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

Question

(\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}

(PS05410)

magbot · Accepted Answer

Brackets here is misleading

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

Answer: C

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BrentGMATPrepNow · Answer

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

Answer: C

Cheers,
Brent

avigutman · Answer

Video solution from Quant Reasoning:
 https://www.youtube.com/watch?v=F1pVz8THBBc

EgmatQuantExpert · Answer

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.

Answer: C

Mo2men · Answer

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

Answer: C

Srajagopal21 · Answer

Cancel out + and - terms, effectively comes down to 1/2 - 1/6 = 1/3

FANewJersey · Answer

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

Bunuel · Answer

That's a code of a question in OG. All OG's: https://gmatclub.com/forum/gmac-officia ... 40610.html

TheNightKing · Answer

Did not see that coming. Nice one

Prasannathawait · Answer

cancel out the terms.

1/2 - 1/6 remains.. 1/3 is the answer

BijayKru · Answer

(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

Himali24 · Answer

Cancel out the positive and negative terms so that you are left with - 1/2 - 1/6 = 1/3

Hence option C

Neena96 · Answer

what about solving the bracket first ?

TheNightKing · Answer

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

Kinshook · Answer

(\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

BijayKru · Answer

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

kajaldaryani46 · Answer

Bunuel , are there more difficult Questions tested on this same Question type/ pattern?
I think I have seen one and it tested the same thing. Could you please provide a list of the same here?

Not sure if there’s some specific thing being tested here - is there a specific name of the concept being tested? It’d be great if you could help me with these

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Bunuel · Answer

You can look for similar questions under the Arithmetic tag: https://gmatclub.com/forum/search.php?s ... &tag_id=51 You can also check similar questions at the bottom of this page in SIMILAR QUESTIONS block. 1. Arithmetic Theory Mathematical Grouping Symbols GMAT Question Patterns: Arithmetic The Many Meanings of Minus How to Solve Simple Math Equations on the GMAT Questions GMAT Practice Questions with Fractions and Decimals Addition/Subtraction/Multiplication Tables ALPHAMETIC QUESTIONS ON THE GMAT Symbols Representing Arithmetic Operations Problems Conversion Problems DS Arithmetic Questions PS Arithmetic Questions For more check below: ALL YOU NEED FOR QUANT ! ! ! Ultimate GMAT Quantitative Megathread

prateekchugh · Answer

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

Remove the bracket: many fraction will cancel out: We are left with
 (\frac{1}{2}−\frac{1}{6})=\frac{1}{3}

A. − \frac{1}{6}

B. 0

C.  \frac{1}{3}

D.  \frac{1}{2}

E.  \frac{2}{3}

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

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

Prep Toolkit

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My Rewards