The average (arithmetic mean) of fifteen consecutive integers is 88.

Question

The average (arithmetic mean) of fifteen consecutive integers is 88. What is the greatest of these integers?

A. 93
B. 94
C. 95
D. 96
E. 97

GMATinsight · Answer

CONCEPT : Average consecutive integers = Median of consecutive Integers

i.e. _ _ _ _ _ _ _ 88 _ _ _ _ _ _ _

i.e. Greatest of them can be obtained by simply writing next consecutive terms

i.e. _ _ _ _ _ _ _ 88 89 90 91 92 93 94  95

Answer: Option C

ALTERNATIVE:

Let, smallest number = a

i.e. Largest number = a+14

Mean = a+7 = 88

i.e. a = 81

i.e. a+14 = 95

Answer: Option C

JamesSauerChambers · Answer

The average mean of 15 consecutive integer is the 8th integer. The greatest of these integers would be the 15th. Thus 88+7=95

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KSBGC · Answer

8th integer = 88

We need to find out 15th integer.

15 - 8 = 7.

So, 88 + 7 = 95

C is the correct answer.

Archit3110 · Answer

a+7= 88
a= 81
a+14 ; 81+14 = 95
IMO C

MHIKER · Answer

For consecutive integers, each increases by  1  than its previous number.

So, if the First number is  = x

The second number will be  =x+1

The third number is = x+2, So, we see each incremental number is 1 less than its position.

So, the fifth number is  x+14

The average of the consecutive number is the average of the first number and the last number.

Thus,  \frac{x+x+14}{2}=88

2x+14=176

2x=162

x=81

The largest number is  = 81+14=95

The answer is  95

BrushMyQuant · Answer

Given that The average (arithmetic mean) of fifteen consecutive integers is 88 and we need to find the greatest of these integers

============================================================

Theory
 ‣‣‣ In Case of consecutive number Mean = Middle term   
============================================================

Let the middle term be x

=> Mean = middle term = x = 88

Now, the numbers are consecutive so the greatest or the last term will be 7 more than the middle term = x + 7 = 88 + 7 = 95

So,  Answer will be C .
Hope it helps!

Watch the following video to Learn the Basics of Statistics

https://www.youtube.com/watch?v=Cvy_HHw4KIs

The average (arithmetic mean) of fifteen consecutive integers is 88.

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