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What is the value of the integer n?

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by Max@Math Revolution » Tue Jan 01, 2019 5:39 am

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[Math Revolution GMAT math practice question]

What is the value of the integer n?

1) n is a prime factor of 21
2) n is a factor of 49
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Jan 01, 2019 8:33 am
Max@Math Revolution wrote:What is the value of the integer n?
1) n is a prime factor of 21
2) n is a factor of 49
Target question: What is the value of the integer n?

Statement 1: n is a prime factor of 21
21 = (3)(7)
So, EITHER n = 3 OR n = 7
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is a factor of 49
49 has three positive factors: 1, 7, and 49
So, n could equal 1, 7 or 49
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that n is either 3 or 7
Statement 2 tells us that n is 1, 7 or 49
Since only one value (x = 7) satisfies BOTH statements, it MUST be the case that n = 7
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Wed Jan 02, 2019 2:29 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

What is the value of the integer n?

1) n is a prime factor of 21
2) n is a factor of 49
$$? = n\,\,\,\,\left( {n\,\,{\mathop{\rm int}} } \right)$$
$$\left( 1 \right)\,\,n \in \left\{ {3,7} \right\}\,\,\,\,\,\left[ {\,{\rm{primes}}\,\,{\rm{are}}\,\,{\rm{positive}}\,\,{\rm{integers}}\,} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}{\rm{.}}\,\,\,$$
$$\left( 2 \right)\,\,n \in \left\{ { - 1, - 7, - 49,1,7,49} \right\}\,\,\,\,\,\left[ {\,{\rm{factors}}\,\,{\rm{are}}\,\,{\rm{integers}},\,\,{\rm{not}}\,\,{\rm{necessarily}}\,\,{\rm{positive}}\,} \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.$$
$$\left( {1 + 2} \right)\,\,\,n = 7\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Max@Math Revolution » Wed Jan 02, 2019 11:12 pm
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

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)
n is a prime factor of 21 = 3*7 and n is 3 or 7.
Since it does not give a unique answer, condition 1) is not sufficient.

Condition 2)
If n is a factor of 49 = 7^2, then n is 1, 7 or 49.
Since it does not give a unique answer, condition 2) is not sufficient.

Conditions 1) & 2)
The unique integer satisfying both conditions is n = 7.
Both conditions are sufficient, when taken together.

Therefore, C is the answer.
Answer: C

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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