Test code 52, section 4, question 10

[irfan_m1973]

If a < x < b and c < y < d, is x < y?

(1) a < c
(2) b < c

OA is B.

Plz explain

[Testluv]

If a < x < b and c < y < d, is x < y?

(1) a < c
(2) b < c

OA is B.

Plz explain

(1) a < c

From the stem we know that a is also smaller than x, which, in turn, is smaller than b. But knowing that a is smaller than c and that a is also smaller than x < b does not allow us to relate c's size to x.

For example, a can be 1 while c can be 10. We know x is bigger than a, so x can be ANY number bigger than 1 (of course, x can be ANY number bigger than 1 so long as x is smaller than b; but we don't have to worry about b here). And we know y is bigger than c, so y can be ANY number bigger than 10.

So, x can be 20 while y can be 100, in which case the answer to the question (is x < y?) is "yes". But, it can also be the other way around: x can be 100, while y can be 20; in this case, the answer to the question is "no". Because the first statement yields both a "yes" and "no" answer, it is not sufficient.

(2) b < c

This allows us to set-up the following inequality:

a < x < b < c < y < d

Therefore, x < y.

The second statement is sufficient by itself but the first one is not; choose B.