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NO CALCULATOR?

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
by rdawood » Sun Jul 19, 2009 7:18 pm
How do you calculate things without a calculator? I was a math major and believe it or not I have a lot of trouble making calculations in my head or on paper, and it slows me down considerably.

On the mcgraw hill practice test CD, this was the second quant problem- very easy with a calculator, but time consuming and annoying and frustrating without:

Mr Garcia, the losing candidate in a two-party election, received 43,400 votes, which was 35% of the total votes cast. How many more of the total votes cast would Mr. Garcia have had to receive in order to win at least 50% of the vote?
A.18,600
B.24,800
C.35,500
D.62,000
E.124,000

This is easier when I use 1/3 instead of 35%, and 43,400/(1/3) = 130,200. 130,200/2 = 65,100. 65,100-43400=21,700, which is closest to A. Is this how we are supposed to do it?

Are there any tricks for how to multiply or divide large and weird numbers? There was another problem where I needed to divide 510 by 17. How do you do this? Long division? I feel so slow doing that. HELP

Thanks!
RAD
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Source: — Quantitative Reasoning |

Hope it helps...

by struggling_guy2001 » Sun Jul 19, 2009 11:48 pm
Mr Garcia, the losing candidate in a two-party election, received 43,400 votes, which was 35% of the total votes cast.

==> (0.35) *x = 43400, where x is the total number of votes cast.

===> x = (43400) / (0.35).

How many more of the total votes cast would Mr. Garcia have had to receive in order to win at least 50% of the vote?

0.50* x = [(43400)/(0.35)] * 0.5

Therefore, 0.50*x - 0.35*x = ((43400*0.5)/(0.35))- 43400.

= 43400 ( (0.5/0.35)-1))

= 43400* (3/7)

= 6200*3

=18600.


What I can suggest is...

Never go with complete calculations until you get a final equation as 43400 * (3/7) here....

These questions will be framed ( atleast 99% probability ) such that the equations can be cancelled in one or other step.


Hope it helps...
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by submariner » Mon Jul 20, 2009 5:54 pm
Another way to do it with mental math is to convert to fractions and don't solve the intermediate steps:

43400 * 100/35 = total number of votes...
Since we need 50% of total number of votes:

= 43400 * 100/35 * (1/2)
= 43400 * 50/35
= 43400 * 10/7
= 434000/7
= 62000

He already has 43400, so he needs 62000-43400 additional = 18600 (A).

Again, the key to this method is not computing the intermediate steps, just reducing the fractions when you get to the end equation.
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by DCJ » Sat Jul 25, 2009 5:26 pm
Another way
If 35%=43,400
Then 5% (i.e. 1/7 of 35%) of 43,400=6,200

Garcia needs 15% (i.e. 50%-35%) more to get 50% of the votes. 15% is just 3(5%)=3*6200=18600
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by gmatplayer » Sat Jul 25, 2009 6:54 pm
DJC's approach is good. Just an easy calc would be 35% = 43,400 & if you need 15% more, which is slightly less than half of 35%. The only value which is less than half of 43,400 is 18,600 so it must be the answer.
The problem would be difficult if there are more than one values available which are less than half of 43,400. And more difficult if those values are very close to each other. But mostly GMAT does not expect you to calculate tedius calculation but use a sense.
I would prefer to do some calc if this was problem among first 10 Questions. But analysing this with my approach is good enough to guess that answer is 18,600. Also I would prefer my approach because I can slove this problem in less than 30 sec and thus get time advantage.
Thats my strategy
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