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y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16. Best approximation fo

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y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16. Best approximation fo  [#permalink]

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New post 24 Dec 2012, 16:09
1
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (02:19) correct 37% (02:44) wrong based on 123 sessions

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Best approximation for y is

A. 0.1

B. 0.31

C. 0.35

D. 0.4

E. 0.6

Source: HULT
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Re: y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16. Best approximation fo  [#permalink]

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New post 24 Dec 2012, 22:04
= 0.5 - 0.33+ 0.166 - 0.1 + 0.083 - 0.071 + 0.06
= 0.5 - 0.166 - 0.017 - 0.01
=0.5 - 0.19(approx)
=0.31 (approx)
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Re: y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16. Best approximation fo  [#permalink]

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New post 02 Apr 2014, 11:02
Any shortcuts for this type of question ?
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Re: y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16. Best approximation fo  [#permalink]

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New post 02 Apr 2014, 12:35
2
y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16

The terms are arranged from the largest to smallest. The smaller terms are pretty negligible, so it suffices to only worry about the bigger terms.

So I would start with 1/2 - 1/3.
Hm, that's 1/6. Hey, the next term is 1/6 too, might as well include that since the math is easy.
So 1/6 + 1/6 = 1/3 = 0.33

Now let's have a look at the rest of the terms: - 1/10 + 1/12 - 1/14 + 1/16
-1/10 + 1/12 is something slightly negative.
-1/14 + 1/16 is something slightly negative.

So now we have 0.33 + something slightly negative, or something slightly under 0.33.

Looking at the answer choices, B fits the bill.
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Re: y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16. Best approximation fo  [#permalink]

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New post 03 Apr 2014, 00:24
\(y = \frac{1}{2} - \frac{1}{3} + \frac{1}{6} - \frac{1}{10} + \frac{1}{12} - \frac{1}{14} + \frac{1}{16}\)

\(= \frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{16} - (\frac{1}{3} + \frac{1}{10} + \frac{1}{14})\)

\(= \frac{39}{48}- \frac{106}{210}\)

\(= \frac{13}{16} - \frac{53}{105}\)

\(\frac{13}{16} = 0.812 (Approx)\)

\(\frac{53}{105} = 0.504 (Approx)\)

Answer = 0.31 = B
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Re: y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16. Best approximation fo  [#permalink]

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New post 09 Oct 2018, 21:50
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Re: y = 1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16. Best approximation fo   [#permalink] 09 Oct 2018, 21:50
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