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Suggest some fast calculation techniques

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 !
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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

≈ 19/13 * 10^6

≈ 1.5 * 10^6.
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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 ≈ (9/6)*10^6 ≈ 1.5*10^6
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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.
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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.
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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
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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.
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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.
Anju Agarwal
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Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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