Problem Solving

If ar = pc = ln = bq = m^2 and a, b, c, l, m, n, p, q and r are all distinct, then which of the following could be the value of m ?

a) 4

b) 5

c) 6

d) 9

e) 11

Please help.

When a question is about multiplying you can normally look to the concept of factors to see what is going on.

The question is saying that m^2 must have 8 distinct factors - the best way I see is to look at the answers and plug them in. NOrmally when you use this method you start with c

6^2= 36 which has 8 factors (1,36; 2,18; 3, 12; 4,9) - therefore the answer is C.

I did this sum a little intuitively.

If you use the answer choices and check m^2, you will realize that 6 is the only number with which you can have so many distinct factors.

For instance by looking at 11^2 and 5^2, you can be very sure that there would not be so many distinct pairs of numbers that would lead to m^2.

6^2 definitely satisfies that requirement