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# 7 tricky PS and DS!!!

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Intern
Joined: 21 Jan 2007
Posts: 23

Kudos [?]: 1 [0], given: 0

7 tricky PS and DS!!! [#permalink]

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18 Feb 2007, 14:44
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Hi to all!!! I have problems in understanding the answers to also these questions (which i put in bold)
Could you please help me out in explaining them to me??
I managed to finish these sets, these are the last questions about them..
thanks alot!!

Riccardo

Q8:
An equilateral triangle that has an area of 9√3 is inscribed in a circle. What is the area
of the circle?
A. 6pi
B. 9pi
C. 12pi
D. 9pi √3
E. 18pi √3

Q16:
In the sequence of nonzero numbers t1, t2, t3, â€¦, tn, â€¦, tn+1 = tn / 2 for all positive integers
n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

Answer is C, but canâ€™t u find it out also with each alone? (I chose D)

Q16:
If n is an integer greater than 6, which of the following must be divisible by 3?
A. n*(n+1)*(n-4)
B. n*(n+2)*(n-1)
C. n*(n+3)*(n-5)
D. n*(n+4)*(n-2)
E. n*(n+5)*(n-6)

SET 29

Q9:
A total of 100 customers purchased books at a certain bookstore last week. If these
customers purchased a total of 200 books, how many of the customers purchased only 1
book each?
(1) None of the customers purchased more than 3 books.
(2) 20 of the customers purchased only 2 books each.

Answer is C.. but actually shouldnâ€™t it be E?

Q16:
On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per
hour for the remaining 3 hours. What was her average speed, in miles per hour, for the
entire trip?
(1) 2x + 3y = 280
(2) y = x + 10

SET 31

Q18:
2x + y = 12
|y| less or equal than 12

6
For how many ordered pairs (x , y) that are solutions of the system above are x
and y both
integers?
A. 7
B. 10
C. 12
D. 13 E. 14

Q26:
What is the greatest common factor of the positive integers j and k?
(1) k = j + 1
(2) jk is divisible by 5.

Answer is D, why??

Kudos [?]: 1 [0], given: 0

Intern
Joined: 04 Apr 2006
Posts: 35

Kudos [?]: 6 [0], given: 0

Re: 7 tricky PS and DS!!! [#permalink]

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18 Feb 2007, 15:29
eribold wrote:
Q8:
An equilateral triangle that has an area of 9√3 is inscribed in a circle. What is the area
of the circle?
A. 6pi
B. 9pi
C. 12pi
D. 9pi √3
E. 18pi √3

Area of an triangle is ah/2
Equilateral triangle has height h=√(aÂ²-(a/2)Â²) = a√3/2

Area is aÂ²√3/4
If aÂ²√3/4=9√3
then aÂ²/4=9, a/2=3
h=3√3

If equilateral triangle is inscribed in a circle, that circle has radius
r = 2/3*h

r = 2/3*3√3 = 2√3

Area of circle is rÂ²pi = 2√3pi = 12pi

Kudos [?]: 6 [0], given: 0

Intern
Joined: 04 Apr 2006
Posts: 35

Kudos [?]: 6 [0], given: 0

Re: 7 tricky PS and DS!!! [#permalink]

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18 Feb 2007, 15:40
eribold wrote:
Q18:
2x + y = 12
|y| less or equal than 12

6
For how many ordered pairs (x , y) that are solutions of the system above are x
and y both
integers?
A. 7
B. 10
C. 12
D. 13 E. 14

Y have to be even in order to have the result when x is integer. You have 6 positive even numbers <12> -12, which gives us 13

Kudos [?]: 6 [0], given: 0

Intern
Joined: 04 Apr 2006
Posts: 35

Kudos [?]: 6 [0], given: 0

Re: 7 tricky PS and DS!!! [#permalink]

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18 Feb 2007, 16:23
eribold wrote:
Q16:
If n is an integer greater than 6, which of the following must be divisible by 3?
A. n*(n+1)*(n-4)
B. n*(n+2)*(n-1)
C. n*(n+3)*(n-5)
D. n*(n+4)*(n-2)
E. n*(n+5)*(n-6)

One of the multiples must be divisible by 3

Picking numbers should be fast enough, bc the pattern repeats itself after 3 numbers

A
9 10 5
10 11 6
11 12 7
12 13 8
13 14 9

B
10 12 9
11 13 10

C
9 12 4
10 13 5

D
9 13 7
10 14 8

E
9 14 3
10 15 4
11 16 5

Kudos [?]: 6 [0], given: 0

Re: 7 tricky PS and DS!!!   [#permalink] 18 Feb 2007, 16:23
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# 7 tricky PS and DS!!!

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