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Is estimation the best way to solve such problems??

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Source: — Problem Solving |

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Re: Is estimation the best way to solve such problems??

by Ian Stewart » Sun Oct 19, 2008 6:39 pm
beater wrote:(6.804)^6 (1.701)^-13 / (2) ^19(3.402) ^-7

A. 0.8502
B. 1.0000
C. 1.7010
D. 3.4020
E. 6.8040
There are a couple of reasons why estimation could lead you to the wrong answer here- a couple of answers are close together, and the quantities aren't easy to estimate. If it's a GMAT question, you can be pretty sure you're going to have a lot of simplification- it must be easier than it looks. If you notice that 4*1.701 = 6.804, and 2*1.701 = 3.402, there's a lot of cancellation:

(6.804)^6 (1.701)^-13 / (2) ^19(3.402) ^-7

= (6.804)^6 (3.402) ^7 / (2) ^19 (1.701)^13

= [ (2^2 * 1.701)^6 * (2 * 1.701)^7 ] / [2^19 * (1.701)^13 ]

= [2^12 * 1.701^6 * 2^7 * 1.701^7] / [2^19 * 1.701^13]

= (2^19 * 1.701^13)/(2^19 * 1.701^13)

= 1
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by beater » Mon Oct 20, 2008 5:34 am
Ian - Thanks for your input
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by sam117 » Thu Apr 26, 2012 11:13 am
Is this a realistic question? Is it possible to get a question with so many calculation steps on the GMAT?
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by GMATGuruNY » Thu Apr 26, 2012 5:44 pm
beater wrote:(6.804)^6 (1.701)^-13 / (2) ^19(3.402) ^-7

A. 0.8502
B. 1.0000
C. 1.7010
D. 3.4020
E. 6.8040
The trick is to recognize the relationships between the decimals.
Use SUBSTITUTION to make the math easier.

Let x = 1.701.
Then 3.402 = 2x and 6.804 = 4x.

Substituting for the decimals in the equation, we get:

(4x)� * x^-13 / 2¹� * (2x)^(-7)

= (2²x)� * x^-13 / 2¹� * 2^-7 * x^-7

= 2¹² * x^-7 / 2¹² * x^-7

= 1.

The correct answer is B.
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