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If X is a factor of 30, is X even?

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If X is a factor of 30, is X even?  [#permalink]

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New post Updated on: 13 Aug 2018, 01:17
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A
B
C
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E

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If X is a factor of 30, is X even?

1) X is a prime number less than 5
2) X is a factor of 10.

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

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Originally posted by EgmatQuantExpert on 27 Feb 2018, 09:14.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:17, edited 2 times in total.
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Re: If X is a factor of 30, is X even?  [#permalink]

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New post 27 Feb 2018, 09:53
EgmatQuantExpert wrote:

Question:



If X is a factor of 30, is X even?

1) X is a prime number less than 5
2) X is a factor of 10.

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


Statement 1: \(x\) can be 2 or 3. Insufficient

Statement 2: \(x\) can be 2 or 5. Insufficient

Combining 1 & 2: \(x=2\). Sufficient

Option C
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Re: If X is a factor of 30, is X even?  [#permalink]

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New post 27 Feb 2018, 22:37

Solution:



Step 1: Analyse Statement 1:
\(X\) is a prime number \(<5\)
  • We know that there are only \(2\) prime numbers below \(5\).
      o They are\(2\) and \(3\) respectively.
      From the inference segment, both \(2\) and \(3\) are the factors of \(30\).
    As we do not know the exact value of \(X\), we cannot determine its even-odd nature.
    Statement 1 alone is NOT sufficient to answer the question.
    Hence, we can eliminate answer choices A and D.
    Step 2: Analyse Statement 2:
    \(X\) is a factor of \(10\).
    • \(10\)can be written as \(2*5\).
    • Let us write all the factors of \(10\).
        o Factors of \(10: 1,2,5,10\)
    • Comparing this with the inference segment, we see all the \(4\) numbers: \(1, 2, 5\) and\(10\) are factors of \(30\) as well.

    Since we do not know the exact value of \(X\), we cannot determine its even-odd nature.
    Statement 2 alone is NOT sufficient to answer the question.
    Hence, we can eliminate answer choice B.
    Step 5: Combine both Statements:
    • From the first statement we got: \(X\) can be either \(2\) or \(3\)
    • From the second statement we got: \(X\) can be any one of \(1, 2, 5\) and \(10\).
    • The only number which is common to both the lists obtained is \(2\).
    Thus, we got a unique value of \(X\), which is \(2\) and we can say that \(X\) is Even in nature.
    By combining both statements we got a unique answer.
    Correct Answer: Option C
    _________________








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    Re: If X is a factor of 30, is X even? &nbs [#permalink] 27 Feb 2018, 22:37
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