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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: 60460
(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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Question Stats:

94% (00:54) correct 6% (01:27) wrong based on 1011 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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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, 22:04
8
Brackets here is misleading

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

Posted from my mobile device
##### General Discussion
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Posts: 3203
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
1

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
1
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

Only one answer left

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Joined: 12 Sep 2015
Posts: 4214
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
4
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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26 Jun 2018, 15:42
Cancel out + and - terms, effectively comes down to 1/2 - 1/6 = 1/3
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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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08 Oct 2018, 05:32
Hi Bunuel
What does PS05410 signify? Does this mean that there is list on GMATCLUB, in which all of the OG questions have been numbered.
Warmly,
FANJ
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Joined: 02 Sep 2009
Posts: 60460
Re: (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =  [#permalink]

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08 Oct 2018, 05:39
FANewJersey wrote:
Hi Bunuel
What does PS05410 signify? Does this mean that there is list on GMATCLUB, in which all of the OG questions have been numbered.
Warmly,
FANJ

That's a code of a question in OG.

All OG's: https://gmatclub.com/forum/gmac-officia ... 40610.html
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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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07 Jul 2019, 10:19
magbot wrote:
Brackets here is misleading

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

Posted from my mobile device

Did not see that coming. Nice one
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15 Jul 2019, 00:18
cancel out the terms.

1/2 - 1/6 remains.. 1/3 is the answer
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15 Jul 2019, 02:16
(1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6)

Opening up the brackets
we will get: 1/2 + 0 + 0 + 0 - 1/6

Simplify: 1/2 - 1/6 =1/3
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18 Jul 2019, 04:05
Cancel out the positive and negative terms so that you are left with - 1/2 - 1/6 = 1/3

Hence option C
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27 Aug 2019, 08:31
GMATPrepNow wrote:

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

what about solving the bracket first ?
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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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27 Aug 2019, 08:35
Neena96 wrote:
GMATPrepNow wrote:

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

what about solving the bracket first ?

Neena96
Will it really matter? (2+3)-(1+1) results in 3. Which is same as 2+3-1-1 and results in 3. Now in our case the sign outside the brackets is +. So you can deal with them as you want

I hope that helps
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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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16 Sep 2019, 08:14
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)

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

IMO C
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16 Jan 2020, 22:54
1/2 -1/3 = 1/6
1/3 -1/4=1/12.....1/20...1/30

LCM = 60

10+5+3+2 = 20/60 = 1/3

This is lengthy method.So just open all the brackets you will get 1/2- 1/6 = 2/6= 1/3
Re: (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) =   [#permalink] 16 Jan 2020, 22:54
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