W is as much younger than X as he is older than Y. If the sum of the ages of X…

When a problem says one person is "as much younger than A as he/she is older than B", the middle person's age sits exactly halfway between A and B. Algebraically, if the middle person is P, this means (A minus P) equals (P minus B), which rearranges to A plus B equals 2P.

Applying this to the given data:

1. The statement "W is as much younger than X as he is older than Y" gives the equation X minus W equals W minus Y.

2. Rearranging this equation: X plus Y equals 2W.

3. Substituting the given sum X plus Y equals 60: 2W equals 60, so W equals 30.

4. The quantity asked for is X minus W, which by the same equation equals W minus Y, that is, 30 minus Y.

5. Only the sum X plus Y equals 60 is known; the individual ages of X and Y are not fixed, so Y (and therefore X minus W) cannot be pinned to a single value.

For example, X equals 35 and Y equals 25 satisfies X plus Y equals 60 and gives X minus W equals 5; but X equals 33 and Y equals 27 also satisfies X plus Y equals 60 and gives X minus W equals 3. Two age-pairs consistent with all the given information produce two different differences, confirming the value cannot be determined.

Hence the difference between X and W's age cannot be determined from the data given -- the correct choice is "data insufficient".