<p>I'm not sure if a thread like this already exists, but people should post the most difficult SAT Math problems. Either type the problem into the thread (a pain i know), post a link, or give a page reference to the blue book or another book. </p>
<p>Ill start.
If a and b are positive intergers and (a^1/2 * b^1/3)^6 = 432 what is the value of ab?
A- 6
B-12
C-18
D-24
E-36</p>
<p>B (10 character)
EDIT: Simplify 432^(1/6)
to rad(3)<em>2^(2/3)
or rad(3)</em>4^(1/3)
and compare</p>
<p>Simplified:
a^3 * b^2=432</p>
<p>Since you said they are integers, then a and b must be factors of 432. Factor 432 to get 2,2,2,2,3,3,3.</p>
<p>Since there are three 3's, then a=3 (a^3 means there are three a's as facotrs of 432).</p>
<p>You are left with finding b^2 and have 2x2x2x2 (16) left to account for. 16=b^2. b=4</p>
<p>ab=3(4)=12</p>
<p>Answer: B</p>