The number of tournament games is represented as...

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

The number of tournament games is represented as...

by BTGmoderatorLU » Sun Nov 12, 2017 11:30 am

The number of tournament games is represented as G(n) where n is the number of attendees of the games. 2 attendees play a game such that G(n+1)=G(n)+n, G(2)=1. If the attendees number is 30, what is the total number of games?

A. 380
B. 435
C. 455
D. 510
E. 520

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

Quote

Source: Beat The GMAT — Problem Solving | Sun Nov 12, 2017 11:30 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Tue Nov 14, 2017 1:44 am

LUANDATO wrote:The number of tournament games is represented as G(n) where n is the number of attendees of the games. 2 attendees play a game such that G(n+1)=G(n)+n, G(2)=1. If the attendees number is 30, what is the total number of games?

A. 380
B. 435
C. 455
D. 510
E. 520

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

G(n+1)=G(n)+n

G(2)=1
G(3)=G(2)+2 = 1+2 = 3
G(4)=G(3)+3 = 1+2 + 3
G(5)=G(4)+4 = 1+2 + 3+4

i.e. G(30)=1+2 + 3+4+5+.......+29 = (1/2)*29*(29+1) = 29*15 = 435

Answer: option B

I hope this helps!

"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

Quote

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

Answer

by EconomistGMATTutor » Thu Nov 16, 2017 1:06 pm

Hello LUANDATO.

In this question we will use the Gauss Sum, which says that the sum of the integers from 1 to n is $$\frac{n\cdot\left(n+1\right)}{2}.$$
It tell us $$G\left(n+1\right)=G\left(n\right)+n, and \ G\left(2\right)=1.$$
So, $$G\left(3\right)=G\left(2\right)+2=1+2.$$ $$G\left(4\right)=G\left(3\right)+3=1+2+3.$$ $$G\left(5\right)=G\left(4\right)+4=1+2+3\ +5.$$ As you can see, we can say that $$G\left(n\right)=1+2+3 +.\ .\ .\ +\ \left(n-1\right).$$ In other words, G(n) is the Gauss Sum from 1 to n-1.
So, $$G\left(30\right)=1+2+3 +\ .\ .\ .\ +\ 29\ =\ \frac{29\cdot30}{2}=15\cdot29=435.$$
The correct answer is B .
I hope this explanation may help you.
I'm available if you'd like a follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8087; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 26, 2019 7:50 am

BTGmoderatorLU wrote:The number of tournament games is represented as G(n) where n is the number of attendees of the games. 2 attendees play a game such that G(n+1)=G(n)+n, G(2)=1. If the attendees number is 30, what is the total number of games?

A. 380
B. 435
C. 455
D. 510
E. 520

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

We see that G(3) = G(2) + 2 = 1 + 2 = 3, G(4) = G(3) + 3 = 3 + 3 = 6, G(5) = G(4) + 4 = 6 + 4 = 10, and so on. In other words, if n â‰¥ 2, G(n) = 1 + 2 + 3 + ... + (n - 1). Therefore, G(30) = 1 + 2 + 3 + ... + 29. In other words, G(30) is the sum of the first 29 positive integers. The first 29 positive integers comprise an evenly-spaced set, and so we can use the formula Sum = Average x Number to calculate the sum of the first 29 positive integers. Therefore, we have:

G(30) = (1 + 29)/2 x 29 = 15 x 29 = 435

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]