The number x and y are not integers. The value of x is closest to what integer?

1. 4 is the integer that is closest to x+y
2. 1 is the integer that is closest to x-y

Can someone recommend the best approach to solve this problem? I set up the following approach - am I going in the right direction?

1. 3.5 < x+y < 4.49

Not sufficient

2. .5 < x-y < 1.49

Not sufficient.


I added the inequalities to get the following:

4 < 2x < 6

Therefore, 2 < x < 3

Hence, x is either closest to 2 or 3. Insufficient. Answer is E.

Is this correct?

The correct answer is E.

Thanks. Any explanations of how you actually got that answer?

You're doing well. Your process is exactly right but the inequalities you set up are slightly problematic. (In fact, you made a mistake in the setup but then also made a calculation error that saved you from picking the wrong answer.)

For (1) it should be 3.5 < x+y < 4.5
3.5 should be included in the possibilities (hence less than or equal to) b/c 3.5 rounds up to 4. 4.5 is the upper limit and is NOT included (hence simply less than). Same thinking for 2.

You end up with:
3.5 < x+y < 4.5
.5 < x-y < 1.5

and this correctly lets you get to:
4 < 2x < 6 - notice that you calculated 6 down below but 6 is not what you get when you add 4.49 and 1.49 (and if you had added 4.49 and 1.49 to get 5.98, you might have changed your answer to the problem and gotten it wrong).