The sum of a sequence of consecutive integers is 1,125 and the median

Question

The sum of a sequence of consecutive integers is 1,125 and the median is 45. What is the value of the greatest integer in the sequence?

A. 33
B. 45
C. 56
D. 57
E. 58

BrentGMATPrepNow · Accepted Answer

We are told that the median is  45 
In other words, when all of the consecutive numbers are arranged in ascending order,  45  is the middlemost number. 
Now let's add a number on either side of  45  to get: 44,  45 , 46
This is the same as writing: (45-1),  45 , (45+1), and if we add these three values, the -1 and +1 cancel out to get: 45 + 45 + 45

The same applies to when we add TWO numbers on either side of  45 
We get: (45-2), (45-1),  45 , (45+1), (45+2)
If we add these five values, the -1 and +1 cancel out, and the -2 and +2 cancel out to get : 45 + 45 + 45 + 45 + 45

1,125/45 = 25
So our sequence must consist of 25 values.
12 values must be greater than  45 
12 values must be less than  45 
And 1 value is equal to  45

So our sequence looks like this: (45-12), (45-11), (45-10), ..... (45-2), (45-1),  45 , (45+1), (45+2)...., (45+10), (45+11), (45+12)

What is the value of the greatest integer in the sequence?   
The greatest possible value = (45+12), which equals 57

Answer: D

Cheers,
Brent

gagan543 · Answer

From the question we can derive that median is 45 meaning the sequence contains odd number, from our previous learning we know that in consecutive set

median *number of digits = sum of the digits
45*number of digits=1125
so number of digits comes out to be 25
so this meaning the 13th digit is 45 
adding 12 to 45 so that we can get the last digit
which comes out to be 57 
so 57 is the answer.

gracie · Answer

1125 sum/45 median=25 terms in sequence
median is term 13
greatest integer is term 25
25-13=12
45+12=57 value of greatest integer
D

ScottTargetTestPrep · Answer

When we have a set of consecutive integers, the average and the median are equal. Since the median of this set of consecutive integers is 45, the average is 45; thus:

1125 = quantity x 45

25 = quantity

Since the number of integers in the sequence is 25, we see that 12 of them are greater than the median (and 12 of them are less than the median). Since they are consecutive integers, the greatest integer is 45 + 12 = 57.

Answer: D

adityasuresh · Answer

The sum of a sequence of consecutive integers is 1,125 and the median is 45. What is the value of the greatest integer in the sequence?

A. 33
B. 45
C. 56
D. 57
E. 58

I used PIN (Plugging In Numbers) Approach.
Stem: Median = 45 (This is the central term). And Sum of consecutive integers -
If Greatest integer is 57. Central term = 45, so no of terms greater than 45 = 57-45 = 12, since 45 is the median no of terms lesser than 45 = 12.(Least term = 45 - 12 = 33.
No of terms (inclusive) = 57 - 33 + 1 =25
Since terms are in AP: Sum of terms =  N/2 (F + L) =  25/2 (33 + 57) = 25 * 45 = 1225.
 D

steffe440 · Answer

The number of integers is just the sum / avg which means we get 1125 / 45 = 25, then we know we have 25 integers, and since they are consecutive integers that means we have 12 numbers to the right of the median to add, hence we get 45 + 12 = 57

The sum of a sequence of consecutive integers is 1,125 and the median

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The sum of a sequence of consecutive integers is 1,125 and the median

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