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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.

hogann wrote:

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?

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. _________________

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.

(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. _________________

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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. _________________

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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 [E]

(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.

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.

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. _________________

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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 _________________

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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.

(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.