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Which of the following is the best approximation for y? 1/2 - 1/3 + 1/

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Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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New post 16 Oct 2016, 04:39
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

60% (02:24) correct 40% (02:42) wrong based on 124 sessions

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Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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New post 16 Oct 2016, 04:56
1/2 - 1/3 +1/6-1/10+1/12-1/14+1/16

=> 1/2 [1+1/3-1/5+1/6-1/7+1/8] - 1/3
=> 0.5 [ 1+0.33-0.2+0.167-0.142+0.125] - 0.33
=> 0.31

Option B
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Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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New post 16 Oct 2016, 05:04
1
Bunuel wrote:
Which of the following is the best approximation for y?
\(\frac{1}{2}- \frac{1}{3} + \frac{1}{6} - \frac{1}{10} + \frac{1}{12} - \frac{1}{14} + \frac{1}{16}\)

A. 0.1
B. 0.31
C. 0.35
D. 0.4
E. 0.6


Hi we can find the general range to get to our answer....
1) make pair starting from beginning..
So we have (1/2-1/3) + (1/6-1/10)........
Each pair has POSITIVE value more so ans will be > 1/2-1/3 or > 0.5-0.33 or > .17
So A is out...
2) NOW take first term separately and then take pair.....
That is 1/2.....-1/3+1/6....and so on..
Here we have first term POSITIVE and there after each pair has NEGATIVE term greater...
So there will be subtraction after first term 1/2...
-1/3+1/6= -0.16..
So our answer has to be less than 1/2-0.16= 0.5-0.16=0.34...
C,D and E are out

ONLY B left
Ans 0.31
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Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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New post 16 Oct 2016, 12:14
1
Bunuel wrote:
Which of the following is the best approximation for y?
\(\frac{1}{2}- \frac{1}{3} + \frac{1}{6} - \frac{1}{10} + \frac{1}{12} - \frac{1}{14} + \frac{1}{16}\)

A. 0.1
B. 0.31
C. 0.35
D. 0.4
E. 0.6


In general, it pays to know the decimal equivalents for fractions \(\frac{1}{x}\) for \(x = 1, 2,...,10\) because you will see them everywhere. And once you've mastered those, you will have essentially mastered fractions like \(\frac{1}{14}\), because it's just \(\frac{1}{7}*\frac{1}{2}\), in other words, one of the aforementioned fractions divided by two. Btw, 1/7 = 0.1428.

As for this question, it asks for an approximation, and the answer choices are relatively spread out, so I just crunched this the old fashioned way. I hate subtraction, so I summed the positive terms, summed the negative terms, and then found the difference. Though I knew the exact decimal equivalents, to save time I just went out to two decimals, noting that the first sum will slightly understate the actual sum.

\(\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{16} = 0.5 + 0.16 + 0.08 + 0.06 = 0.8 < actual\)

\(\frac{1}{3} + \frac{1}{10} + \frac{1}{14} = .033 + 0.1 + 0.07 = 0.5\)

\(0.8 - 0.5 = 0.3\), and since this is slightly smaller than the actual sum, the best answer choice is answer B.
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Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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New post 17 Oct 2016, 08:30
1
Bunuel wrote:
Which of the following is the best approximation for y?
\(\frac{1}{2}- \frac{1}{3} + \frac{1}{6} - \frac{1}{10} + \frac{1}{12} - \frac{1}{14} + \frac{1}{16}\)

A. 0.1
B. 0.31
C. 0.35
D. 0.4
E. 0.6


1/2 = 0.50
1/3 = 0.33
1/6 = 0.16
1/10 = 0.10
1/12 = 0.08
1/14 = 0.07
1/16 = 0.06

Its good to learn the reciprocal of a few common fraction -
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Now, \(\frac{1}{2}- \frac{1}{3} + \frac{1}{6} - \frac{1}{10} + \frac{1}{12} - \frac{1}{14} + \frac{1}{16}\)

=> 0.50 - 0.33 + 0.16 - 0.10 + 0.08 - 0.07 + 0.06

=> ( 0.50 + 0.16 + 0.08 + 0.06 ) - ( 0.33 + 0.10 + 0.07 )

=> 0.80 - 0.50 = 0.30

Hence answer will be (B) 0.30

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Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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New post 17 Oct 2016, 09:49
Bunuel wrote:
Which of the following is the best approximation for y?
\(\frac{1}{2}- \frac{1}{3} + \frac{1}{6} - \frac{1}{10} + \frac{1}{12} - \frac{1}{14} + \frac{1}{16}\)

A. 0.1
B. 0.31
C. 0.35
D. 0.4
E. 0.6


Look at it this way: \(y = (\frac{1}{2}- \frac{1}{3} + \frac{1}{6}) + (\frac{1}{12} - \frac{1}{10}) + (\frac{1}{16} - \frac{1}{14}\))

\((\frac{1}{2}- \frac{1}{3} + \frac{1}{6})=\frac{1}{3}=0.33\)

\((\frac{1}{12} - \frac{1}{10}) = -\frac{2}{120}= -\frac{1}{60} = -\frac{1}{6}*\frac{1}{10} = -0.016\)

So, at this stage our running total is \(0.33 - 0.016 = 0.314\)

Now, notice that since \((\frac{1}{12} - \frac{1}{10}) < (\frac{1}{16} - \frac{1}{14})\), the final fraction will subtract a number of smaller magnitude than \(0.016\) from the running total.

Therefore we have \(y = 0.314\) \(-\)(something slightly smaller than \(0.016\))

Thus, answer B.
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Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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New post 06 Sep 2019, 01:50
Bunuel wrote:
Which of the following is the best approximation for y?
\(\frac{1}{2}- \frac{1}{3} + \frac{1}{6} - \frac{1}{10} + \frac{1}{12} - \frac{1}{14} + \frac{1}{16}\)

A. 0.1
B. 0.31
C. 0.35
D. 0.4
E. 0.6


1/2 - 1/3 = 0.5 - 0.33 = 0.167
1/6 - 1/10 = 0.166 - 0.1 = 0.06
Adding them = 0.227 + small value from remaining terms

It will be approx 0.3 as the the difference between rest of the terms will keep on decreasing.

B is correct.
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Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/   [#permalink] 06 Sep 2019, 01:50
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