The number of tournament games is represented as...

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BTGmoderatorLU: Moderator; Posts: 2547; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

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.

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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 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

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!

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

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.

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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

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