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

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Question Stats:

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

A) 8

B) 9

C) 10

D) 11

E) 12

Re: The sum of x distinct integers
[#permalink]
13 Sep 2018, 19:22

4

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

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]
28 Sep 2018, 00:52

pranab01 wrote:

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

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

if n<11.5 so option a,b,c,d all are less then 11.5. why only d is correct answer choose??

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Re: The sum of x distinct integers
[#permalink]
28 Sep 2018, 03:40

Expert Reply

shivankkhanna wrote:

if n<11.5 so option a,b,c,d all are less then 11.5. why only d is correct answer choose??

Because it says greatest possible value of x and 11 would be the greatest among the 4.

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Re: The sum of x distinct integers
[#permalink]
28 Feb 2020, 04:13

How do we foil n^2+n–150<0 w/out using the quadratic formula?

Re: The sum of x distinct integers
[#permalink]
04 Mar 2020, 14:37

1

I drew a blank.

So just counted all the numbers from 1+2+3.....12. The answer is 78.

Therefore subtract 12 and that's enough to give you a sum of under 74.

Therefore 11 is x

So just counted all the numbers from 1+2+3.....12. The answer is 78.

Therefore subtract 12 and that's enough to give you a sum of under 74.

Therefore 11 is x

Re: The sum of x distinct integers
[#permalink]
04 Aug 2021, 06:46

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