consecutive numbers

[AJ2009]

Are the integers q , r , and s consecutive?

(1) The average (arithmetic mean) of q , r , and s is r .

(2) r – q = s – r

[anniev2]

Is the correct answer, C?

[Bidisha_800]

(E)

from (1), we get 2r=p+q
numbers in arithmetic progression will satisfy this ...3, 5, 7 or 3, 14, 25

from (2) again the same thing 2r=p+q

numebers in AP will satisfy.

[scoobydooby]

E

stmnt 1: r=(q+r+s)/3
or q+s=2r
or r=(q+s)/2
=> r is at the midpoint of q and s
=> q,r,s are evenly spaced, need not be consecutive. not sufficient


stmnt 2: r-q=s-r
or r is at the midpoint of q and s (same info as stment 1)

together, no additonal info, not sufficient

[manoj0609]

Is the correct answer, C?

IMO : E

Simple example 1,5,9
here avg =5 and median is also 5 --st 1
diff is 4 betwn each --st 2
but still not consecutive

[cramya]

It would be E as both statements provide the same info and each statement by itself is INSUFF

Stmt I

r+s+q/3 = r => 2r = q+s => r = q+s/2

1 3 5 NO

1 2 3 YES

insuff

Stmt II

2r = q+s => r = q+s/2

1 3 5 NO

1 2 3 YES

insuff


Together:

1 3 5 NO

1 2 3 YES

insuff

Choose E