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
fast way to solve??
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 93
- Joined: Mon Apr 25, 2016 2:22 pm
- Thanked: 1 times
- Followed by:1 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
One option is to rewrite each fraction with the same denominator (a bit of work).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
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
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
Cheers,
Brent
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20boomgoesthegmat 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
= 1/60 * 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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- OptimusPrep
- Master | Next Rank: 500 Posts
- Posts: 410
- Joined: Fri Mar 13, 2015 3:36 am
- Location: Worldwide
- Thanked: 120 times
- Followed by:8 members
- GMAT Score:770
The easiest and the most efficient way to calculate this is by taking the LCMboomgoesthegmat 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
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
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Sweet!!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
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
Math never gets old, does it?Brent@GMATPrepNow wrote:Sweet!!
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Agreed. It's one of the oldest subjects, and it never gets old!Matt@VeritasPrep wrote:Math never gets old, does it?Brent@GMATPrepNow wrote:Sweet!!