Suggest some fast calculation techniques

Expert replies

Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members; Location: International Space Station; Thanked: 11 times

by Aman verma » Thu Apr 04, 2013 3:24 am

Hi fellows,

I came across this division sum : 193664000000/130722 .

Is there any technique that let us calculate this division sum under 30 seconds without using a calculator ? If anybody has any fast calculation technique for such calculations please give an elaborate explanation. Also please suggest some fast calculation technique for comparing 3 or more digits ratios, other than cross multiplication. Will appreciate if a simple and lucid method is suggested !

800. Arjun's-Bird-Eye

Like this post

Source: Beat The GMAT — Problem Solving | Thu Apr 04, 2013 3:24 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Apr 04, 2013 4:10 am

Aman verma wrote:Hi fellows,

I came across this division sum : 193664000000/130722 .

Is there any technique that let us calculate this division sum under 30 seconds without using a calculator ? If anybody has any fast calculation technique for such calculations please give an elaborate explanation. Also please suggest some fast calculation technique for comparing 3 or more digits ratios, other than cross multiplication. Will appreciate if a simple and lucid method is suggested !

193664000000/130722

= 193664/130722 * 10^6

â‰ˆ 19/13 * 10^6

â‰ˆ 1.5 * 10^6.

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

Like this post

GMAT/MBA Expert

Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Thu Apr 04, 2013 4:12 am

Aman verma wrote:I came across this division sum : 193664000000/130722

Are you sure about this?
The dividend and divisor for this particular division has no common factors other than 2.
Hence, this division cannot be expressed as a simple fraction let alone complete division.

193664000000/130722 = 96832000000/65361

We cannot proceed after that.

GMAT (for that matter, any competitive exam) will never design questions which asks for such futile and cumbersome calculation. However, you may come across approximate calculation. In that case, proceed as follows.

96832000000/65361 â‰ˆ (9/6)*10^6 â‰ˆ 1.5*10^6

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

Â§ GMAT with Gurome Â§ Admissions with Gurome Â§ Career Advising with Gurome Â§

Like this post

rairavig: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Wed Mar 20, 2013 2:22 am; Thanked: 2 times

by rairavig » Thu Apr 04, 2013 4:24 am

193664000000/130722
= 193664000000/0.130722 x 1000000
= 193664/0.130722

in such cases:
take it as
=(1/0.13) x 193664 (0.13 ~ 0.130722 if you really wana do this without CalC)
= Approx~ 7.7 x 193664
= 14,91,212 (Approx)

Actual Ans is- 14,81,495
Difference is only 10,000 which is negligible in such calculations.

Like this post

Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members; Location: International Space Station; Thanked: 11 times

by Aman verma » Thu Apr 04, 2013 5:49 am

Anju@Gurome wrote:
Aman verma wrote:I came across this division sum : 193664000000/130722
Are you sure about this?
The dividend and divisor for this particular division has no common factors other than 2.
Hence, this division cannot be expressed as a simple fraction let alone complete division.

Hi Anju,

Thanks for the response. Now you misunderstood me when I mentioned comparison of 3 or more digits fractions. What I meant was comparing fractions e.g 12345/67347 > 34623/56378, not this particular division sum. For such comparisons we generally use cross multiplication but that will make calculations more complicated. So is there a simple method to make such comparisons i.e determining ascending or descending order.

800. Arjun's-Bird-Eye

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Apr 04, 2013 6:33 am

Aman verma wrote:Hi fellows,

I came across this division sum : 193664000000/130722 .

Is there any technique that let us calculate this division sum under 30 seconds without using a calculator ? If anybody has any fast calculation technique for such calculations please give an elaborate explanation. Also please suggest some fast calculation technique for comparing 3 or more digits ratios, other than cross multiplication. Will appreciate if a simple and lucid method is suggested !

For this question (and many other GMAT questions), your approach should be guided by the answer choices.

If the answer choices look like this:
A) 1,481,475
B) 1,481,485
C) 1,481,495
etc . . . then you will need to be quite precise.

Conversely, if the answer choices look like this:
A) 1.481495
B) 148.1495
C) 14,814.95
etc . . . then you can be quite aggressive with your estimation.

Keep in mind that the test-makers are not trying to identify the human calculators out there. They want to identify people with a "feel" for numbers. Given this, you will typically find answer choices that allow you to estimate.

If you're interested, we have a free video about using the answer choices to direct your solution: https://www.gmatprepnow.com/module/gener ... es?id=1111

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members; Location: International Space Station; Thanked: 11 times

by Aman verma » Thu Apr 04, 2013 6:40 am

Brent@GMATPrepNow wrote:
Aman verma wrote:Hi fellows,

I came across this division sum : 193664000000/130722 .

Is there any technique that let us calculate this division sum under 30 seconds without using a calculator ? If anybody has any fast calculation technique for such calculations please give an elaborate explanation. Also please suggest some fast calculation technique for comparing 3 or more digits ratios, other than cross multiplication. Will appreciate if a simple and lucid method is suggested !
For this question (and many other GMAT questions), your approach should be guided by the answer choices.

If the answer choices look like this:
A) 1,481,475
B) 1,481,485
C) 1,481,495
etc . . . then you will need to be quite precise.

Conversely, if the answer choices look like this:
A) 1.481495
B) 148.1495
C) 14,814.95
etc . . . then you can be quite aggressive with your estimation.

Keep in mind that the test-makers are not trying to identify the human calculators out there. They want to identify people with a "feel" for numbers. Given this, you will typically find answer choices that allow you to estimate.

If you're interested, we have a free video about using the answer choices to direct your solution: https://www.gmatprepnow.com/module/gener ... es?id=1111

Cheers,
Brent

Awesome ! and also many thanks to Mitch Hunt for showing the faster technique.

800. Arjun's-Bird-Eye

Like this post

GMAT/MBA Expert

Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Thu Apr 04, 2013 10:57 am

Aman verma wrote:Now you misunderstood me when I mentioned comparison of 3 or more digits fractions. What I meant was comparing fractions e.g 12345/67347 > 34623/56378, not this particular division sum. For such comparisons we generally use cross multiplication but that will make calculations more complicated. So is there a simple method to make such comparisons i.e determining ascending or descending order.

Different problems requires different strategies.
But in general, this type of problems should be solved by estimating the values of the fractions or approximating accordingly.

For the example you have chosen : comparison of 12345/67347 and 34623/56378,
We can see that the numerator and denominator of 12345/67347 are far apart but the numerator and denominator of 34623/56378 are closer. Hence, there is a pretty good chance that 34623/56378 will be the larger one. We can prove the same as follows,
12345/67347 < 12345/65000 < 13000/65000 = 1/5
34623/56378 > 34623/60000 > 30000/60000 = 1/2 > 1/5

Hence, 34623/56378 > 12345/67347

We can do the same comparison by estimating the values of the fractions as I have done in my previous post.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review