let area of first triangle be A and B. A=2B --5 let height of A be P and B be H for first triangle A= P.S/2 --1 tan x = P/S --2 for second triangle B=H.s/2 --3 tan x= H/s --4 equating 2 = 4 -> P/S=H/s -> P/H=S/s equating 5 -> A=2B -> replacing 1 and 3 -> P.S/2=2.H.s/2 -> P/H=2.s/S -> S/s=2.s/S -> S^...

sorry but cybermusing seems easier. try breaking any given number into prime numbers. they tend to show a much more clearer relation

5^21 * 4^11 = 2 * 10^n
=> 5^21 * (2^2)^11 = 2 * 10^n
=> 5^21 * 2^22 = 2 * 10^n
=> 2 * 10^21 = 2 * 10^n
equating n on both sides
we have n=21

What is the smallest positive integer n for which 324 is a factor of 6^n? A. 2 B. 3 C. 4 D. 5 E. 6 6^1 = (2^1)*(3^1) 6^n = (2^n)*(3^n) 324 = (2^2)*(3^4) So if 324 is a factor it should divide 6^n completely (without any remainder) 6^n / [(2^2)*(3^4)] = An Interger Thus n's minimum value is 4 f20012...

oh .. u mean the condition to be satissifed is if b is (x,y) then distance between them

x^2 +y^2=100 must be satisfied

Unfortunately, my only explanation is drawing from what I read during GMAT prep a few months ago. Apparently the Pythagorean triangle that appears most frequently on the exam are those with sides of lengths 3:4:5 or multiples of such. I spent probably 15+ minutes trying to figure out how to even ap...

Since a Fixed cost of 20$ dollars plus twice the cost af a x cycle in first week will always be involved the product of y cycle in second week and cost of each should always be greater.

also y>x always.
answer is E.

please tell what i left out if am wrong

Since area must be 100 possible porduct are = 10 * 10 only so a line must of length 10 since it is to be a square, We get four square's with vertices on origin and square in each quadrant only . The diagonal length is = 2* (10)^(1/2) This is not an integer. so diagonals wont be on axis with integral...