Given f(x) = 3x-5, for what value of x does 2*[f(x)-1] = f(3x-6)?
(A) 0
(B) 4
(C) 6
(D) 7
(E) 13
What is the shortcut way to solve this kind of problem?
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The problem has been transcribed incorrectly.
It should read as follows:
When the correct answer choice is plugged in, 2f(x) - 1 = f(3x-6).
Both the original function -- f(x) = 3x-5 -- and the equation above involve multiplication.
Generally, the smaller the value, the less the value will be affected by multiplication.
Implication:
2f(x) - 1 = f(3x-6) will likely be true for a relatively small value of x.
Answer choice B: x=4
2f(x) - 1:
f(x) = f(4) = 3*4 - 5 = 7.
Thus, 2f(x) - 1 = 2*7 - 1 = 13.
f(3x - 6):
f(3x - 6) = f(3*4 - 6) = f(6).
f(6) = 3*6 - 5 = 13.
Success!
2f(x) - 1 = f(3x-6) = 13.
The correct answer is B.
It should read as follows:
We can PLUG IN THE ANSWERS, which represent the value of x.Given f(x) = 3x-5, for what value of x does 2f(x) - 1 = f(3x-6)?
(A) 0
(B) 4
(C) 6
(D) 7
(E) 13
When the correct answer choice is plugged in, 2f(x) - 1 = f(3x-6).
Both the original function -- f(x) = 3x-5 -- and the equation above involve multiplication.
Generally, the smaller the value, the less the value will be affected by multiplication.
Implication:
2f(x) - 1 = f(3x-6) will likely be true for a relatively small value of x.
Answer choice B: x=4
2f(x) - 1:
f(x) = f(4) = 3*4 - 5 = 7.
Thus, 2f(x) - 1 = 2*7 - 1 = 13.
f(3x - 6):
f(3x - 6) = f(3*4 - 6) = f(6).
f(6) = 3*6 - 5 = 13.
Success!
2f(x) - 1 = f(3x-6) = 13.
The correct answer is B.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Hi NaimaB,
I'm a big fan of TESTing THE ANSWERS (the approach that Mitch used); this question can also be solved algebraically.
We're given the function: f(X) = 3X - 5
We're given an equation that uses the function, so we can plug in the respective values (X and [3X-6]) into the function and solve:
2f(X) - 1 = f(3X - 6)
Left side:
2[f(X)] - 1 = 2(3X - 5) - 1 = 6X - 10 - 1 = 6X - 11
Right side:
f(3X - 6) = 3(3X-6) - 5 = 9X - 18 - 5 = 9X - 23
Now set them equal to one another:
6X - 11 = 9X - 23
12 = 3X
4 = X
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
I'm a big fan of TESTing THE ANSWERS (the approach that Mitch used); this question can also be solved algebraically.
We're given the function: f(X) = 3X - 5
We're given an equation that uses the function, so we can plug in the respective values (X and [3X-6]) into the function and solve:
2f(X) - 1 = f(3X - 6)
Left side:
2[f(X)] - 1 = 2(3X - 5) - 1 = 6X - 10 - 1 = 6X - 11
Right side:
f(3X - 6) = 3(3X-6) - 5 = 9X - 18 - 5 = 9X - 23
Now set them equal to one another:
6X - 11 = 9X - 23
12 = 3X
4 = X
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
