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fast way to solve??

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by Brent@GMATPrepNow » Mon Apr 25, 2016 3:46 pm
boomgoesthegmat 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

Answer: A
One option is to rewrite each fraction with the same denominator (a bit of work).

Another option is to convert each fraction to a decimal.
To do so, we need to know some BASE CONVERSIONS.

Let's use this chart
Image
For example, if we know that 1/7 ≈ 0.14, then 2/7 ≈ 0.28
Likewise, if 1/6 ≈ 0.17, then 5/6 ≈ 0.83 [since 5/6 = 1 - 1/6 ≈ 1 - 0.17 ≈ 0.83]

So....
1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20 = 0.33 + 0.5 - 0.83 + 0.2 + 0.25 - 0.45
= 0 + 0
= 0
= A

For more on converting fractions to decimals see this video: https://www.gmatprepnow.com/module/gmat ... video/1066

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by [email protected] » Mon Apr 25, 2016 4:13 pm
Hi boomgoesthegmat,

Many GMAT questions are essentially just about pattern-matching. While this prompt includes 6 fractions with different denominators, you do NOT need to calculate a "giant" common denominator to get the correct answer. In that same way, you actually don't have to do a lot of math at all to get to the correct answer. By 'grouping' the fractions into sets of 3, a pattern emerges...

1/3 + 1/2 --> the common denominator is 6....and THAT is the denominator of the next fraction....-5/6

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

5/6 - 5/6 = 0 so the first three fractions "cancel out"

With the next 3 fractions, we have....

1/5 + 1/4 --> the common denominator is 20....and THAT is the denominator of the next fraction....-9/20

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

9/20 - 9/20 = 0 so the last three fractions "cancel out"

In the end, we have.... 0 + 0 = 0

Final Answer: A

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by GMATGuruNY » Mon Apr 25, 2016 4:25 pm
boomgoesthegmat 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

Answer: A
1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20

= 1/60 * 60(1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20)

= 1/60 * (20 + 30 - 50 + 12 + 15 - 27)

= 1/60 * 0

= 0.

The correct answer is A.
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by OptimusPrep » Mon Apr 25, 2016 8:12 pm
boomgoesthegmat 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

Answer: A
The easiest and the most efficient way to calculate this is by taking the LCM
However, we can be a bit creative in grouping the terms.
Group the terms in the following way

(1/3 + 1/2) - 5/6 + (1/5 + 1/4) - 9/20 = 5/6 - 5/6 + 9/20 - 9/20 = 0
Option A
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by Matt@VeritasPrep » Wed Apr 27, 2016 2:16 pm
One more solution for you!

If we have

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

We can multiply both sides by 60 to clear the denominators.

20 + 30 - 50 + 12 + 15 - 27 = 60x

50 - 50 + 27 - 27 = 60x

0 = 60x

0 = x
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by Brent@GMATPrepNow » Wed Apr 27, 2016 2:27 pm
Matt@VeritasPrep wrote:One more solution for you!

If we have

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

We can multiply both sides by 60 to clear the denominators.

20 + 30 - 50 + 12 + 15 - 27 = 60x

50 - 50 + 27 - 27 = 60x

0 = 60x

0 = x
Sweet!!
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by Matt@VeritasPrep » Thu Apr 28, 2016 2:43 pm
Brent@GMATPrepNow wrote:Sweet!!
Math never gets old, does it? :)
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by Brent@GMATPrepNow » Thu Apr 28, 2016 4:49 pm
Matt@VeritasPrep wrote:
Brent@GMATPrepNow wrote:Sweet!!
Math never gets old, does it? :)
Agreed. It's one of the oldest subjects, and it never gets old!
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