AbdurRakib wrote:
If m and p are positive integers and \(m^2 + p^2 < 100\), what is the greatest possible value of mp ?
A. 36
B. 42
C. 48
D. 49
E. 51
Let's
test some pairs of values.
Since m and p are POSITIVE INTEGERS, we won't have a ton of options
Try m = 9 and p = 4 (aside: if m = 9, then 4 is the biggest possible value of p)
In this case, mp = (9)(4) = 36
Try m = 8 and p = 5 (aside: if m = 8, then 5 is the biggest possible value of p)
In this case, mp = (8)(5) = 40
Try m = 7 and p = 7 (aside: if m = 7, then 7 is the biggest possible value of p)
In this case, mp = (7)(7) = 49
Try m = 6 and p = 7 (aside: if m = 6, then 7 is the biggest possible value of p)
In this case, mp = (6)(7) = 42
Try m = 5 and p = 8 At this point, we can see that, if we continue, we'll be duplicating the work we did earlier.
That is, this case (m = 5 and p = 8) is the SAME as the 2nd case we examined.
If we continue, the next case we test will be m = 4 and p = 9. which is the SAME as the 1st case we examined, etc.
Since we've now tested all possible (and relevant) cases, we can see that the maximum value of mp is 49
Answer:
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more