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# Best approximation for y is

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Math Expert
Joined: 02 Sep 2009
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Best approximation for y is  [#permalink]

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10 Oct 2019, 21:28
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:15) correct 39% (01:59) wrong based on 33 sessions

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Competition Mode Question

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

Best approximation for y is

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

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Re: Best approximation for y is  [#permalink]

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10 Oct 2019, 21:55
1
y=1/2−1/3+1/6−1/10+1/12−1/14+1/16
y = 1/2 + 1/6+ 1/12+ 1/16 - (1/3+ 1/10+ 1/14)
As percentage are easy to remember,we can solve it with the help of relevant percentage numerals.
1/2 = 50 %, 1/6 = 16.66 %, 1/12 = 8.33 % and 1/16 = 6.25 % = 50 + 16.66 + 8.33 + 6.25 = 81.24
1/3 = 33.33 %, 1/10 = 10 % and 1/14 = 7.14 = 33.33 + 10 + 7.14 = 50.47
81.24-50.47 = 30.77
30.77/100 ( divided by 100 to convert percentage to decimals) = 0.3077 = 0.31
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Re: Best approximation for y is  [#permalink]

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Updated on: 13 Oct 2019, 01:00
1
How I missed this one is a mystery to me.

we are to determine the best approximation for y=1/2 - 1/3 + 1/6 - 1/10 + 1/12 - 1/14 + 1/16
since the answer choices are approximated up to 2 decimal places, there is no need to approximate beyond three decimal places
y=0.5 - 0.333 + 0.167 - 0.1 + 0.5(0.167) - 0.5(0.143) + 0.5(0.125)
y=0.224 + 0.084 - 0.072 + 0.063
y=0.287 + 0.012
y=0.299
hence y is approximately 0.30

Originally posted by eakabuah on 10 Oct 2019, 22:17.
Last edited by eakabuah on 13 Oct 2019, 01:00, edited 1 time in total.
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Best approximation for y is  [#permalink]

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Updated on: 14 Oct 2019, 04:11
1
y=$$\frac{1}{2}−\frac{1}{3}+\frac{1}{6}−\frac{1}{10}+\frac{1}{12}−\frac{1}{14}+\frac{1}{16}$$

Best approximation for y is

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

y=$$\frac{1}{2}−\frac{1}{3}+\frac{1}{6}−\frac{1}{10}+\frac{1}{12}−\frac{1}{14}+\frac{1}{16}$$
= $$\frac{1}{6}+\frac{1}{6}−\frac{1}{10}+\frac{1}{12}−\frac{1}{14}+\frac{1}{16}$$
= $$\frac{1}{3}−\frac{1}{10}+\frac{1}{12}−\frac{1}{14}+\frac{1}{16}$$
= $$\frac{1}{3}−\frac{1}{60}−\frac{1}{112}$$

As $$\frac{1}{10}-\frac{1}{12}=\frac{1}{60}$$ and $$\frac{1}{14}-\frac{1}{16}=\frac{1}{112}$$
Above both values make a difference in hundredth position only.

Hence among values less than 0.33 B is nearer.

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Originally posted by lnm87 on 10 Oct 2019, 22:54.
Last edited by lnm87 on 14 Oct 2019, 04:11, edited 1 time in total.
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Re: Best approximation for y is  [#permalink]

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11 Oct 2019, 00:57
1
solve for given expression

IMO B ; 0.31

y=1/2−1/3+1/6−1/10+1/12−1/14+1/16
Best approximation for y is

A. 0.1
B. 0.31
C. 0.35
D. 0.4
E. 0.6
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Joined: 29 Jun 2019
Posts: 470
Re: Best approximation for y is  [#permalink]

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11 Oct 2019, 01:13
1
23/48 - 12/70=0.307
So is closed to option B

Posted from my mobile device
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Re: Best approximation for y is  [#permalink]

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11 Oct 2019, 02:12
1
My best approximation for the addition is 0.31

the first 3 fractions lead to 0

-1/10+1/12-1/14+1/16
cant give ending of /10 therefore 0.1,0.4, and 0.6 is out

now left with 0.31 and 0.35
I chose the ending with 1 because it seems like.
Therefore, B
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Re: Best approximation for y is  [#permalink]

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11 Oct 2019, 05:39
1
Quote:
y=1/2−1/3+1/6−1/10+1/12−1/14+1/16

Best approximation for y is

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

common denominator for (1/2−1/3+1/6−1/10+1/12) is 60:
60•(1/2−1/3+1/6−1/10+1/12)/60=(30-20-10-6+5)/60=19/60
y=19/60-1/14+1/16=~20/60-1/15+1/15<~1/3=0.31

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Re: Best approximation for y is  [#permalink]

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12 Oct 2019, 06:43
1
Y= $$\frac{1}{2}–\frac{1}{3}+\frac{1}{6}–\frac{1}{10}+\frac{1}{12}–\frac{1}{14}+\frac{1}{16}$$=

=$$\frac{1}{2}–\frac{1}{3}+(\frac{1}{2}–\frac{1}{3})—\frac{1}{10}+(\frac{1}{3}–\frac{1}{4})—(\frac{1}{14}–\frac{1}{16}$$=

= $$\frac{1}{2}–\frac{1}{3}+\frac{1}{2}–\frac{1}{3}–\frac{1}{10}+\frac{1}{3}–\frac{1}{4}–(\frac{1}{14}–\frac{1}{16})$$=

$$1–\frac{1}{3}–\frac{1}{10}–\frac{1}{4}–\frac{(16–14)}{(14*16)}$$=

$$1–0.(3)—0.1–0.25–(\frac{1}{112})$$=

= $$0.65–0.(3)—\frac{1}{112}$$= $$0.32–\frac{1}{112}$$

Let’s simplify $$\frac{1}{112}$$ :
—> it is less than $$\frac{1}{100}$$=0.01

—> 0.32–0.01= 0.31

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Re: Best approximation for y is   [#permalink] 12 Oct 2019, 06:43
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