GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 30 May 2020, 11:24

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64246
Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

### Show Tags

16 Oct 2016, 03:39
10
00:00

Difficulty:

75% (hard)

Question Stats:

59% (02:24) correct 41% (02:43) wrong based on 137 sessions

### HideShow timer Statistics

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

_________________
Manager
Joined: 11 Jul 2016
Posts: 77
Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

### Show Tags

16 Oct 2016, 03:56
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
Math Expert
Joined: 02 Aug 2009
Posts: 8610
Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

### Show Tags

16 Oct 2016, 04:04
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
_________________
Intern
Joined: 08 Aug 2011
Posts: 21
Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

### Show Tags

16 Oct 2016, 11:14
2
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.
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4992
Location: India
GPA: 3.5
Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

### Show Tags

17 Oct 2016, 07:30
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 -
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

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Joined: 08 Aug 2011
Posts: 21
Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

### Show Tags

17 Oct 2016, 08:49
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 $$0.016$$)

Senior Manager
Joined: 27 Feb 2014
Posts: 277
Location: India
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/  [#permalink]

### Show Tags

06 Sep 2019, 00:50
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.
_________________
Inspired by great content in some best books on GMAT, I have created my own YouTube channel-QUANT MADE EASY! I would love some support and feedback. Please hit subscribe and check it out!

Re: Which of the following is the best approximation for y? 1/2 - 1/3 + 1/   [#permalink] 06 Sep 2019, 00:50