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# The sum of x distinct integers

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Intern
Joined: 15 Sep 2017
Posts: 34
Followers: 0

Kudos [?]: 13 [0], given: 2

The sum of x distinct integers [#permalink]  12 Sep 2018, 22:42
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Question Stats:

50% (01:22) correct 50% (00:45) wrong based on 2 sessions
The sum of x distinct integers greater than zero is less than 75.What is the greatest possible value of x?

A) 8

B) 9

C) 10

D) 11

E) 12
[Reveal] Spoiler: OA
Director
Joined: 20 Apr 2016
Posts: 678
Followers: 5

Kudos [?]: 444 [1] , given: 75

Re: The sum of x distinct integers [#permalink]  13 Sep 2018, 19:22
1
KUDOS
AchyuthReddy wrote:
The sum of x distinct integers greater than zero is less than 75.What is the greatest possible value of x?

A) 8

B) 9

C) 10

D) 11

E) 12

Sum of n distint numbers is given by $$\frac{n(n + 1)}{2}$$

so,
$$\frac{n(n + 1)}{2}$$ < 75

or n(n + 1) < 150

Solving we have n = 11.5 and -12.5 (we cannot have negative value)

so n < 11.5

so the value should be 11 i.e. option D
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Re: The sum of x distinct integers   [#permalink] 13 Sep 2018, 19:22
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