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02 Jun 2018, 13:19
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If \(g(f(3)) = 19\), what is \(f(g(3))\)?
(1) \(f(x) = 2x\)
(2) \(g(x) = 3x + 1\)
(1) \(f(x) = 2x\)
(2) \(g(x) = 3x + 1\)
02 Jun 2018, 13:36
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Bunuel
If \(g(f(3)) = 19\), what is \(f(g(3))\)?
(1) \(f(x) = 2x\)
(2) \(g(x) = 3x + 1\)
(1) \(f(x) = 2x\)
(2) \(g(x) = 3x + 1\)
To know the value of f(g(3)), we need to know the value of g(3) and that of f(x).
We'll look for statements that give us this information, a Logical approach.
(1) does not help us calculate g(3)
Insufficient.
(2) does not help us calculate f(x).
Insufficient.
Combined. We can now calculate both g(3) and f(x), sufficient.
(C) is our answer.
23 Jun 2021, 03:56
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From question data, g(f(3)) = 19. We have to compute the value of f(g(3)).
From statement I alone, f(x) = 2x.
Therefore, f(3) = 6 and hence g(6) = 19.
But, we do not know how g(6) gives us 19 i.e. the definition of g(x) is unknown.
Statement I alone is insufficient. Answer option A and D can be eliminated.
From statement II alone, g(x) = 3x + 1.
Therefore, g(f(3)) = 3*f(3) + 1 = 19 or 3*f(3) = 18 or f(3) = 6.
Again, we don’t know how f(3) gives 6 i.e. definition of f(x) is unknown.
Statement II alone is insufficient. Answer option B can be eliminated.
Combining statements I and II, we have the following:
From statement I, f(x) = 2x; from statement II, g(x) = 3x + 1
Therefore, f(g(3)) = f(10) = 20.
The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is C
The question data g(f(3)) = 19 seems almost redundant here because it does not contribute to solving the question in any way.
Hope that helps!
Aravind B T
From statement I alone, f(x) = 2x.
Therefore, f(3) = 6 and hence g(6) = 19.
But, we do not know how g(6) gives us 19 i.e. the definition of g(x) is unknown.
Statement I alone is insufficient. Answer option A and D can be eliminated.
From statement II alone, g(x) = 3x + 1.
Therefore, g(f(3)) = 3*f(3) + 1 = 19 or 3*f(3) = 18 or f(3) = 6.
Again, we don’t know how f(3) gives 6 i.e. definition of f(x) is unknown.
Statement II alone is insufficient. Answer option B can be eliminated.
Combining statements I and II, we have the following:
From statement I, f(x) = 2x; from statement II, g(x) = 3x + 1
Therefore, f(g(3)) = f(10) = 20.
The combination of statements is sufficient. Answer option E can be eliminated.
The correct answer option is C
The question data g(f(3)) = 19 seems almost redundant here because it does not contribute to solving the question in any way.
Hope that helps!
Aravind B T
