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# 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

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1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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Updated on: 23 Jun 2018, 12:02
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Question Stats:

95% (00:57) correct 5% (02:02) wrong based on 1553 sessions

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$$\frac{1}{3} + \frac{1}{2} - \frac{5}{6} + \frac{1}{5} + \frac{1}{4} - \frac{9}{20} =$$

A. $$0$$

B. $$\frac{2}{15}$$

C. $$\frac{2}{5}$$

D. $$\frac{9}{20}$$

E. $$\frac{5}{6}$$

Kudos for a correct solution.

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Originally posted by Bunuel on 14 Oct 2015, 21:15.
Last edited by carcass on 23 Jun 2018, 12:02, edited 1 time in total.
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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15 Oct 2015, 02:12
10
Even though it could be tempting to find the common denominator (60), and operate, the way the terms are ordered is inviting us to group the first and last three terms -common denominator (6 and 20 respectively)- to operate more easily:

Doing this, we can rewrite the given expression as

$$1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 = A + B$$, where

$$A = 1/3 +1/2 - 5/6 = 2/6 + 3/6 - 5/6 = 0$$

$$B = 1/5 + 1/4 - 9/20 = 4/20 + 5/20 – 9/20 = 0$$

Thus, $$1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 = 0 + 0 = 0$$

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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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11 Dec 2015, 03:10
1
Remember for addition/subtraction its easier to work with decimals. we all should have these fraction memorized for decimal values-

.33+.5-.83+.2+.25-.45=0
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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11 Apr 2016, 10:39
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The following free videos cover the concepts/strategies that are useful for answering this question:

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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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03 May 2016, 08:51
2
Bunuel wrote:
1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

A. 0
B. 2/15
C. 2/5
D. 9/20
E. 5/6

Kudos for a correct solution.

Solution:

We need to determine the result of 1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20

Let’s add the given fractions in two groups. In the group of the first three fractions, notice that 1/3 and 1/2 share a common denominator of 6 with 5/6.

1/2 + 1/3 = 3/6 + 2/6 = 5/6

Thus, 5/6 – 5/6 = 0

Looking at the 2nd group of the fractions (1/5, 1/4, and 9/20), notice that 1/5 and 1/4 share a common denominator of 20 with 9/20.

1/5 + 1/4 = 4/20 + 5/20 = 9/20

Thus, 9/20 – 9/20 = 0.

Thus, the result of 1/3 + 1/2 – 5/6 + 1/5 + 1/4 – 9/20 is 0.

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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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08 May 2016, 06:02
I got D

solved bit by bit
1/3 +1/2 = 5/6 -
5/6+1/5+1/4 = 125/120 -
9/20

100-152-54/120 = -9/20
I know I answered incorrectly, but why did I falter?
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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08 May 2016, 06:24
paidlukkha wrote:
I got D

solved bit by bit
1/3 +1/2 = 5/6 -
5/6+1/5+1/4 = 125/120 -
9/20

100-152-54/120 = -9/20
I know I answered incorrectly, but why did I falter?

you are wrong in highlighted portion..
the highlighted portion is -5/6 +1/4+1/2 and you have worked for -(5/6+1/4+1/2)..
..
You can add all those with - sign together , here -(5/6+9/20)..
and all those with +sign...
- sign before 5/6 is ONLY for 5/6 and not for all terms after that..
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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08 May 2016, 06:29
chetan2u wrote:
paidlukkha wrote:
I got D

solved bit by bit
1/3 +1/2 = 5/6 -
5/6+1/5+1/4 = 125/120 -
9/20

100-152-54/120 = -9/20
I know I answered incorrectly, but why did I falter?

you are wrong in highlighted portion..
the highlighted portion is -5/6 +1/4+1/2 and you have worked for -(5/6+1/4+1/2)..
..
You can add all those with - sign together , here -(5/6+9/20)..
and all those with +sign...
- sign before 5/6 is ONLY for 5/6 and not for all terms after that..

every time I have this bracket issue
Which topic should I revise?

also for x(sq)=36, so x = 6/-6
but underroot 36, in GMAT is only 6 & -6 is not valid
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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08 May 2016, 06:32
paidlukkha wrote:
I got D

solved bit by bit
1/3 +1/2 = 5/6 -
5/6+1/5+1/4 = 125/120 -
9/20

100-152-54/120 = -9/20
I know I answered incorrectly, but why did I falter?

