The average of 15 consecutive integers is 88. What is the greatest of

Question

The average (arithmetic mean) of 15 consecutive integers is 88. What is the greatest of these integers?

(A) 78
(B) 90
(C) 94
(D) 95
(E) 98

LevanKhukhunashvili · Answer

For consecutive integers, mean=median
median for 15 consecutive integers is the eighth term.

If the 8th term is 88, then the 15th term must be 95

IMO
Ans:  D

Mo2men · Answer

.......88, 89, 90, 91, 92, 93 , 94, 95

Answer: D

AyushCrackVerbal · Answer

Let the first integer be  x .

Since 15 consecutive integers are part of the given sequence, the greatest integer would be " x + 14 "

The average of 15 consecutive integers =  88

\frac{(x) + (x+1) + (x+2) + .......... + (x+14)}{15} =  88

15x + (1+2+3+.....+14) = 1320

Sum of first n natural numbers =  \frac{(n)(n+1)}{2}

(1+2+3+.....+14) =  \frac{(14)(14+1)}{2}   = 7*15 = 105

15x + 105 = 1320

15x = 1215

x = 81

The greatest integer in the sequence  = x + 14 = 81 + 14 = 95

The correct answer is  D

Ishat16189 · Answer

D

Average of 15 consecutive integers is 88.
Median=mean for evenly spaced set.
So 8th term will be median=88.

As numbers are consecutive, 9th,10th,.. so on, 15th integer will be 95. Which will be greatest of these integers.

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EgmatQuantExpert · Answer

Given

• 15 consecutive integers have an average as 88.

To Find

• Find the largest of them.

Approach and Working Out

• An arithmetic progression of consecutive integers will have the middle number as the average. (When the number of terms is odd).
 o Hence the middle number 88 is the 8th one so the 15th one is 95.

Correct Answer: Option D

Mizar18 · Answer

88, 89, 90, 91, 92, 93 , 94, 95

Answer: D

MathRevolution · Answer

As it is consecutive integers, hence Average = Median.

Number of terms = 15.

Median = 88. (7 numbers are less than 88 and 7 numbers are more than 88)

Greatest term : 88 + 7 = 95

Answer D

harshbirsingh · Answer

15 consecutive numbers can be created such that the middle number is x and there are 7 numbers greater than x   and 7 numbers less than x  .

On adding these numbers and dividing by 15 (to take an average), you'll get 15x/15=88.

As such, x=88.

To get the maximum value, you need x+7 = 88+7 = 95.

Option D.

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ScottTargetTestPrep · Answer

Solution:

Since the average of any number of consecutive integers is also the median, we see that the median is 88. Since the median is the 8th number of the 15 consecutive integers, the greatest of the 15 integers must be 7 more than the median. Thus, the greatest integer is 88 + 7 = 95.

Answer: D

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

saaiid · Answer

the numbers are :x,x+1-----+(x+14)
x+7 = 88(avg=avg)
x=81
so, x+14
81+14
95
answer : D

shishimaru · Answer

Middle term = 88; 
Greatest integer = 88 + (15 - 1) / 2 = 88 + 7 = 95;

Answer:  (D) 95 .

The average of 15 consecutive integers is 88. What is the greatest of

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GMAT Problem Solving (PS) Questions

The average of 15 consecutive integers is 88. What is the greatest of

Prep Toolkit

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