd, not sufficient
Statement 2 : 5a + 3b = even.
5a must be odd and 3b must be odd
or
5a must be even and 3b must be even
b can be even / odd, not sufficient
statement 1 + 2 : a must be even from statement 1
so, b must be even
sufficient
Answer C
