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Approximation

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by kanha81 » Wed Jun 24, 2009 2:30 pm
4.896 / [(1/0.07) + (1/0.16)] is approximately equal to-

A) .238
B) .262
C) .625
D) .649
E) 6.25
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by ssmiles08 » Wed Jun 24, 2009 3:05 pm
Convert the decimals into fractions.

1/.07 = 1/(7/100) = 100/7

1/.16 = 1/(16/100) = 100/16 = 25/4

100/7 + 25/4

7*14 = 98
4*6 = 24

(14+6) = 20 (the denominator, approximately)

4.895 ~ 5

5/20 ~ 1/4 = .25

Notice that the denominator would be larger if we actually divided the actual values. SO the number should be smaller than .25 which would be (A)
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Re: Approximation

by pops » Wed Jun 24, 2009 9:46 pm
kanha81 wrote:4.896 / [(1/0.07) + (1/0.16)] is approximately equal to-

A) .238
B) .262
C) .625
D) .649
E) 6.25
1/0.07 = 100/7 < 14
1/0.16 = 100/16 < 6
hence
4.896/[(1/0.07) + (1/0.16)] < 4.896/[14+6] = 4.896/20 = 2.248
so the result should be less than 2.248 hence A

In such problems its very important to take care of inequality while approximating.
For e.g. 1/0.17 = 100/17 and can be approximated to 6 but need to keep in mind that
100/17 > 6

comparing this will give an idea what I mean to say:
1/0.16 = 100/16 > 6
1/0.17 = 100/17 < 6
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by kris610 » Sat Jun 27, 2009 6:33 am
In questions like these:

Evaluate the expression using PEMDAS (just google for it):

In the given question, Parenthesis comes first:

So evaluate the denominator and you will get (100*23/112). If you take the 112 up, you have 4.896*112 in the numerator and 100*23 in the denominator. Round the numerator values up (to 5 and 115) and simplify -- you will get 1/4 which is 0.25. Because you rounded *up* the numerator, the final value will be somewhat lesser than 0.25 and 0.238 fits the answer.
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