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=<9IL8IP What is the sum of the integers between 1 and 300 that are divisible by 11 or 13 (or both)? Find three consecutive odd numbers such that the sum of their squares is a four-digit number with all four digits the same. ( A stack of 100 nickels is 6.25 inches high. To the nearest cent, how much would a stack of nickels 8 feet high be worth? Determine the largest prime divisor of 87! + 88!. What is the ratio of the area of an equilateral triangle to that of a regular hexagon inscribed in the same circle? ) The sum of three numbers is 98. The first number is 2/3 of the second, and the second is 5/8 of the third. What is the second number? * Find the value in degrees of the sum of the six angles indicated in the diagram. B C D E A B C D A E + A , F Four congruent rectangles are arranged as shown in the figure to form a large rectangle. A The area of the large rectangle is 768. What is the area of a square that has the same perimeter as the large rectangle? D Solve for N if 6! • 7! = N!. D C / Find the measure of the angle z in the diagram here, given that the two horizontal segments are parallel. The number 2008 is a four-digit number having two zeros and two even digits that are not zeros. How many four-digit numC can also be described bers besides 2008 this way? B 0 145° How many distinct triangles can be90° conz structed by choosing three vertices from among the corners of a unit cube? 90° 1 2 3 z4 5 6 7 8 9 90° 10 11 12 13 14 15 16 135° Among the triangles of problem 13, how many distinct (noncongruent) triangles exist? 90° A 10 5 11 1 2 6 12 C3 4 D 7 8 9 X Y Z 13 14 15 Find the exact value of (111,111,111) . B C D A E F (( Given a three-digit number, interchange 1 the units digit and the hundreds digit. The 2 3 4 product of 5the6original and the 7 8 number 9 new number is 65,125. What is the smaller 10 11 12 13 14 15 16 three-digit1 factor? 145° 9 135° 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 () If you continued the triangular array of numbers shown in the figure, what number would be directly below 122? B . 2 (' 135° 145° F B (* B How long will it take a two-mile-long train C traveling 12 miles per hour to travel completely through a mile-long tunnel? A X (+ Given theEdigits 1, 3, 6, and 9, find the probability that a four-digit number D formed by using each of them only once is Y Z F divisible by 7. E 16 F (In the sum of the expression 7 + 77 + 777 + 7777 + ... + 7,777,777,777,777,777,777, what digit will be in the tens place? O' (. The number 64 is divisible O' by its units digit (4). How many whole numbers less than 64 are A' divisible by their respective units digit? (/ The sum of the positive divisors of 480 is 1512. Find the sum of the reciprocals of the positive divisors of 480. (, A The five-square numerical puzzle below requires the vertical column to be filled with the digits from a three-digit integral power of 5 and the horizontal row to be filled with the digits from a three-digit integral power of 2. A' What digit will be in the shaded square? O' (0 B' For the sequence 1, –2, 3, –4, 5, –6, 7, . . . , what is the difference between the mean of the sequence’s first 400 terms and theA mean of its first 200 terms? B' A' B' )' Arrange the digits 1, 1, 2, 2, 3, and 3 to form O a six-digit number such that the 1s have one digitBbetween them, the 2s have two digits between them, and the 3s have three digits between them. What is A the sum of all possible six-digit numbers formed under these conditions? O If [x] represents the greatest integer less than or equal to x, solve for x: x • [x] = 40. A )+ B Two students, Katelyn and Carly, are playing a game that uses ten different numbered cards lying face down on a table. The faces of the cards are labeled with one of the numbers from 1 to 10 (each card has a different number). If EKatelyn and Carly each turn C D over a differentF card, what is the probability that the sum of the two cards is even? )/ )( B ), )) A group of friends went to dinner and received a bill totaling $288. The group decided to treat two people whose birthdays were that month and split the charges equally among the rest of the group. This resulted in each person having to pay $4.80 more than each would have paid had the bill been split equally among the entire group. How many people were in the dinner group? )* Determine the measure (in degrees) of an angle whose complement is four-ninths its supplement. )- Quadrilateral ABCD is a rhombus. Its diagonals are 12 and 20 units in length. Find the diameter of the circle inscribed in rhombus ABCD. Round your answer to the nearest A B hundredth. D C )0 EXk`feXc:fleZ`cf]K\XZ_\ijf]DXk_\dXk`Zj#(0'-8jjfZ`Xk`fe;i`m\#I\jkfe#M8)'(0($(,') Copyright © 2008 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or distributed electronically or in any other format without written permission from NCTM. B ). O