7/28/2019 Practice October 21

http://slidepdf.com/reader/full/practice-october-21 1/2

MATHCOUNTS Practice October 21, 2011

(1) How many integers between 100 and 300 have both 11 and 8 as factors?

(2) What is the sum of the two values of  x  for which (x  + 3)2 = 121?

(3) The function f   is defined by f  (n) = f  (n − 1) + f  (n − 2). It is also true that

f  (1) = 3 and f  (3) = 10. What is the value of  f  (6)?

(4) The positive diff erence of the cube of an integer and the square of the same

integer is 100. What is the integer?

(5) Erika, who is 14 years old, flips a fair coin whose sides are labeled 10 and 20,

and then she adds the number on the top of the flipped coin to the number she rolls on astandard die. What is the probability that the sum equals her age in years? Express your

answer as a common fraction.

(6) What is the value of  x  + y  if the sequence 2, 6, 10, . . . , x, y, 26 is an

arithmetic sequence?

(7) What is the digit in the tens place when 72005 is expressed in decimal

notation?

(8) Nathan will roll two six-sided dice. What is the probability that he will roll a

number less than three on the first die and a number greater than three on the second die?

Express your answer as a common fraction.

(9) Thad has an unlimited supply of 3-cent and 4-cent stamps. If he has to put

exactly 37 cents of postage on a letter, how many diff erent combinations of 3-cent and/or

4-cent stamps could Thad use?

(10) Lisa has 10 friends and 34 marbles. What is the minimum number of 

additional marbles she needs so that she can give each friend at least one marble and no

two friends receive the same number of marbles?

7/28/2019 Practice October 21

http://slidepdf.com/reader/full/practice-october-21 2/2

(11) John is on the middle rung of a ladder. He climbs up three rungs, down five

rungs, up six rungs and then climbs the last eight rungs to the top. How many rungs are on

the ladder?

(12) For a set of five positive integers, none greater than 100, the mean is 1.5

times the mode. If 31, 58, 98, x  and x  are the five integers, what is the value of  x ?

(13) If one quart of paint is exactly enough for two coats of paint on a 9-foot by

10-foot wall, how many quarts of paint are needed to apply one coat of paint to a 10-foot

by 12-foot wall? Express your answer as a common fraction.

(14) The price of a stereo is $200 on Monday. On Tuesday the price from

Monday is reduced by 10%. On Wednesday, Tuesday’s price is increased by 10%. What is

the price of the stereo on Wednesday?

(15) A number is called perfect if the sum of its divisors, except itself, is equal to

the original number. What is the sum of the two perfect numbers between 2 and 30?

(16) On a standard clock, how many degrees does the minute hand rotate during

the time period from 4:12 pm to 4:48 pm of the same day?

(17) The median of the set {n, n + 5, n + 6, n + 9, n + 15} is 9. What is themean?

Copyright MATHCOUNTS Inc. All rights reserved