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

Question

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

chetan2u · Answer

How can the RANGE be less than DIFFERENCE between any two integers in the set

After all RANGE is the difference between the largest and smallest integer of the set. How can it be less ??

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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

GMATinsight · Answer

Did some fumble in making statement. Have edited it.. Thank you...

Archit3110 · Answer

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..

exc4libur · Answer

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)

TestPrepUnlimited · Answer

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

chetan2u · Answer

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

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

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