mean range

[Brent@GMATPrepNow]

a, b, c, d and e are positive integers such that a<b<c<d<e.
If the average (airthmetic mean) of the five numbers is 6, and d-b=3, what is the greatest possible range of the five numbers?
A) 12
B) 15
C) 18
D) 20
E) 23

Answer: C

[720dreaming]

18, C.

I worked from the answer choices. The Sum is 30 so it Can't be 23 since that simply does not leave enough room for the others, nevermind that d-b=3. 20 does not work for the same reason - sum will be 1+2+3+4+21=31.

1+2+3+5+19=30.

[vishubn]

a+b+c+d+e=30

sum is 30 range is a-e.. and a positive integer

minimum value a can take is 1 and maximum value e < 30

a=1, b=2 we know on first shot

now d-b=3
d-2=3
d=5

so d>c the possible values for c 3,4

if 3

1+2+3+5+e=30
we get e =19

value of c=4 fails... ( reason stated above)

Max range is 18

Vishu

[Brent@GMATPrepNow]

Great explanation, vishubn!

[raunekk]

b=2 we know on first shot

@vishubn...

how did u came to this conclusion??

thanks in advance.

[vishubn]

b=2 we know on first shot

@vishubn...

how did u came to this conclusion??

thanks in advance.

a, b, c, d and e are positive integers such that a<b<c<d<e.

a= positive integer..
so a=1

a<b or b>a we get b=2...

thank u

Vishu

[vishubn]

@raunekk
I am sure u overlooked it

Vishu

[raunekk]

ok vishubn... i got it..

actually was getting confused as to how u took b=2 when the question doesnt mention that they are consecutive numbers..actually i missed the point that We need to find the greatest range..

thanks once again bro..

[logitech]

a b c d e

MAX E ---> MIN ( a+b+c+d)

Let's start with a. The smallest positive integer:1

a=1

b=2 ( since we are trying to minimize the a+b+c+d )

We know d=b+3

d= 2+3 = 5

c is between a and d, choose the smallest value possible c=3

5 numbers x average = SUM

5x6 = 30

30 - (a+b+c+d) = Max E

Max E = 19

a=1

Range : Max - Min = 19 - 1 = 18


P.S. I would put 17 as one of the answers to trick people in case they chose 4 for c :!:

[Brent@GMATPrepNow]

P.S. I would put 17 as one of the answers to trick people in case they chose 4 for c

Great idea, Logitech! I always find it difficult to think of distractors that students may get as their answer.