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

 It is currently 21 Jan 2020, 02:04

### 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

# Best approximation for y is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60527
Best approximation for y is  [#permalink]

### Show Tags

10 Oct 2019, 21:28
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:15) correct 45% (02:18) wrong based on 38 sessions

### HideShow timer Statistics

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

_________________
Senior Manager
Joined: 22 Feb 2018
Posts: 446
Re: Best approximation for y is  [#permalink]

### Show Tags

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
Director
Joined: 18 May 2019
Posts: 649
Re: Best approximation for y is  [#permalink]

### Show Tags

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

The answer is therefore B.

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.
Director
Joined: 07 Mar 2019
Posts: 579
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Best approximation for y is  [#permalink]

### Show Tags

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.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019

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.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5700
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Best approximation for y is  [#permalink]

### Show Tags

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
Senior Manager
Joined: 29 Jun 2019
Posts: 470
Re: Best approximation for y is  [#permalink]

### Show Tags

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

Posted from my mobile device
_________________
Always waiting
Manager
Joined: 17 Jan 2019
Posts: 144
Re: Best approximation for y is  [#permalink]

### Show Tags

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
VP
Joined: 24 Nov 2016
Posts: 1076
Location: United States
Re: Best approximation for y is  [#permalink]

### Show Tags

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

Senior Manager
Joined: 25 Jul 2018
Posts: 468
Re: Best approximation for y is  [#permalink]

### Show Tags

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

The answer is B.

Posted from my mobile device
Re: Best approximation for y is   [#permalink] 12 Oct 2019, 06:43
Display posts from previous: Sort by

# Best approximation for y is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne