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# (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =

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Math Expert
Joined: 02 Sep 2009
Posts: 49271
(1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =  [#permalink]

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25 Jun 2018, 22:00
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Difficulty:

5% (low)

Question Stats:

93% (00:46) correct 7% (01:22) wrong based on 224 sessions

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$$(\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{6}) =$$

A. $$-\frac{1}{6}$$

B. 0

C. $$\frac{1}{3}$$

D. $$\frac{1}{2}$$

E. $$\frac{2}{3}$$

NEW question from GMAT® Official Guide 2019

(PS05410)

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Joined: 02 Sep 2015
Posts: 40
(1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =  [#permalink]

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25 Jun 2018, 22:04
2

Cancel out terms and the remaining is 1/2 - 1/6 = 1/3

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 1995
Re: (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =  [#permalink]

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25 Jun 2018, 22:08

Solution

To find:
• The value of the expression $$(\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{6})$$

Approach and Working:
From the expression $$(\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{6})$$, if wwe rewrite it by removing the brackets, we get:
• $$\frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + \frac{1}{4} - \frac{1}{5} + \frac{1}{5} - \frac{1}{6}$$
= $$\frac{1}{2} - \frac{1}{6}$$
= $$\frac{1}{3}$$

Hence, the correct answer is option C.

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Re: (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =  [#permalink]

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26 Jun 2018, 05:40
Bunuel wrote:
$$(\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{6}) =$$

A. $$-\frac{1}{6}$$

B. 0

C. $$\frac{1}{3}$$

D. $$\frac{1}{2}$$

E. $$\frac{2}{3}$$

NEW question from GMAT® Official Guide 2019

(PS05410)

After canceling all term we left with:

$$\frac{1}{2}$$ - $$\frac{1}{6}$$

Both are not equal...........result can't equal zero...............Eliminate B

$$\frac{1}{2}$$>$$\frac{1}{6}$$...result Must be POSITIVE and less than $$\frac{1}{2}$$..........Eliminate A& D & E

CEO
Joined: 12 Sep 2015
Posts: 2864
Re: (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =  [#permalink]

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26 Jun 2018, 07:23
1
Top Contributor
Bunuel wrote:
$$(\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{6}) =$$

A. $$-\frac{1}{6}$$

B. 0

C. $$\frac{1}{3}$$

D. $$\frac{1}{2}$$

E. $$\frac{2}{3}$$

NEW question from GMAT® Official Guide 2019

(PS05410)

GIVEN: (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6)

The terms with the same colors combine to get 0.
So, we get: 1/2 + 0 + 0 + 0 - 1/6

Simplify: 1/2 - 1/6

Rewrite with same denominators: 3/6 - 1/6

Evaluate: 2/6, which simplifies to get: 1/3

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

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Joined: 15 May 2017
Posts: 25
Re: (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =  [#permalink]

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26 Jun 2018, 15:42
Cancel out + and - terms, effectively comes down to 1/2 - 1/6 = 1/3
Re: (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) = &nbs [#permalink] 26 Jun 2018, 15:42
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