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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!!!!!

207)
If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?

a)2
b)3
c)4
d)6
e)8

228)
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?

a)3
b)4
c)5
d)6
e)7

248)
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?

207)
answer is 2 (a)
4p has 2 and 4 as its only positive even factors.

228)
answer is 3 (a)
check for example 3 and 6 (63-36=27), or any other combination...

248)
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

Previous posts didn't address Q#207 correctly so I'm addressing only that.

Question :
If n=4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?

n = 2 ^2 * P

Therefore total number of factors = (2+1) * (1+2) = 6
Now p is a prime factor (other than 2) and not even and 1 is not even.
So total number of evem factors/divisiors = (6-2)=4

Answer: C _________________

"Education is what remains when one has forgotten everything he learned in school."

Re: Questions from OG11 [#permalink]
03 Jan 2007, 11:54

LetÂ´s see.

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.

gmatclubot

Re: Questions from OG11
[#permalink]
03 Jan 2007, 11:54

Wow...I'm still reeling from my HBS admit . Thank you once again to everyone who has helped me through this process. Every year, USNews releases their rankings of...