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f(x) denotes the maximum prime factor of x, where x is a pos

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f(x) denotes the maximum prime factor of x, where x is a pos

by Max@Math Revolution » Thu Oct 03, 2019 11:23 pm
[GMAT math practice question]

f(x) denotes the maximum prime factor of x, where x is a positive integer. For example, f(30)=f(2*3*5)=5. What is the value of f(abc)?

1) f(a) = 2
2) f(b)+f(c)=14
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Source: — Data Sufficiency |
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edited:

by deloitte247 » Sun Oct 06, 2019 7:29 am
f(x) = highest prime factor of x
Where x = positive integer
If x=6, then f(x) = f(2*3) = 3
If x = 30, then f(x) = f(30) = F(2*3*4) = 5
Question=> What is the value of f(abc)?
Statement 1: f(a)=2
f(abc)=> f(2*b*c) =...
Value of b and c is still unknown, hence, we cannot assert the highest prime factor as 'b' and 'c' can be any number. So, statement 1 is NOT SUFFICIENT.

Statement 2: f(b) + f(c) = 14
The sum of these two function takes the value of b and c as arguments respectively and return 14. It does not give reference to the exact value. Hence, statement 2 is NOT SUFFICIENT.

Combining both statement together
Statement 1: f(a)=2
Statement 2: f(b) + f(c) = 14
For f(b) + f(c) = 14, the possible combinations in which both are f(b) and f(c) are prime number is 3 and 11; 7 and 7.
If f(b)=3 and f(c)=11, then f(abc)=(2*3*11) = 11
If f(b)=7 and f(c)=7, then f(abc)=(2*7*7) = 7
Sine we cannot arrive at a definite value for the function f(abc), then both statement combined together are NOT SUFFICIENT.

Answer is therefore option E
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by Max@Math Revolution » Sun Oct 06, 2019 5:56 pm
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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.
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Since we have 3 variables and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

If a = 2, b = 7 and c = 7, then f(abc) = f(2*7^2) = 7.
If a = 2, b = 3 and c = 11, then f(abc) = f(2*3*11) = 11.
Both conditions together do not yield a unique solution, so they are not sufficient.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with "3 variables", or "4 variables and 1 equation", or "5 variables and 2 equations", conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions when the answer is A, B, C, or D.
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