GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 01:09

### 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

# What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?  [#permalink]

### Show Tags

29 Mar 2019, 00:19
00:00

Difficulty:

55% (hard)

Question Stats:

40% (01:28) correct 60% (02:13) wrong based on 15 sessions

### HideShow timer Statistics

[GMAT math practice question]

What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?

$$A. \frac{49}{50}$$
$$B. \frac{51}{50}$$
$$C. \frac{99}{100}$$
$$D. \frac{101}{100}$$
$$E. \frac{49}{100}$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7983 What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2? [#permalink] ### Show Tags 29 Mar 2019, 06:22 1 MathRevolution wrote: [GMAT math practice question] What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2? $$A. \frac{49}{50}$$ $$B. \frac{51}{50}$$ $$C. \frac{99}{100}$$ $$D. \frac{101}{100}$$ $$E. \frac{49}{100}$$ $$\frac{1}{3C2}+\frac{1}{4C2}+\frac{1}{5C2}+.......\frac{1}{100C2}$$.. $$\frac{2}{3*2}+\frac{2}{4*3}+\frac{2}{5*4}+.......\frac{2}{100*99}$$.. $$2(\frac{1}{3*2}+\frac{1}{4*3}+\frac{1}{5*4}+.......\frac{1}{100*99})$$.. $$2((\frac{1}{2}-\frac{1}{3})+(\frac{1}{3}-\frac{1}{4})+(\frac{1}{4}-\frac{1}{5})+.......(\frac{1}{98}-\frac{1}{99})+(\frac{1}{99}-\frac{1}{100}))$$.. $$2(\frac{1}{2}-\frac{1}{100})=2*\frac{49}{100}$$.. $$\frac{49}{50}$$.. A _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8017 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2? [#permalink] ### Show Tags 31 Mar 2019, 18:33 => nCr = $$\frac{{ n(n-1)…(n-r+1) }}{{ 1*2*… *r }}$$ So, nC2 = $$\frac{n(n-1)}{2}$$ and 1/nC2 = $$\frac{2}{{n(n-1)}}$$. Recall that $$\frac{1}{{k(k+1)}} = \frac{1}{k} – \frac{1}{(k+1)}.$$ So, 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2 $$= \frac{2}{(2*3)} + \frac{2}{(3*4)} + \frac{2}{(4*5)} + … + \frac{2}{(99*100)}$$ $$= 2{ \frac{1}{(2*3)} + \frac{1}{(3*4)} + \frac{1}{(4*5)} + … + \frac{1}{(99*100)} }$$ $$= 2{ ( \frac{1}{2} – \frac{1}{3} ) + ( \frac{1}{3} – \frac{1}{4} ) + ( \frac{1}{4} – \frac{1}{5} ) + … + ( \frac{1}{99} – \frac{1}{100} ) }$$ $$= 2( \frac{1}{2} – \frac{1}{100} )$$ $$= 2 ( \frac{50}{100} – \frac{1}{100} )$$ $$= 2(\frac{49}{100})$$ $$= \frac{49}{50}$$ Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: What is the value of 1/3C2 + 1/4C2 + 1/5C2 + … + 1/100C2?   [#permalink] 31 Mar 2019, 18:33
Display posts from previous: Sort by