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

It is currently 05 Apr 2020, 18:08

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 62498
If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10  [#permalink]

Show Tags

New post 04 Feb 2020, 02:41
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

56% (02:12) correct 44% (01:56) wrong based on 63 sessions

HideShow timer Statistics

If \(P = \frac{1}{10^2 + 1} + \frac{2}{10^2 + 2} + \frac{3}{10^2 + 3} + ... + \frac{10}{10^2 + 10}\) then which of the following is the best approximate value of P.

A. 0.42
B. 0.52
C. 0.57
D. 0.62
E. 0.72


Are You Up For the Challenge: 700 Level Questions


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS

_________________
Senior Manager
Senior Manager
avatar
G
Joined: 16 Feb 2015
Posts: 355
Location: United States
Re: If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10  [#permalink]

Show Tags

New post 04 Feb 2020, 02:53
2
Explanation:

Approximating the denominator of each fraction, one gets P as follows:
= (1+2+3+4+5)/100 + (6+7+8+9+10)/110
= 15/100 + 40/110
= 0.15 + 0.36 = 0.51 Aprox.

IMO-B
Director
Director
avatar
G
Joined: 14 Dec 2019
Posts: 504
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Premium Member CAT Tests
Re: If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10  [#permalink]

Show Tags

New post 04 Feb 2020, 03:00
1
1st term -> \(\frac{1}{(10^2+1)} \) =\( \frac{1}{101}\) -> slightly < 0.01
2nd term -> \(\frac{2}{(10^2+2)} \) =\( \frac{2}{102}\) -> slightly < 0.02
.
.
.
10th term -> \(\frac{10}{(10^2+10)} \) =\( \frac{1}{11}\) -> slightly < 0.1

Therefore -> Total slightly < (0.01 + 0.02 + 0.03 + .... + 0.1) -> slightly less than 0.55 -> Answer B -> 0.52
Intern
Intern
avatar
B
Joined: 16 Oct 2018
Posts: 9
Re: If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10  [#permalink]

Show Tags

New post 04 Feb 2020, 03:07
2
(1+2+3...+10)/(10^2+10) < P < (1+2+3...+10)/(10^2)

This implies 55/110 < P < 55/100

0.5 < P < 0.55
Option B should be the Answer

Posted from my mobile device
Senior Manager
Senior Manager
avatar
P
Joined: 27 Feb 2014
Posts: 290
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10  [#permalink]

Show Tags

New post 04 Feb 2020, 03:12
1
\(P = \frac{1}{10^2 + 1} + \frac{2}{10^2 + 2} + \frac{3}{10^2 + 3} + ... + \frac{10}{10^2 + 10}\)

Analyzing the question, there is addition of 1, 2,3...10 to \(10^2\) in the denominator.
Adding a small value to \(10^2\) will slightly decrease value of the fraction. Lets understand:
\(\frac{1}{100}\) = 0.01 and \(\frac{1}{101}\)=0.009
\(\frac{2}{100}\) = 0.02 and \(\frac{2}{102}\) = 0.196


hence, lets take common denominator as \(10^2\) for approximation
Adding the numerator, we get 1+2+3+....+10 = 55
55/\(10^2\) = 0.55

As denominator will be greater than \(10^2\), hence the value of the fraction will be slightly less that 0.55

Therefore, IMO B.
_________________
Permutation (https://youtu.be/oRyquKBDSH0), When To Use Combination? (https://youtu.be/OnqHOLkCqSE)
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1333
Location: United States
Re: If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10  [#permalink]

Show Tags

New post 04 Feb 2020, 07:33
1
Bunuel wrote:
If \(P = \frac{1}{10^2 + 1} + \frac{2}{10^2 + 2} + \frac{3}{10^2 + 3} + ... + \frac{10}{10^2 + 10}\) then which of the following is the best approximate value of P.

A. 0.42
B. 0.52
C. 0.57
D. 0.62
E. 0.72


1/101˜0.01
2/102˜0.02
3/103˜0.03

10/110˜0.0909
sum first 10 positive integers: n(n+1)/2=10(11)/2=55
since difference 10/100=0.1 and 10/110=0.09 is 0.01
sum sequence must be less than 0.54, which closest to 0.52

Ans (B)
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9960
Location: United States (CA)
Re: If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10  [#permalink]

Show Tags

New post 08 Feb 2020, 19:21
1
Bunuel wrote:
If \(P = \frac{1}{10^2 + 1} + \frac{2}{10^2 + 2} + \frac{3}{10^2 + 3} + ... + \frac{10}{10^2 + 10}\) then which of the following is the best approximate value of P.

A. 0.42
B. 0.52
C. 0.57
D. 0.62
E. 0.72


Are You Up For the Challenge: 700 Level Questions


Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS


We see that each denominator is actually very close to 100 (notice that the smallest denominator is 10^2 + 1 = 101 and the largest is 10^2 + 10 = 110). Therefore, 1/(10^2 + 1) is essentially 1/100, 2/(10^2 + 2) is essentially 2/100 and so on. Approximating all the fractions using the denominator 100, we have

P ≈ 1/100 + 2/100 + 3/100 + … + 10/100 = (1 + 2 + 3 + … + 10)/100 = 55/100 = 0.55

However, since 1/(10^2 + 1) is slightly less than 1/100, 2/(10^2 + 2) is slightly less than 2/100 and so on, P should be slightly less than 0.55. Therefore, the best approximate value of P is 0.52.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10   [#permalink] 08 Feb 2020, 19:21
Display posts from previous: Sort by

If P = 1/(10^2 + 1) + 2/(10^2 + 2) + 3/(10^2 + 3) + ... + 10/10^2 + 10

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





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