Download WSMC Potpourri `11

Potpourri – 5th Grade
Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely. You do not need
to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If your answer is a
fraction like
, bubble in 316.
1. 2 points: If the first four terms of a sequence are 3, 6, 12, and 24, what is the sum of the next
three numbers in the sequence?
2. 2 points: Suppose the numbers 1 through 34, inclusive, are written in sequential order around the
circumference of a circle such that they are equally spaced apart. What number will be directly
across from 11?
3. 2 points: Two one-digit prime numbers are randomly selected, with replacement allowed. What
is the probability that the product of these two primes will be even? Express your answer as a
reduced fraction.
4. 3 points: How many perfect squares are there between 2011 and 314159?
5. 3 points: What is
expressed as a base nine number?
6. 3 points: Suppose A = {1, 2, 3, 4, 5, 10, 15} and B = {2, 4, 5, 6, 10, 12, 15}. How many
elements are in the set
?
7. 3 points: How many unordered pairs of integers have a product of 400?
8. 4 points: If a, b, c, d, and e are distinct integers between 1 and 9, inclusive, what is the maximum
possible value of the expression
? Express your answer to the nearest whole
number.
9. 4 points: A palindrome is defined as a number whose digits are the same when read both from
left to right and right to left. For example, 434 is a palindrome. How many three-digit numbers
are palindromes?
10. 4 points: How many positive integers less than 1000 are divisible by 4 and 6 but not 8?
Potpourri – 6th Grade
Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely. You do not need
to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If your answer is a
fraction like
, bubble in 316.
1. 2 points: How many perfect squares are there between 2011 and 314159?
2. 2 points: What is
expressed as a base nine number?
3. 2 points: Suppose A = {1, 2, 3, 4, 5, 10, 15} and B = {2, 4, 5, 6, 10, 12, 15}. How many
elements are in the set
?
4. 3 points: How many unordered pairs of integers have a product of 400?
5. 3 points: If a, b, c, d, and e are distinct integers between 1 and 9, inclusive, what is the maximum
possible value of the expression
? Express your answer to the nearest whole
number.
6. 3 points: A palindrome is defined as a number whose digits are the same when read both from
left to right and right to left. For example, 434 is a palindrome. How many three-digit numbers
are palindromes?
7. 3 points: How many positive integers less than 1000 are divisible by 4 and 6 but not 8?
8. 4 points: If you begin writing down the counting numbers in increasing order, beginning with 1,
what three-digit number will you be in the process of writing when writing your 403rd digit?
9. 4 points: How many positive two-digit integers have an odd number of positive factors?
10. 4 points: If
and
for
, what is the eighth term of the sequence defined by
? Express your answer as a decimal.
Potpourri – 7th Grade
Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely. You do not need
to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If your answer is a
fraction like
, bubble in 316.
1. 2 points: How many unordered pairs of integers have a product of 400?
2. 2 points: If a, b, c, d, and e are distinct integers between 1 and 9, inclusive, what is the maximum
possible value of the expression
? Express your answer to the nearest whole
number.
3. 2 points: A palindrome is defined as a number whose digits are the same when read both from
left to right and right to left. For example, 434 is a palindrome. How many three-digit numbers
are palindromes?
4. 3 points: How many positive integers less than 1000 are divisible by 4 and 6 but not 8?
5. 3 points: If you begin writing down the counting numbers in increasing order, beginning with 1,
what three-digit number will you be in the process of writing when writing your 403rd digit?
6. 3 points: How many positive two-digit integers have an odd number of positive factors?
7. 3 points: If
and
for
, what is the eighth term of the sequence defined by
? Express your answer as a decimal.
8. 4 points: What is the sum of the unique positive prime factors in the prime factorization of
174420?
9. 4 points: In the following diagram, if you can only move to the right or downwards, how many
unique paths are there between A and B?
A
B
10. 4 points: What is the smallest positive integer that is divisible by each of the numbers 1 through
8, inclusive?
Potpourri – 8th Grade
Bubble in your answers on the answer sheet. Be sure to erase all mistakes completely. You do not need
to bubble in leading zeros – the answer of “7” does not need to be answered as “007”. If your answer is a
fraction like
, bubble in 316.
1. 2 points: How many positive integers less than 1000 are divisible by 4 and 6 but not 8?
2. 2 points: If you begin writing down the counting numbers in increasing order, beginning with 1,
what three-digit number will you be in the process of writing when writing your 403rd digit?
3. 2 points: How many positive two-digit integers have an odd number of positive factors?
4. 3 points: If
and
for
, what is the eighth term of the sequence defined by
? Express your answer as a decimal.
5. 3 points: What is the sum of the unique positive prime factors in the prime factorization of
174420?
6. 3 points: In the following diagram, if you can only move to the right or downwards, how many
unique paths are there between A and B?
A
B
7. 3 points: What is the smallest positive integer that is divisible by each of the numbers 1 through
8, inclusive?
8. 4 points: What is the sum of terms of the infinite geometric sequence: 500, 100, 20, 4, 0.8, ...?
9. 4 points: In Major League Soccer, you receive three points for a win, one point for a draw, and
zero points for a loss. If the Seattle Sounders were to score 44 points in the thirty-game season,
how many unique records could they have?
10. 4 points: If the least common multiple of two distinct numbers is 24, how many different greatest
common factors are possible?