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# Is N odd? (1) N is a factor of 100. (2) N is a factor of 135.

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Is N odd? (1) N is a factor of 100. (2) N is a factor of 135.  [#permalink]

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29 Apr 2020, 02:20
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25% (medium)

Question Stats:

78% (00:47) correct 22% (01:01) wrong based on 36 sessions

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Is integer N odd?

(1) N is a factor of 100.

(2) N is a factor of 135.

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Re: Is N odd? (1) N is a factor of 100. (2) N is a factor of 135.  [#permalink]

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29 Apr 2020, 02:24
St b is sufficient

All the factors of 135 are odd.

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Re: Is N odd? (1) N is a factor of 100. (2) N is a factor of 135.  [#permalink]

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29 Apr 2020, 02:30
1
Bunuel wrote:
Is integer N odd?

(1) N is a factor of 100.

(2) N is a factor of 135.

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Question: Is integer N odd?

Statement 1: N is a factor of 100

n may be 2 or 5

Not Sufficient

Statement 2: N is a factor of 135.

135 is odd hence every factor of odd is odd

Sufficient

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Re: Is N odd? (1) N is a factor of 100. (2) N is a factor of 135.  [#permalink]

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29 Apr 2020, 02:37
1
Bunuel wrote:
Is integer N odd?

(1) N is a factor of 100.

(2) N is a factor of 135.

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Solution

Step 1: Analyse Question Stem

• N is an integer.
We need to find whether N is odd or even.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: N is a factor of 100
• $$100= 2^2*5^2$$
o N can be 1, 2, 4, 5, 20, 25, 50 and 100
o We cannot say whether N is odd or not.
Hence, statement 1 is not sufficient, we can eliminate answer options A and D.
Statement 2: N is a factor of 135.
• $$135 = 3^3*5$$
o All of the factors of 135 are odd.
 N will be an odd number.
Hence, statement 2 is sufficient, the correct answer is Option B.

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Re: Is N odd? (1) N is a factor of 100. (2) N is a factor of 135.  [#permalink]

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29 Apr 2020, 12:13
1
Bunuel wrote:
Is integer N odd?

(1) N is a factor of 100.

(2) N is a factor of 135.

Project PS Butler

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 1 variable (N) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)

Since $$1$$ is a factor of $$100$$ and $$1$$ is an odd integer, the answer is 'yes'.
Since $$2$$ is a factor of $$100$$ and $$2$$ is an even integer, the answer is 'no'.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)

Since $$135=3^3 \cdot 5$$ does not a prime factor $$2$$, $$135$$ does not have an even factor and N must be an odd number.

Since condition 2) yields a unique solution, it is sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: Is N odd? (1) N is a factor of 100. (2) N is a factor of 135.   [#permalink] 29 Apr 2020, 12:13