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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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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?
$$\frac{1}{2}- \frac{1}{3} + \frac{1}{6} - \frac{1}{10} + \frac{1}{12} - \frac{1}{14} + \frac{1}{16}$$

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

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Manager  Joined: 11 Jul 2016
Posts: 78
Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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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
Math Expert V
Joined: 02 Aug 2009
Posts: 7971
Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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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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Intern  Joined: 08 Aug 2011
Posts: 21
Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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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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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 -
Attachment: Must for speeding DI.pdf [162.07 KiB]

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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Intern  Joined: 08 Aug 2011
Posts: 21
Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

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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 $$0.016$$)

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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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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. 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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