Are the distinct Integers of Set {a, b, c, d, e} consecutive? 1) The

GMATinsight

Are the distinct positive Integers of Set {a, b, c, d, e} consecutive?

1) The mean of a, b, c, d, e is c
2) Range of the integers = c-a+2

for stmnt1 : we get considering sequence (1,2,3,4,5) yes and (1,2,3,4,6) mean 3.2 ~3 so no

for stmnt 2: if we say range of integers = middle value- first value +2
=> range of integers (e-a) -2=c-a
=> e=c+2

we know relation about e and c but a,b,d are not clear so NO

Combining stmnts we can conclude that a,b,c,d,e have to be consecutive nos.

IMO C should be correct..

Bunuel could you provide a better solution, please?

Consecutive integers are terms in which the preceding terms differ by 1: |a-b|=1

1) The mean of a, b, c, d, e is c insufic.

{a,b,c,d,e}={5,6,7,8,9}: mean=c=7; yes.
{a,b,c,d,e}={3,5,7,9,11}: mean=c=7; no.

2) Range of the integers = c-a+2 insufic.

{a,b,c,d,e}={1,2,3,4,5}: range=5-1=4…c-a+2=3-1+2=4; yes.
{a,b,c,d,e}={1,2,6,7,8}: range=8-1=7…c-a+2=6-1+2=7; no.

(1 & 2) sufic.

c-a+2=range, c-a+2=e-a, c+2=e, c+1=d, c-1=b, c-2=a;
{a,a+1,a+2,a+3,a+4}: a+2-a+2=a+4-a…4=4=consecutive.

Answer (C)

Analyzing the question:
Always check if all consecutive numbers is possible. If we cannot have consecutive numbers the statement is automatically sufficient. Since they are distinct integers let us assume a < b < c < d < e.

Statement 1:
We can have 5 consecutive integers or 1, 3, 4, 5, 7. Insufficient. However this does imply a + b + d + e = 4c.

Statement 2:
\(e\) is the biggest integer of the set, then \(e - a = c - a + 2\) gives \(e = c + 2\). We are allowed to have consecutive numbers with \(a = c - 2\). We could also let \(c - a = 3\) and fill in the numbers, therefore this is insufficient.

Combined:
\(e = c + 2\), this was assuming \(e\) was the greatest integer of the set. We only have one space for \(d\), which is between \(e\) and \(c\). Therefore \(d = c + 1\). From statement 1 we had \(a + b + d + e = 4c\), removing \(d\) and \(e\), we have \(a + b = 2c - 3\). The only way to make both less than \(c\) is to have \(b = c - 1\) and \(a = c - 2\). Therefore all 5 integers must be consecutive, sufficient.

Ans: C

Since the question has been edited, the solution would be..

Are the distinct Integers of Set {a, b, c, d, e} consecutive?

1) The average of a, b, c, d, e is c
So, 5c=a+b+c+d+e


2) c=e-2
Nothing much

Combined..
If a, b, c, d,e are in order....d=c+1, e=c+2...5c=a+b+c+c+1+c+2........2c=a+b+3.....c+c-3=a+b=(c-2)+(c-1)...so consecutive
If a, b, c, d, e are not in order...Not necessary

It should be E as the way it is given