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If a, b, c, d are 4 nonnegative integers. Is (a+c) even?
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Updated on: 13 Aug 2018, 02:46
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eGMAT Question: If a, b, c, d are 4 nonnegative integers. Is (a+c) even? 1. \(a^2 +b^2 + c^2\) is even 2. \(b^2 + c^2 + d^2\) is even A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statements (1) and (2) TOGETHER are NOT sufficient This is Question 4 of The eGMAT Number Properties Marathon Go to Question 5 of the Marathon
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Re: If a, b, c, d are 4 nonnegative integers. Is (a+c) even?
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27 Feb 2018, 12:49
EgmatQuantExpert wrote: Question: If a, b, c, d are 4 nonnegative integers. Is (a+c) even? 1. \(a^2 +b^2 + c^2\) is even 2. \(b^2 + c^2 + d^2\) is even A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statements (1) and (2) TOGETHER are NOT sufficient we know even + even = even odd + odd = even so 1) \(a^2 +b^2 + c^2\) is even now here a b c are even or 2 out a/b/c are odd and one is even now a and b even c odd a+c not even now a and c odd b even a+c even insufficient 2) \(b^2 + c^2 + d^2\) is even insufficient similar to b c even d odd we don't know value of a now combining \(a^2 +b^2 + c^2\) + \(b^2 + c^2 + d^2\) = \(a^2 + 2 b^2 + 2 c^2 + d^2\) here a^2 + d^2 is even as b/c can be odd or even and still the result is even we know nothing about C being even/odd (E) imo



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Re: If a, b, c, d are 4 nonnegative integers. Is (a+c) even?
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27 Feb 2018, 13:11
We need to know the following oddeven properties even^2 = even  odd^2 = odd  even + even = even  odd + odd = even  even + odd = odd Is a+c even?1. \(a^2 + b^2 + c^2\) is even If \(a^2\), \(b^2\),and \(c^2\) are all even, then a+c is even If \(a^2\) and \(b^2\) are odd and \(c^2\) is even, a+c is odd (Insufficient)2. \(b^2 + c^2 + d^2\) is even This statement contains no information about a. We cannot say if a+c is even or not. (Insufficient)On combining the information in both the statements, We can have a case where a,b, and d are odd, whereas c is even. Here, a+c is odd But, if a,b,c, and d are all even, then a+c will be even (Insufficient  Option E)
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Re: If a, b, c, d are 4 nonnegative integers. Is (a+c) even?
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28 Feb 2018, 11:37
Solution: Step 1: Analyse Statement 1:\(a^2 +b^2 + c^2\) is Even • If \(a^2 +b^2 + c^2\) is Even, it gives rise to two possibilities:
o Either one of \(a/b/c\) is Even and the rest two are Odd o Or, all the three numbers: \(a, b\) and \(c\)are Even. Per our conceptual knowledge, let’s make a table to understand this. It is clear from the table that the evenodd nature of \((a + c)\)varies, and we cannot conclude anything about it. As we do not know the exact evenodd nature of\((a + c)\), Statement 1 alone is NOT sufficient to answer the question. Hence, we can eliminate answer choices A and D. Step 2: Analyse Statement 2:\(b^2 +c^2 + d^2\) is Even • If \(b^2 +c^2 + d^2\) is Even, it gives rise to two possibilities:
o Either one of \(b/c/d\) is Even and rest two are Odd o Or, all the three numbers: \(b, c\) and \(d\) are Even. Let’s make a table to understand this. It is clear from the table that the evenodd nature of \((a + c)\) varies, and we cannot conclude anything about it. As we do not know the exact evenodd nature of \((a + c)\), Statement 2 alone is NOT sufficient to answer the question. Hence, we can eliminate answer choice B. Step 3: Combine both Statements:From the first statement, we have: \(a^2 +b^2 + c^2\) = Even From the second statement, we have: \(b^2 +c^2 + d^2\) = Even Combining both the statements, we have: a\(^2 +b^2 + c^2 + b^2 +c^2 + d^2\) = Even + Even = Even Therefore, \(a^2 +2b^2 + 2c^2 + d^2\) is even We know that, \(2b^2 + 2c^2\) is always even irrespective of the evenodd nature of \(b\) and \(c\), since they are multiplied by an even number \((2)\) So, our expression reduces to: \(a^2 + d^2\) is even. This will lead to two possibilities: • Either both a and d are Odd. • Or both a and d are Even. Per our conceptual understanding, let us draw a table combining both the tables from Step 3 and Step 4 to see how will the even odd nature of the numbers affect the evenodd nature of the expression: \((a + c)\): From the table it is evident that the evenodd nature of the expression \((a + c)\) cannot be determined uniquely. By combining both statements we did not get a unique answer. Correct Answer: Option E
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Re: If a, b, c, d are 4 nonnegative integers. Is (a+c) even?
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22 May 2019, 12:21
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Re: If a, b, c, d are 4 nonnegative integers. Is (a+c) even?
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