Correct Answer: C
Explanation:
Arithmetic Statistics
The range of a set of integers is equal to the difference between the largest integer and the
smallest integer. The range of the set of integers 3, 4, 5, and 6 is 3, which is derived from 6-3.
- (1) Although it is known that y > 3x, the value
of* is unknown. If, for example,* = 1, then the
value of y would be greater than 3. However, if
* = 2, then the value of y would be greater than 6,
and, since 6 would no longer be the largest
integer, the range would be affected. Because the
actual values of * and y are unknown, the value of
the range is also unknown; NOT sufficient.
- (2) If * > 3 and y > x, then * could be 4 and y
could be 5. Then the range of the 6 integers would
still be 6 - 3 or 3. However, if * were 4 and y were
15, then the range of the 6 integers would be
15-3, or 12. There is no means to establish the
values of* and y, beyond the fact that they both
are greater than 3; NOT sufficient.
Taking (1) and (2) together, it is known that
* > 3 and that y > 3*. Since the smallest integer
that x could be is thus 4, then y >3(4) or y >12.
Therefore, the integer y must be 13 or larger.
When y is equal to 13, the range of the 6 integers
is 13- 3 = 10, which is larger than 9. As y increases
in value, the value of the range will also increase.
The correct answer is C;
both statements together are sufficient.