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04 May 2022, 04:00
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E
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Difficulty:
55%
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Question Stats:
58% (02:07) correct
42%
(02:11)
wrong
based on 33
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If a and b are positive integers, is a even?
(1) ab + b is an even number.
(2) ab + a is an even number.
(1) ab + b is an even number.
(2) ab + a is an even number.
04 May 2022, 08:01
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Step 1: Analyse Question Stem
a and b are positive integers. Therefore, they could be odd or even.
We have to find out if a is even.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: ab + b is an even number.
Always factor out terms in common, always try to convert a sum/difference of terms to a product of terms.
Clearly, b is common; therefore, ab + b = b (a + 1) = even.
This only means that at least one of these terms is even. Nothing can be said conclusively about a being even.
The data in statement 1 is insufficient to answer the question with a definite YES or NO.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: ab + a is an even number.
Factoring out a, a (b + 1) = even.
This situation is similar to the one that we saw in statement 1. Again, nothing can be said conclusively about a being even.
The data in statement 2 is insufficient to answer the question with a definite YES or NO.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: ab + b = even
From statement 2: ab + a = even
Subtracting the two equations, we have an equation,
a – b = even.
This only means that a and b have the same nature. However, this too, is insufficient to say anything conclusively about a being even.
The combination of statements is insufficient to answer the question with a definite YES or NO.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.
The correct answer option is E.
a and b are positive integers. Therefore, they could be odd or even.
We have to find out if a is even.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: ab + b is an even number.
Always factor out terms in common, always try to convert a sum/difference of terms to a product of terms.
Clearly, b is common; therefore, ab + b = b (a + 1) = even.
This only means that at least one of these terms is even. Nothing can be said conclusively about a being even.
The data in statement 1 is insufficient to answer the question with a definite YES or NO.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: ab + a is an even number.
Factoring out a, a (b + 1) = even.
This situation is similar to the one that we saw in statement 1. Again, nothing can be said conclusively about a being even.
The data in statement 2 is insufficient to answer the question with a definite YES or NO.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: ab + b = even
From statement 2: ab + a = even
Subtracting the two equations, we have an equation,
a – b = even.
This only means that a and b have the same nature. However, this too, is insufficient to say anything conclusively about a being even.
The combination of statements is insufficient to answer the question with a definite YES or NO.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.
The correct answer option is E.
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