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# Value at x=5....

Author Message
Intern
Joined: 12 Jan 2017
Posts: 3
Location: India
Concentration: Finance, Accounting
GMAT 1: 710 Q50 V35
GPA: 4

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18 Oct 2018, 10:03
00:00

Difficulty:

65% (hard)

Question Stats:

58% (00:51) correct 42% (00:49) wrong based on 19 sessions

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Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1043
Location: India
GPA: 3.64

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18 Oct 2018, 10:20
1
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None

f(5) = 1/6
f{f(5)} = $$\frac{1}{(1+{1/6})}$$ = $$\frac{6}{7}$$
f[f{f(x)}] = $$\frac{1}{(1+{6/7})}$$ = $$\frac{7}{13}$$.
Checking the answer choices and reducing to lowest terms,
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Senior Manager
Joined: 22 Feb 2018
Posts: 420

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18 Oct 2018, 10:24
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None

OA: B

$$f(x)=\frac{1}{1+x}$$

$$f(5)=\frac{1}{1+5}=\frac{1}{6}$$

$$f(\frac{1}{6})=\frac{1}{1+\frac{1}{6}}=\frac{6}{7}$$

$$f(\frac{6}{7})=\frac{1}{1+\frac{6}{7}}=\frac{7}{13}$$

$$f[f{f(x)}],$$ at $$x=5$$ is $$\frac{7}{13}$$ or $$\frac{21}{39}$$
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Senior Manager
Joined: 18 Jun 2018
Posts: 263

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18 Oct 2018, 10:38
1
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None

OA:B

f(x)$$=\frac{1}{1+x}$$
f{f(x)}$$=\frac{1}{1+\frac{1}{1+x}}=\frac{x+1}{x+1+1}=\frac{x+1}{x+2}$$
f[f{f(x)}]$$=\frac{1}{1+\frac{x+1}{x+2}}=\frac{x+2}{x+2+x+1}=\frac{x+2}{2x+3}$$

f[f{f(5)}]$$=\frac{5+2}{2*5+3}=\frac{7}{13}$$

Multiplying denominator and numerator by $$3$$ , we get

f[f{f(5)}]$$=\frac{7*3}{13*3}=\frac{21}{39}$$
Manager
Joined: 01 Mar 2015
Posts: 69

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18 Oct 2018, 11:04
1
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None

This type of questions are tricky one, after finding answer for
f[f{f(5)}] = 7/13

At first instant, not finding the exact answer in answer choices, one is tempted to mark choice E, i.e. None, but as answer choices are tricky, one has to convert them to simplest form to find exact answer.
i.e. choice (B) = 21/39 = 7/13

Posted from my mobile device
Manager
Joined: 13 Jun 2012
Posts: 199
Location: United States
WE: Supply Chain Management (Computer Hardware)

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18 Oct 2018, 15:59
Q: If f(x)= 1/(1+x), then find the value of f[f{f(x)}],at x=5:

A. 21/27
B. 21/39
C. 15/39
D. 15/27
E. None

One has to be careful. We should always reduce the numerator & the denominator if it allows. I got the answer 7/13 and went with E
Re: Value at x=5....   [#permalink] 18 Oct 2018, 15:59
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