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neokeynesian
10-19-2004, 04:29 AM
1) If n ¹ 0, which of the following must be greater than n?

I)2n II)n3 II)4-n

a)None b)I only c)II 0nly d)I & II e)I & II

2) The distance from point X to point Y is 20 miles, & the distance from point X to point Z is 12 miles. If d is the distances, in miles, between points Y & Z, then the range of possible values for d is indicated by

a)8≤d≤20 b)8≤d≤32 c)12≤d≤20

d)12≤d≤32 e)20≤d≤32

3) C is a circle, L is a line, & P is a point on line L. If C, L & P are in the same plane & P is inside C, how many points do C & L have in common?

a)0 b)1 c)2 d)3 e)4

4) If one number exceeds another number by 13 & the larger number is 3/2 times the smaller number, then the smaller number is

a)13 b)26 c)31 d)39 e)65

5) A board of length L feet is cut into two pieces such that the length of one piece is 1 foot more than twice the length of the other piece. Which of the following is the length, in feet, of the longer piece?

a) (L+2)/2 b) (2L+1)/2 c) (L−1)/3 d) (2L+3)/3
e) (2L+1)/3

6) How many positive integers are both multiples of 4 & divisors of 64?

a)2 b)3 c)4 d)5 e)6

7) A watch gains 7 minutes & 6 seconds every 6 days. If the rate of gain is constant, how much does the watch gain in one day?

a)1 min 1 sec b)1 min 6 sec c)1 min 11 sec

d)1 min 16 sec e)1 min 21 sec

Answere: 1)a 2)b 3)c 4)b 5)e 6)d 7)c

neokeynesian
10-19-2004, 04:32 AM
1) If n ¹ 0, which of the following must be greater than n?

I)2n II)n^3 )4-n

bbm833
10-19-2004, 08:07 AM
1) I) n > 2n ,where n<0

II) n > n^3 , where n<-1 or 0<n<1

III) n > 4-n, where n > 0

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2) longest distance : X is between Y and Z (for example: Y X Z)
dmax = YX+ XZ = 20+12 = 32
shortest distance: Z is in between X and Y (for example: X Z Y )
dmin = XY - XZ = 20 - 12 = 8

8<= YZ <=32

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3) Line cuts the circle ( like Æ )

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4) x = y +13
&
x = 3y/2

-->3y/2 = y+13
--> y=26

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5) x : longer piece, y: shorter piece
x+y=L
&
x=2y+1 --> y=(x-1)/2

--> x + ( (x-1)/2 ) = L
(3x-1)/2 = L
x=(2L+1)/3

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6)64 = 2^6
divisors of 2 ^6 are 2^6 , 2^5, 2^4, 2^3 , 2^2, 2^1, 2^0

multiples of 4 and divisors of 64 are 2^6 , 2^5, 2^4, 2^3 , 2^2

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7) If a watch gains 7 minutes 6 seconds in 6 days, it will gain

(7minutes+6second)/6 in one day

= 7/6 minute +6/6 seconds
= 1 minute + 10 seconds + 1 seconds
= 1 minute +11 seconds

ps. 7/6 minutes = 1 minute + 60/6 seconds
= 1 minute + 10 seconds

Hope helps

Econ
10-19-2004, 08:16 AM
(1) 2n>n ? , not always, try n=-1; n^3>n ? , not always try n=-2, 4-n>n ? , not always, try n=3. Thus (a)

(2) __________________________________________________ _______

Z2-----12-------X------12-------Z1 ---8-------Y

Take a line segment. If Z is like Z1 then 8 is the min distance and if Z is like Z2 the distance from Z2 to Y is 32. Thus (b).
Comment: The triangle inequality is very important: a-b < c < a+b and it also holds for line segments with the < becoming =<.

(3) Only 2 points can be the answer. 0 point then P outside C, 1 points then P on the circumference of C. 3 points and 4 points are out of the question because L is a line.

(4) Let L be the larger number and S the smaller, then setup the system:
L=13+S and L=(3/2)S -------------> S=26 and L=39, thus (b)

(5) Let x be the big and the y be the small, then:
x+y=L
x=2y+1 ---------------> y=(L-1)/3 and x=(2L+1)/3

(6) (d) {64, 32, 16, 4 satisfy the conditions}

(7) 7 min and 6 sec = 426 seconds -----------------> 6 days
71 seconds -----------------> 1 day
Thus 1 min and 11 seconds.

bbm833
10-19-2004, 12:40 PM
1) III) n > 4-n, where n> 0

should be :

n > 4-n, where n>2

Sorry for the mistake