If the sum of x distinct, positive integers is less than 75, what is

Question

If the sum of x distinct, positive integers is less than 75, what is the greatest possible value of x ?

A. 8
B. 9
C. 10
D. 11
E. 12

Archit3110 · Answer

sum of distinct integers < 75 
1+2+3... +11;
IMO D ;11 will be the largest integer..

Bunuel · Answer

First of all notice that we are told that the sum is LESS than 75. Next, the question asks about the greatest possible NUMBER of distinct, positive integers the sum of which is LESS than 75.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66 < 75. If you add the next one, 12, then the sum would be 78. So, the greatest possible NUMBER of distinct, positive integers the sum of which is LESS than 75 is 11 (from 1 to 11, inclusive).

Answer: D.

Hope it helps.

Abhishek009 · Answer

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

Now check using the given options...

11*\frac{12}{2} = 66 < 75  , Answer ,must be (D)

KSBGC · Answer

we are looking for the number of integers whose sum is less then 75.

Number of integers = x. we are asked to maximize x.

All the integers are positive. Thus we must start with 1 and continue the series with lower integers to get the maximum value of x.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66 which is less than 75. It is not possible to add any other integers.

Thus, x =11.

D is the correct answer.

eswarchethu135 · Answer

What if the numbers are 2,4,5,6,7,8,9,10,11,12? The sum of these numbers is 74. The question hasn't said the numbers are consecutive? It just said x distinct positive integers, that's it! Why is this case not possible? Why can't E be the choice?

eswarchethu135 · Answer

What if the numbers are 2,4,5,6,7,8,9,10,11,12? The sum of these numbers is 74. The question hasn't said the numbers are consecutive? It just said x distinct positive integers, that's it! Why is this case not possible? Why can't E be the choice?

Shivam710 · Answer

Because in your explanation the value of x is 10. This is because the question is asking for the maximum numbers of distinct integers that can be added to get a sum<75. The question is not asking for the greatest of those integers.

eswarchethu135 · Answer

Got it. Thanks for clarification.

Posted from my mobile device

ScottTargetTestPrep · Answer

Let’s analyze the answer choices in reverse order since we are looking for the greatest possible value of x.

E. 12

Since we want x to be as large as possible, we want the smallest of the x integers to be 1. Therefore, if x = 12, the sum of the first 12 positive integers is:

1 + 2 + 3 + … + 12 = 12 x (1 + 12)/2 = 6 x 13 = 78

This is not less than 75, so x can’t be 12.

D. 11

We see that 1 + 2 + 3 + … + 11 = 78 - 12 = 66.

This is less than 75, thus the greatest possible value of x is 11.

Answer: D

mykrasovski · Answer

Bunuel  is there any other solution rather than the brute force one? The problem does not feel like the 500-600 one....

bumpbot · Answer

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If the sum of x distinct, positive integers is less than 75, what is

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If the sum of x distinct, positive integers is less than 75, what is

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