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y=1/2-1/3+1/6

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y=1/2-1/3+1/6 [#permalink] New post 24 Dec 2012, 16:09
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A
B
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D
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Difficulty:

  35% (medium)

Question Stats:

65% (02:13) correct 35% (02:42) wrong based on 37 sessions
Image
best approximation for y....
0.1

0.31

0.35

0.4

0.6

Source: HULT

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Re: y=1/2-1/3+1/6 [#permalink] 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 [#permalink] 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 [#permalink] New post 02 Apr 2014, 12:35
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 [#permalink] 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   [#permalink] 03 Apr 2014, 00:24
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