Difference between revisions of "1995 AHSME Problems"

A list of five positive integers has mean 12 and range 18. The mode and median are both 8. How many different values are possible for the second largest element of the list?

$\mathrm{(A) \ 4 } \qquad \mathrm{(B) \ 6 } \qquad \mathrm{(C) \ 8 } \qquad \mathrm{(D) \ 10 } \qquad \mathrm{(E) \ 12 }$

Solution

Problem 26

In the figure, $\overline{AB}$ and $\overline{CD}$ are diameters of the circle with center $O$ , $\overline{AB} \perp \overline{CD}$ , and chord $\overline{DF}$ intersects $\overline{AB}$ at $E$ . If $DE = 6$ and $EF = 2$ , then the area of the circle is

A. $23 \pi$ B. $\frac {47}{2} \pi$ C. $24 \pi$ D. $\frac {49}{2} \pi$ E. $25 \pi$

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

Solution

Problem 27

Consider the triangular array of numbers with 0,1,2,3,... along the sides and interior numbers obtained by adding the two adjacent numbers in the previous row. Rows 1 through 6 are shown.

An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.

A table really needs to go there... Link: http://www.artofproblemsolving.com/Forum/viewtopic.php?search_id=1526011879&t=62471

Let $f(n)$ denote the sum of the numbers in row $n$ . What is the remainder when $f(100)$ is divided by 100?

$\mathrm{(A) \ 12 } \qquad \mathrm{(B) \ 30 } \qquad \mathrm{(C) \ 50 } \qquad \mathrm{(D) \ 62 } \qquad \mathrm{(E) \ 74 }$

Solution

Problem 28

Two parallel chords in a circle have lengths 10 and 14, and the distance between them is 6. The chord parallel to these chords and midway between them is of length $\sqrt {a}$ where $a$ is

$\mathrm{(A) \ 144 } \qquad \mathrm{(B) \ 156 } \qquad \mathrm{(C) \ 168 } \qquad \mathrm{(D) \ 176 } \qquad \mathrm{(E) \ 184 }$

Solution

Problem 29

For how many three-element sets of positive integers $\{a,b,c\}$ is it true that $a \times b \times c = 2310$ ?

$\mathrm{(A) \ 32 } \qquad \mathrm{(B) \ 36 } \qquad \mathrm{(C) \ 40 } \qquad \mathrm{(D) \ 43 } \qquad \mathrm{(E) \ 45 }$

Solution

Problem 30

A large cube is formed by stacking 27 unit cubes. A plane is perpendicular to one of the internal diagonals of the large cube and bisects that diagonal. The number of unit cubes that the plane intersects is

$\mathrm{(A) \ 16 } \qquad \mathrm{(B) \ 17 } \qquad \mathrm{(C) \ 18 } \qquad \mathrm{(D) \ 19 } \qquad \mathrm{(E) \ 20 }$

Solution

@@ Line 104: / Line 104: @@
 == Problem 26 ==
+In the figure, <math>\overline{AB}</math> and <math>\overline{CD}</math> are diameters of the circle with center <math>O</math>, <math>\overline{AB} \perp \overline{CD}</math>, and chord <math>\overline{DF}</math> intersects <math>\overline{AB}</math> at <math>E</math>. If <math>DE = 6</math> and <math>EF = 2</math>, then the area of the circle is
+A. <math>23 \pi</math>
+B. <math>\frac {47}{2} \pi</math>
+C. <math>24 \pi</math>
+D. <math>\frac {49}{2} \pi</math>
+E. <math>25 \pi</math>
+{{image}}
 [[1995 AMC 12 Problems/Problem 26|Solution]]

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Difference between revisions of "1995 AHSME Problems"

Revision as of 11:17, 7 January 2008

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

See also