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

Since these are Simple Fraction therefore you may choose to write their actual value and solve arithmatically

i.e. \(\frac{1}{3} + \frac{1}{2} - \frac{5}{6} + \frac{1}{5} + \frac{1}{4} - \frac{9}{20} =\) \(0.33+0.5-0.83\)\(+0.2+0.25-0.45\) \(= 0\)

Hi LithiumIon,

This is one of the *new* questions form the OG2016. A PDF listing of all the new questions (by number) can be found here:

empowergmat-blog-198415.html

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. 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:
GMAT assassins aren't born, they're made,
Rich

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

Related Resources
The following free videos cover the concepts/strategies that are useful for answering this question:

- Conversions with fractions and decimals: https://www.gmatprepnow.com/module/gmat ... video/1066
- Operations with fractions: https://www.gmatprepnow.com/module/gmat ... video/1068

Cheers,
Brent

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.

Answer: A

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..

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

We have been asked to find the value of the expression \(\frac{1}{3} + \frac{1}{2} - \frac{5}{6} + \frac{1}{5} + \frac{1}{4} - \frac{9}{20}\)

This involves knowing the concept of expressing the denominators as a common base and simplifying the entire equation.
We can express each of these fractions with a common base. Since, we have the numbers 5,6,20 the LCM of these numbers must be 60.

\(\frac{1}{3} + \frac{1}{2} - \frac{5}{6} + \frac{1}{5} + \frac{1}{4} - \frac{9}{20}\) = \(\frac{1*20}{3*20} + \frac{1*30}{2*30} - \frac{5*10}{6*10} + \frac{1*12}{5*12} + \frac{1*15}{4*15} - \frac{9*3}{20*3}\)

= \(\frac{20 + 30 - 50 +12 + 15 - 27}{3*20}\) = \(\frac{0}{60}\) = 0(Option A)

\(\frac{1}{3} + \frac{1}{2} - \frac{5}{6} + \frac{1}{5} + \frac{1}{4} - \frac{9}{20} = [(\frac{1}{3} + \frac{1}{2}) - \frac{5}{6}] + [(\frac{1}{5} + \frac{1}{4}) - \frac{9}{20}] = (\frac{5}{6} - \frac{5}{6}) + (\frac{9}{20} - \frac{9}{20}) = 0\). Ans - A.

Getting a common denominator of 60, we have:

20/60 + 30/60 - 50/60 + 12/60 + 15/60 - 27/60 = 0

Answer: A

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

IMO A

In case you're a noob like me and using LCM to solve this - take LCM b/w 6 and 20 itself, the rest of the denominators got covered in these two...

What I noticed in this kind of a questions. the more complicated the question looks like by looking around you can find the more simpler answer

Adding the co-primes reciprocals lead to addition/multiplication of the 2 numbers. So, let's say we can \(\frac{1}{5 } +\frac{1}{7 }\) result is \(\frac{12}{35}\) i.e.
\(\\
\\
\frac{addition of 5 and 7}{ multiplication of 5 and 7}\\
\\
\)

Realise that 2,3 are co-prime and \(\frac{5}{6} \) is their multiplication.
\(\frac{1}{3} + \frac{1}{2} = \frac{5}{6}\)
This cancels out \(\frac{5}{6}\)

Similarly for 4 and 5
\(\frac{1}{5} + \frac{1}{4} = \frac{9}{20}\)