For a sequence of seven integers, the difference between the largest a

Question

For a sequence of seven integers, the difference between the largest and the smallest numbers is 14 and the arithmetic mean of the seven integers is 26. What is the greatest possible value of the largest number of the sequence?

A. 24
B. 29
C. 31
D. 35
E. 38

A. 24
B. 29
C. 31
D. 35
E. 38

shivani1351 · Answer

Let the seven integers in increasing order be: a < b < c < d < e < f < g
Thus, g-a = 14
a+b+c+d+e+f+g = 182 (As the arithmetic mean of these seven integers is 26)

In my personal opinion, the best way to solve such questions is to check using options:
Let's consider the greatest possible value of g = 38 given in the options (Option E)
As g = 38 => a = g-14 = 24
Now, as there's no restriction given on any of the seven integers, let's assume a=b=c=d=e=f=24
Thus, the sum of the seven integers thus becomes: 24*6 + 38 = 144 + 38 = 182, which is what is given in the question.

As g = 38 satisifies these conditions, and there is no other option that is greater than 38, the answer is 38.

Hence, the correct answer is Option E - 38

Hope this helps!

curatelycurious · Answer

Isn't in an AP, mean = median, which would result 26 as the 4th term, and a+3d = 26, 
and a+6d-a =14, so d =7/3, by equating these two we get the value of a = 19 and l =35

sujoykrdatta · Answer

But the question doesn't mention that's the terms are in AP

sujoykrdatta · Answer

Let the smallest and largest numbers be x and x+14
Sum of the 7 numbers = 182
To maximize the largest number, the other numbers have to minimize. So we can assume the remaining 5 numbers as x each (least possible value).

Thus, sum = 7x+14 = 182
=> x = 24
=> The greatest number = 24+14 = 38

I think this is the easiest way of solving this question.

Answer E

HarshG7 · Answer

if all the other terms are assumed to be equal i.e. 24 in this case and only the largest term is different i.e. 38, does it qualify as a sequence ? i mean doesn't a sequence need to have kind of a pattern

DaMa03 · Answer

Sum of all numbers is 7*26
To maximize the last number, we need to minimize all other numbers. let all other numbers by x, and the largest one be (x+14)
We get the sum of 6x+(x+14) or 7x+14

Sum needs to be equal, so 7*26=7x+14
we can divide by 7, which leaves us the easy equation of 26=x+2 and thus x=24

Largest number is therefore x+14 = 24+14 = 38

Answer E

For a sequence of seven integers, the difference between the largest a

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For a sequence of seven integers, the difference between the largest a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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