If a 0, b 0, and c 0, a + 1/(b + 1/c) =

Question

If  a > 0 ,  b > 0  , and  c > 0  ,  a + \frac{1}{b + \frac{1}{c}}  =

A.  \frac{a + b}{c}

B.  \frac{ac + bc + 1}{c}

C.  \frac{abc + b + c}{bc}

D.  \frac{a + b + c}{abc + 1}

E.  \frac{abc + a + c}{bc + 1}

KSBGC · Answer

It's better to solve this one part to part:

=  b + \frac{1}{c}

= \frac{bc + 1}{c}

Then

= \frac{1}{(bc + 1) / c}

=  \frac{c}{bc + 1}

last part :

= a +  \frac{c}{bc +1}

= \frac{c + abc + a}{bc +1}

The best answer is E.

manjot123 · Answer

assume values for a,b,c and put values of abc in options

BrentGMATPrepNow · Answer

We're looking for an expression that is  equivalent  to the given expression. 
So, if we find the value of the given expression for certain values of a, b and c, then the correct answer choice must also equal the same value for the same value of values of a, b and c.

So, let's see what happens when  a = b = c = 1

Given expression: a + 1/(b + 1/c) =  1  + 1/( 1  + 1/ 1 ) =
= 1 + 1/2
=  3/2

So, when  a = b = c = 1 , the given expression evaluates to be  3/2 
So, the correct answer choice must also evaluate to be  3/2  when we plug in  a = b = c = 1

Check the answer choices....
A. (a + b)/c = (1 + 1)/1 =  2 . No good. We need  3/2 . ELIMINATE.

B. (ac + bc + 1)/c = (1 + 1 + 1)/1 =  3 . No good. We need  3/2 . ELIMINATE.

C. (abc + b + c)/bc = (1 + 1 + 1)/1 =  1 . No good. We need  3/2 . ELIMINATE.

D. (a + b + c)/(abc + 1) = (1 + 1 + 1)/(1 + 1) =  3/2 . Perfect!! KEEP

E. (abc + a + c)/(bc + 1) = (1 + 1 + 1)/(1 + 1) =  3/2 . Perfect!! KEEP

Okay, we have two possible answers: D or E. 
So, we must test one more set of values.

Let's see what happens when  a = b = 1 and c = 2  
Here, the given expression: a + 1/(b + 1/c) =  1  + 1/( 1  + 1/ 2 ) =
= 1 + 1/(3/2)
= 1 + 2/3
=  5/3

So, when  a = b = 1 and c = 2  , the given expression evaluates to be  5/3 
So, the correct answer choice must also evaluate to be  5/3  when we plug in  a = b = 1 and c = 2

Check the REMAINING answer choices....
D. (a + b + c)/(abc + 1) = (1 + 1 + 2)/(2 + 1) =  4/3 . No good. We need  5/3 . ELIMINATE.

E. (abc + a + c)/(bc + 1) = (2 + 1 + 2)/(2 + 1) =  5/3 . Perfect!! KEEP

Answer: E

Cheers,
Brent

bumpbot · Answer

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If a > 0, b > 0, and c > 0, a + 1/(b + 1/c) =

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