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The sum of n different
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19 Jun 2021, 04:25
19 Jun 2021, 04:25
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Question Stats:
100% (01:17) correct
0% (00:00) wrong based on 2 sessions
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The sum of n different positive integers is less than 100. What is the greatest possible value of n?
A) 10
B) 11
C) 12
D) 13
E) 14
A) 10
B) 11
C) 12
D) 13
E) 14
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: The sum of n different
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19 Jun 2021, 06:27
19 Jun 2021, 06:27
1
The sum of n different positive integers is less than 100 and we need to find the greatest possible value of n
So, the n different positive integers should be least
And we know that Sum of first n positive integers = \(\frac{n*(n+1)}{2}\)
=> \(\frac{n*(n+1)}{2}\) < 100
=> n*(n+1) < 200
Lets start with n = 12 we get
12*(12+1)= 12*13 = 156 < 200 , So possible
Lets go higher then, n = 13
13*14 = 182 < 200, so possible
We need to check with 14 now
14*15 = 210 < 200 Not possible
Hence answer will be D
Hope it helps!
So, the n different positive integers should be least
And we know that Sum of first n positive integers = \(\frac{n*(n+1)}{2}\)
=> \(\frac{n*(n+1)}{2}\) < 100
=> n*(n+1) < 200
Lets start with n = 12 we get
12*(12+1)= 12*13 = 156 < 200 , So possible
Lets go higher then, n = 13
13*14 = 182 < 200, so possible
We need to check with 14 now
14*15 = 210 < 200 Not possible
Hence answer will be D
Hope it helps!
gmatclubot
Re: The sum of n different [#permalink]
19 Jun 2021, 06:27
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