joannabanana wrote:If -2<a<11 and 3<b<12, then which of the following is NOT true?
(A) 1<a+b<23
(B) -14<a-b<8
(C) -7<b-a<14
(D) 1<b+a<23
(E) -24<ab<132
I know what the answer is, but I don't quite get how to go about solving this.
Any tips on the quickest way to solve it?
The way I solved this problem is to jot down the two positive equalities (given) and their corresponding negative inequalities and then simply add them up..
-2 < a < 11 (given) ---------------------------------------------> 1
-11< -a < 2 (corresponding -ve inequality) -----------------> 2
3 < b < 12 (given) -----------------------------------------------> 3
-12 < -b < -3 (corresponding -ve inequality) ---------------> 4
So now we have 4 inequalities to deal with..Just add them as per the options..
Options A & D are actually the same and the easiest. Simply add 1 & 3 above and you get
1< a+b < 23 . Hence this is correct.
Option B. Here you need a-b, hence add 1 and 4. You will get
-14 < a-b < 8. Matches and hence correct.
Option C. Here you need b-a, hence add 2 and 3. You will get
-8 < b-a < 14. This does not match and is also not a subset of the range given in option (-7 to 14). Hence this is the incorrect option and thus the answer for this question.
Option E. Here you need ab, hence multiply 1 & 3. You will get
-6< ab < 132. Since this is a subset of the range (-24 to 132), this option is also correct.
This took some time to type, but it didn't take much time to solve..
Not sure if this is the quickest approach but works for me!! How did you approach this question?