Ok , Would like to highlight the same here -

1/3 +1/2 = 5/6 - 5/6 => 0

1/5+1/4 = 9/20 -9/20 => 0

There is something interesting to notice here

(1/3 +1/2 - 5/6 ) + (1/5 + 1/4 - 9/20)

(5/6 - 5/6 ) + (9/20 - 9/20)

The red highlighted part is the sum of its previous terms and is -ve that makes the result zero..

Hope this helps !! :-D
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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08 May 2016, 08:59
1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20

I found it easy to solve by taking LCM (Fractions always look nasty to me )

20+30 -50 +12 +15 -27/60

Just by looking at the numerator I figured out that answer will be '0'
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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28 Aug 2017, 09:24
Bunuel wrote:
1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

A. 0
B. 2/15
C. 2/5
D. 9/20
E. 5/6

Kudos for a correct solution.

- Find the LCM for denominator --> we find 60.
- Convert all of the fraction into 60 in denominator --> $$\frac{(1*20)+(1*30)-(5*10)+(1*12)+(1*15)-(9*3)}{60}$$ --> All of numerator cancelled out, so we can write it $$\frac{0}{60}$$ which is 0.

A.
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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14 Nov 2018, 11:16
Is finding a common denominator first, and doing the arithmetic a good way to approach this question?

Novice to the gmat and only started, so just want to know if I did it in an efficient manner, or should I learn other ways which take less time?

Thanks.
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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14 Nov 2018, 14:47
nust2017 wrote:
Is finding a common denominator first, and doing the arithmetic a good way to approach this question?

Novice to the gmat and only started, so just want to know if I did it in an efficient manner, or should I learn other ways which take less time?

Thanks.

Finding common denominator for all terms is not a good way to solve this type of problems.

Grouping the terms by recognising the terms with common/similar denominator and solving them separately saves lot of time by avoiding lengthy calculations.
We can see this as explained in above solutions.

Posted from my mobile device
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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02 Apr 2019, 18:46
v12345 wrote:
nust2017 wrote:
Is finding a common denominator first, and doing the arithmetic a good way to approach this question?

Novice to the gmat and only started, so just want to know if I did it in an efficient manner, or should I learn other ways which take less time?

Thanks.

Finding common denominator for all terms is not a good way to solve this type of problems.

Grouping the terms by recognising the terms with common/similar denominator and solving them separately saves lot of time by avoiding lengthy calculations.
We can see this as explained in above solutions.

Posted from my mobile device

Agreed. My first instinct was to solve by taking lcm of all and took me around 3 minutes.
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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15 Jul 2019, 02:24
1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =

first take all the positive one side and negative one side

1/3+1/2+1/5+1/4-5/6-9/20
1/3+1/2+1/5+1/4-(5/6+9/20)
77/60 - 77/60 =0
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Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =  [#permalink]

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16 Sep 2019, 08:53
Bunuel wrote:
$$\frac{1}{3} + \frac{1}{2} - \frac{5}{6} + \frac{1}{5} + \frac{1}{4} - \frac{9}{20} =$$

A. $$0$$

B. $$\frac{2}{15}$$

C. $$\frac{2}{5}$$

D. $$\frac{9}{20}$$

E. $$\frac{5}{6}$$

Kudos for a correct solution.

$$\frac{1}{3} + \frac{1}{2} - \frac{5}{6} + \frac{1}{5} + \frac{1}{4} - \frac{9}{20} =$$
$$\frac{1}{3} + \frac{1}{2} - \frac{5}{6} = 0$$
$$\frac{1}{5} + \frac{1}{4} - \frac{9}{20} = 0$$
$$\frac{1}{3} + \frac{1}{2} - \frac{5}{6} + \frac{1}{5} + \frac{1}{4} - \frac{9}{20} = 0 + 0 = 0$$

IMO A
Re: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 =   [#permalink] 16 Sep 2019, 08:53
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