x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT a. x = w b. x > w c. x/y is an integer d. w/z is an integer e. x/z is an integer oa after some discussions

can someone explain me how can y and z be related as they are a set of numbers??? or shuld it have been x and w??? if its w and x then 1 2 3 4 5 6 7 =27 1 2 3 4 5 6 7 8 9 10 =>54 This can be one such set. Someone pls help

Because y=2z and z is an integer, we know that y is even. Whenever you see 'even number of consecutive integers' on the GMAT, one of the first things you should think about is that the average of this set cannot be an integer. This is true because the average of a set of consecutive integers is the same as the median. When the set has an odd number of elements, the median is the middle integer. When a set has an even number of elements, the median is the average of the two middle integers. Since these two integers are consecutive, the average will be a decimal. Since this question asks which of the following CANNOT be true, look for the expression of the average of the set. That's C (sum of the set divided by the number of elements in the set).

sivaelectric wrote:IMO A Be careful. Perhaps you thought that x and y start with the same integer, but it's possible in many scenarios to have x=w.

I am baffled as to how someone could choose (A). All we need to do to rule out answer 'A' is find a single scenario in which X=W. Say Z=1 and Y=2. This satisfies the conditions that Y=2Z AND that Y,Z are positive integers. Say W=11. Can X=11 as the sum of 2 consecutive integers? Yes, if the integers are 5 and 6. Thus, X can equal W, and choice (A) cannot be correct.

Lets say z=1, and thus w is sum of 1 consecutive integer and thus w is any +ve integer. also then y=2, and thus x is sum of 2 consecutive integers which is always odd (odd+even=odd) thus x/y which is (odd no.)/2 in this case is not an integer. Thus C

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT a. x = w b. x > w c. x/y is an integer d. w/z is an integer e. x/z is an integer I am confused between C,D and E as with the various examples, the answer for this question varies....