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f(x) is the greatest prime factor of x. If n is a positive i

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by Max@Math Revolution » Sun Dec 23, 2018 11:35 pm

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[Math Revolution GMAT math practice question]

f(x) is the greatest prime factor of x. If n is a positive integer less than 10, what is the value of n?

1) f(n) = f(1000)
2) f(n) = 5
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by fskilnik@GMATH » Mon Dec 24, 2018 9:25 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

f(x) is the greatest prime factor of x. If n is a positive integer less than 10, what is the value of n?

1) f(n) = f(1000)
2) f(n) = 5
$$1 \leqslant n\,\,\operatorname{int} \leqslant 9\,\,\,\,\,\left( * \right)$$
$$? = n\,$$

$$\left( 1 \right)\,\,\,{\text{max}}\,\,{\text{prime}}\,\,{\text{factor}}\,\,{\text{of}}\,\,n\,\,{\text{equals}}\,\,\,5\,\,\,\,\left( {{\text{ = }}\,\,{\text{max}}\,\,{\text{prime}}\,\,{\text{factor}}\,\,{\text{of}}\,\,{{10}^3} = {2^3} \cdot {5^3}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\,\,\,\,\,\,? = n = 5$$
$$\left( 2 \right)\,\,{\text{max}}\,\,{\text{prime}}\,\,{\text{factor}}\,\,{\text{of}}\,\,n\,\,{\text{equals}}\,\,\,5\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,? = n = 5$$

The correct answer is (D).


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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Tue Dec 25, 2018 11:56 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.

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 1000 = 2^3*5^3, f(1000) = 5.
So, f(n) = 5 and n = 5.
Thus, condition 1) is sufficient, since it gives a unique solution.

Condition 2)
Condition 2) is the same as condition 1).
Thus, condition 2) is also sufficient.

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

Therefore, D is the answer.
Answer: D

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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