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26 May 2021, 17:32
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B
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Difficulty:
85%
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Question Stats:
43% (02:27) correct
57%
(02:23)
wrong
based on 65
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Given ‘a’ and ‘b’ are positive integers, is the number b^2+7b+ab even?
(1) (a+ b)(a - b) is a multiple of 2
(2) (a+2)(a-2) is a multiple of 4
(1) (a+ b)(a - b) is a multiple of 2
(2) (a+2)(a-2) is a multiple of 4
26 May 2021, 18:29
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First we make a table for the original expresion:
a b expresion
even even even
even odd even
odd even even
odd odd odd
(1) (a+b)(a-b)=a^2-b^2 is even
this implies that both a and b are even or odd. If we look at the table we have different results so it is insufficient.
(2) (a+2)(a-2)=a^2-4 is multiple of 4, so it is even
this implies that a must be even. If we look at the table we have that when a is even the expresion is always even, so sufficient.
IMO B
a b expresion
even even even
even odd even
odd even even
odd odd odd
(1) (a+b)(a-b)=a^2-b^2 is even
this implies that both a and b are even or odd. If we look at the table we have different results so it is insufficient.
(2) (a+2)(a-2)=a^2-4 is multiple of 4, so it is even
this implies that a must be even. If we look at the table we have that when a is even the expresion is always even, so sufficient.
IMO B
16 Sep 2023, 03:11
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Can anyone answer this in detail ?
