Data Sufficiency

X is a multiple of 5.what is the value of X?
(1) 1237 < X < 1242.5
(2) 3711 < 3X < 3727.5

arjunshn wrote:X is a multiple of 5.what is the value of X?
(1) 1237 < X < 1242.5
(2) 3711 < 3X < 3727.5

A good test of our ability to avoid complex calculations!

(1) the range given only contains one multiple of 5 (1240), so (1) is certainly sufficient: eliminate (B), (C) and (E).

(2) we could divide all 3 parts by 3, but we'd really rather avoid the math. There are three ways we can deal with (2) much more efficiently.

First, we could see that there are 3 multiples of 5 inside the range (3715, 3720, 3725). We can then reason out that when we divide by 3 we'll be left with exactly 1 multiple of 5.

Second, we could realize that since 3600 is divisible by 3, we can subtract 3600 from the first and last terms to create an analogous range. Working with:

111 < 3x < 127.5

will certainly reduce the hardship of dividing by 3. Sure enough, when we divide all 3 portions of the inequality by 3 we get:

37 < x < 42.5

giving us only 1 possible value of x.

Third, we could recognize that the values in (2) are simply 3 times the values in (1). Since (2) provides identical information to (1), it must also be sufficient.

Choose (D)!

Both options A and B are the same. When you multiply A with 3 throughout, it becomes B.

There is only one value of X(1240) which is divisible by 5 and also lies between the given ranges.
This holds true for option B as well.

So answer must be D.

THE ANSWER SHOULD BE E.
FROM BOTH THE STATEMENT WE DON'T KNOW WHETHER X IS AN INTEGER OR NOT.
SO X CAN BE 1240 OR X CAN BE 1239.5 (BOTH OF THESE ARE MULTIPLE OF 5.