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# I did read the explanations in the book, but I still do not

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Manager
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I did read the explanations in the book, but I still do not [#permalink]

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02 Jan 2007, 17:02
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?

a)110
b)1100
c)9900
d)10,000
e)12,100
Senior Manager
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02 Jan 2007, 18:18
207)
4p has 2 and 4 as its only positive even factors.

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

248)

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
Manager
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02 Jan 2007, 20:38
- For #207, any prime greater than 2 has no even divisors, since 2 is the only even prime integer.

Since we're dealing with 4*p and we know p has no even divisors, just focus on the four. 4 obviously has two even divisors, 2 and 4.

- For #228, the question stem tells you that ab - ba = 27. You can reconstruct this as:

(10a + b) - (10b + a) = 27; since ab is just 10a + b and ba is 10b+ a

combining like terms, we get:
9a - 9b = 27

9 (a - b) = 27
a - b = 3
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02 Jan 2007, 21:53

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

_________________

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

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03 Jan 2007, 03:14
re 207...
you caught me off guard here....

you are correct - answer is 4.

cheers....
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03 Jan 2007, 12:54
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.
Re: Questions from OG11   [#permalink] 03 Jan 2007, 12:54
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