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I did read the explanations in the book, but I still do not [#permalink]
02 Jan 2007, 16:02
I did read the explanations in the book, but I still do not get it!!!!!
If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
If a two-digit positive integer has its digits reversed, the resulting differs from the original by 27. By how much do the two digits differ?
Right triangle PQR is be be constructed in the xy-plane so that the right angle is a P and PR is parallel to the x-axis. The x-and y-coordinates of P, Q, and R are to be integers that satisfy the inequalities -4<x<5 and 6<y<16. How many different triangles with these properties could be constructed?
answer is 2 (a)
4p has 2 and 4 as its only positive even factors.
answer is 3 (a)
check for example 3 and 6 (63-36=27), or any other combination...
answer is 9900 (c)
i guess you meant -4<=x<=5 and 6<=y<=16 (otherwise none of the answers is correct)...
choosing P's coordinates, there are no constraints so we can choose x freely (10 options) and y freely (11 options)... so we can choose P in 110 options.
now R must have the same y value as P (since it PR is parallel to x-axis).. so we can choose any y except the y value of P (10 options).
Q must be with with the same x as P (to keep the right angle). so it has 9 options for y value.
total is 110*10*9 = 9900
Re: Questions from OG11 [#permalink]
03 Jan 2007, 11:54
207) Even factors of 4*p: 2, 2*p, 4, 4*p => C.
208) Let n = ab = 10a + b be the original number. Then (10a + b) - (10b + a) = 9*(a - b) = 27 => a - b = 3 => A.
248) There are (10 + 9 + 8 + ... + 1) * (16 - 6) different triangles with R on (5,6), P to the left of R, and Q above P. There are (10 + 9 + 8 + ... + 1) * (16 - 7) different triangles with R on (5,7) (same reqs as before for P and Q). Iterating: Total number of triangles = (10 * 11 / 2) * (9 * 10 / 2) * 4 = 9900.
Re: Questions from OG11
03 Jan 2007, 11:54