Set M consists of 50 consecutive integers. If the range of the negativ

Question

Set M consists of 50 consecutive integers. If the range of the negative integers in Set M is 36, what is the sum of all positive integers in Set M?

A. 78
B. 91
C. 105
D. 112
E. 120

broall · Answer

If set M has no positive integers, then the range of the negative integers is 49 (if set M has zero) or 50 (if all elements in set M is negative).

Hence, set M must have negative integers and positive numbers.

The range of the negative integers is 36, so that range is {-37, -36, ..., -1}
Next elements of set M are 0, 1, 2,...

Set M consists of 50 consecutive integers, so the last number is 12.
Set M is {-37, -36, -35, ..., 0, ..., 11, 12} (50 numbers)

The sum of all positive numbers in set M is: 12 * (1+12) / 2 = 78

The answer is A

BrentGMATPrepNow · Answer

The greatest  negative  number is -1 
Let k = least negative number
So, if the range of the negative integers is 36, then -1 - k = 36
This tells us that k = -37
Since the negative values go from -1 all the way to -37, we can see that there are  37 negative values  in total.

So, set M = { -37, -36, -35, . . . -1 ,  0 ,  1, 2, ... }
What is the GREATEST value in set M?

Well, we know that the 50 integers consist of  37 negative integers  and 1  zero . So, the remaining  12 numbers must be positive . 
So, set M = { -37, -36, -35, . . . -1 ,  0 ,  1, 2, 3, ..., 11, 12 }

What is the sum of all positive integers in Set M?  
There's a nice formula that says: 1 + 2 + 3 + . . . + n = (n)(n+1)/2
So,  1 + 2 + 3 + + 11 + 12  = (12)(13)/2 = 78

Answer: A

Cheers,
Brent

sravankumar0911 · Answer

For consecutive negative integers with range 36 the negative integer set should be from -1 to -37 as range=max value - min value. The +ive integers will be from 1 to 12. The total count of integers will be 50(inc 0) the sum of positive integers will be n*(n+1)/2 (n=12) hence correct answer is A 78

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Sent from my iPhone using GMAT Club Forum

JeffTargetTestPrep · Answer

Since the range of the negative integers in set M is 36, the negative integers are from -1 to -37 inclusive. Thus, there are 37 negative integers in set M, and after accounting for zero, there are 12 positive integers left, i.e., the integers from 1 to 12 inclusive.

Thus, the sum of the consecutive integers from 1 to 12 is:

Sum = average x quantity

Sum =   x 12

Sum = 13/2 x 12

Sum = 13 x 6 = 78

Answer: A

GMATYoda · Answer

Here you can use the quick method of summing evenly-spaced sets, derived from the formula for the Mean. 
Since Mean = Sum of Values / Number of Values, and you know that in an evenly-spaced set the median equals the mean, you can multiply 12 (the number of values) by 6.5 (the middle value, which you can calculate by just averaging the first and last terms, 1 and 12) to get 78.

The correct answer is A.

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Set M consists of 50 consecutive integers. If the range of the negativ

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