M03 Q33

Question

Are integers  x ,  y , and  z  consecutive?

1.  y  equals the arithmetic mean of  x  and  z 
2.  x = -z

E 
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I don't understand the answer...
shouldn't 1. be enough?

if y = x+z / 2
if they were consecutive, y should be (x+1).
z would then be x+2. 
if x + (x+2) / 2, you do get y = (X+1)

so why isn't 1. enough?

scthakur · Answer

Take the example of y = x+5 and z = x+10. In this case also, y = (x+z)/2, but x,y and z are not consecutive.

hogann · Answer

Is this the correct definition of consecutive integers?

To me consecutive integers could be 1,2,3 but also 2,4,6 or 4,8,12
Is this called something else? Consecutive series?

dzyubam · Answer

2, 4, 6 would be consecutive even integers; 4, 8, 12 would be consecutive multiples of 4. Consecutive integers are 1, 2, 3, 4 and so on unless otherwise stated.

seluka · Answer

Nice one. Thanks for clarifying the term “consecutive XXXX”

phillypointgod21 · Answer

x, y and z are integers. Are they consecutive?

1. y equals to the arithmetic mean of x and z
2. x = -z

So is the correct answer E?

Taking statement 1, y = (x+z)/2 Not sufficient.

Taking statement 2, if x is 1, then the x, y, z could be -1, 0, 1. However, they could also be -2, 0, 2. Not sufficient.

Combining the statements and substituting, y = (-z+z)/2, which simplifies to y = 0/2 or 0. If y is 0 and x = -z, we still do not have enough information to answer the question.

dzyubam · Answer

You're absolutely right. The OA is E.

gmatbull · Answer

(1) y = average of x and z:
x(1), y(2), z(3) --> y is avrg of x & z and x,y,z are consecutives
x(2), y(2), z(2) --> y is avrg of x & z but x,y,z are not consecutives
INSUFFICIENT

(1) x= -z says nothing about y... 
INSUFFICIENT

(1) and (2): 
x(-1), y(0), z(1)... y is avrg of x and z and x,y,z are consecutives
it might be tempting to pick C without trying another set of nos.
x(-2), y(0), z(2)... y is avrg of x and z but x,y,z are not consecutives
INSUFFICIENT

So, E.

ezhilkumarank · Answer

Statement 1: y = (x+z)/2. y is the middle term but we do not know whether the difference between x, y and/or y,z is 1.
Insufficient.

Statement 2: x = -z. This tells us that y = 0, however we do not know whether about the difference between x,y and y,z.

Insufficient.

Combining both: we know that y is the middle term and the mean of x and z but still we cannot determine that the difference between x,y and y,z is 1 (condition for x, y, z to be consecutive.)

Answer E.

karan2483 · Answer

Agree with E for sure.

State 1: y = A.M of X & Y

We get inconclusive answers as if X=3 , Y=4, Z=5
Then Y=(3+5)/2=4 = A.M is true ans consecutive no. but say if X=2, Y=5, Z=8
then also Y=A.M =5 but the number are no consecutive so insufiecient

Answers could be B, C or e

Stat II: X=-Z gives us nothing so insuffiecient .

Taking them together:

If z=2 then X=-2 then y=0 not consecutive 
 Watch out here as all values except 1 the no will come out to be not consecutive. 
 Except 1 If z=1 then x=-1 Y=0 consecutive no. so we have conflicting answers so correct Answer is

Hope this helps

MateoLibre · Answer

Thanks. To me, you did the best job of explaining why the answer isn't "A". Just because all consecutive integers will work for X+Z/2=Y doesn't mean that ONLY consecutive integers will do that.

catfreak · Answer

Its E. 
St1: Every AP has the same property b = (a+c)/2 . So insufficient.
St2: There are infinite series with a = -c eg -5,0,5 ; -2,0,2 So insufficient.

Both statements together doesn't narrow it down. Hence E.

saeedt · Answer

Great question. Made me make a mistake. I simply took Z=1 and X=-1 according to stmt 2. Then according to stmt 1, y must be 0 here. So the three numbers comprise a consecutive integer -1,0,1. But haha what about -2, 0 , 2 which is supported by the statements? It's no a consecutive integer series. So E

arzad · Answer

I picked E

Stm.1- y=(x+z)/2
 2y=x+z
 3y=x+y+z
 y=(x+y+z)/3 ...this statement only means that the mean=median... consecutive and nonconsecutive integers satisfy this condition...therefore not Sufficient.

Stm.2- No data about y...therefore insufficient.

Stm1 and stm2 together (x,y,z)=(-3,0,3) or (-1,0,1) therefore not sufficient.

Bunuel · Answer

REVISED VERSION OF THIS QUESTION IS BELOW:

Are integers  x ,  y , and  z  consecutive?

(1) The average (arithmetic mean) of  x  and  z  equals to  y  -->  y=\frac{x+z}{2} : if  x=y=z=0  then the answer is NO but if  x=-1 ,  y=0  and  z=1  then the answer is YES. Not sufficient.

(2)  x= -z . Not sufficient since no info about  y .

(1)+(2) Examples discussed for statement (1) are still valid, so we can have a NO ( x=y=z=0 ) as well as an YES ( x=-1 ,  y=0  and  z=1 ) answers. Not sufficient.

Answer: E.

thevenus · Answer

Are integers  x ,  y , and  z  consecutive?

1.  y  equals the arithmetic mean of  x  and  z 
2.  x = -z

Nice workout !

(i) take 5,6,7
6 is the AM of 5&7  yes Consecutive 
take 10,12,14
12 is the AM of 10&14  Not consecutive

insufficient

(ii)take -1,0,1 as x,y & z-  possible  because x=(-z)
but if we take z=-5, x will be 5 , then it will not be consecutive- not possible

insufficient

Answer-E

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