Math Practice Problems for High School in Number Sense

HSN-131) Answer: A Venn diagram clearly reveals Carla's error. Many of the students who were accepted into State Univ. were also accepted into Temple Tech. Carla might have been among those applicants who were rejected by both schools.

During the morning senior assembly, Mr. Carter, the school principal, announced that he had good news for the group. He told the students that he has just been informed that 50 percent of those who applied for admission into State University have been accepted. Also, 50 percent of those who applied to Temple Tech have also been accepted. Carla turned to her friend Marcie and said, "Great! I've been accepted I applied to both schools, and 50 percent +50 percent is 100 percent, so I'm in!" Analyze the action. Is Carla correct? Defend your decision.  Explain your answer in detail.

HSN-130) Answer: Store A

On the boardwalk at the shore, there are three stores within a block of one another. On the first day of the season, each store had a sign advertising a sale on gold chains. Store A offered a 70 percent discount plus an additional 10 percent discount for cash. Store B offered a 60 percent discount plus an additional 20 percent discount for cash. Store C accepted cash only, and offered a 2/3 discount. Amy wanted to buy a 26-inch gold chain. If you were Amy, from which store would you buy the chain? What would you do? Defend your decision.  Explain your answer in detail.

HSN-129) Answer: 20

There are four boys and five girls standing outside the new record shop. The sign in the window offers a prize to every couple (one boy and one girl) that enters the store. How many prizes can the nine people get?  Explain your answer in detail.

HSN-128) Answer: Save $911 by itemizing.

Mr. Ryan's total income was $53,750. His deductions were as follows: Contributions-$ 856; Mortgage Interest-$1250; Deductible Taxes-$2630; Casualty Losses-$1550 Mr. Ryan can either take the standard deduction of 10 percent, or he can itemize his deductions. Which method gives the larger deduction and by how much?  Explain your answer in detail.

 HSN-127)   Answer:  Wednesday
Suppose two days ago was Sunday. What day of the week will 365 days from today then be? Explain your answer in detail.

HSN-126)   Answer: Four ways, if you require 3 distinct numbers: 1x2x12, 1x3x8, 1x4x6, and 2x3x4.  Two more with duplication: 1x1x24, and 2x2x6.
The product of three natural numbers is 24. How many different ways can this be done if the order of the 3 numbers does not matter? Explain your answer in detail.

HSN-125)   Answer:  A=1,  B=4,  C=9
For the division problem below A, B, and C are different digits, each of A-B and 7C is a 2-digit number, and each blank space represents a missing digit. What is the value of each of A, B, and C? Explain your answer in detail.

HSN-124)   Answer:  13
A number N divides each of 17 and 30 with the same remainder in each case. What is the largest value N can have?  Explain your answer in detail.

HSN-123)   Answer:  18
Consecutive numbers are whole numbers that follow in order such as 3, 4, 5. Find the smallest of the five consecutive numbers whose sum is 100. Explain your answer in detail.

HSN-122)   Answer:  45
Consider the counting numbers from I to 1000: 1, 2, 3, 4, ... , 1000. Which one of these numbers multiplied by itself, is closest to 1985? Explain your answer in detail.

HSN-121)   Answer:  13
When a natural number is multiplied by itself, the result is a square number. Some examples of square numbers are 1, 4, 9, 16, and 25. How many square numbers are there between 1,000 and 2,000? Explain your answer in detail.

HSN-120)   Answer:  8
The four-digit number   A 5 5 B   is divisible by 36. What is the sum of A and B? Explain your answer in detail.

HSN-119)   Answer:  1936
The result of multiplying a natural number by itself is a square number. For example 1, 4, 9, and 16 are each square numbers because 1x1 = 1, 2x2 = 4, 3x3 = 9, and 4x4 = 16. What year in the 20th century (the years 1901 through 2000) was a square number? Explain your answer in detail.

HSN-118)   Answer:  625 and 16.
The product of two whole numbers is 10,000. If neither number contains a zero digit, what are the two numbers? Explain your answer in detail.

HSN-117)   Answer:  B=1,  A=9,  C=8
In the addition problem below, there are three two-digit numbers in which different letters represent different digits. What digits do A, B, and C represent? Explain your answer in detail.

   A A
   B B
+ C C
B A C

HSN-116)   Answer:  60
A certain natural number is divisible by 3 and also by 5. When the number is divided by 7, the remainder is 4. What is the smallest number that satisfies these conditions? Explain your answer in detail.

HSN-115)   Answer:  A=4,  B=7,  C=5
In the addition problem below to the left A, B, and C are digits. If C is placed in the tens column instead of the units column as shown below and to the right, the sum is 97. What are the values of A, B, and C? Explain your answer in detail.
   A B           A B
 +   C         +C  
   5 2            9 7

HSN-114)   Answer:  A=5,  B=6
A4273B is a six-digit number in which A and B are digits, and the number is divisible by 72 without remainder. Find the value of A and the value of B. Explain your answer in detail.

HSN-113)   Answer:  2 1/6
Of three numbers, two are 1/2 and 1/3. What should the third number be so that the average of all three is 1? Explain your answer in detail.

HSN-112)   Answer:  24, 25, 26
Consecutive numbers are natural numbers that follow in order as in the case of 3, 4, 5, 6, and 7. Find three consecutive numbers whose product is 15,600. Explain your answer in detail.

HSN-111)   Answer:  10
In the division example below A and B represent different digits. What is the sum of A and B if the remainder is zero? Explain your answer in detail.

HSN-110)   Answer:  239
In the multiplication problem below, A, B, C, and D represent different digits. ABC is a three-digit number, and * means multiplication. What three-digit number does ABC represent? Explain your answer in detail.
    A  B  C
          *  D
  1  6  7  3

HSN-109)   Answer:  1296
In the multiplication example below, different letters represent different digits and a blank space may represent any digit. The product WHAT is a four-digit number less than 5000. Find the number that WHAT represents. Explain your answer in detail.

HSN-108)   Answer:  5
What is its value of the expression below in simplest form? Explain your answer in detail.
( 5 1/3 – 2 ½ ) + ( 5 ½ - 3 1/3 )

HSN-107)   Answer:  7521
ABCD represents a four-digit number. The product of its digits is 70. What is the largest four-digit number that ABCD can represent? Explain your answer in detail.

HSN-106)   Answer:  43
A prime number is a whole number, greater than 1, that is divisible only by itself and 1. Some examples of prime numbers are 2, 3, 5, 7, 11, and 13. What is the largest prime number, P, such that 9 times P is less than 400? Explain your answer in detail.

HSN-105)   Answer:  N=1,  M=25
The numbers M and N are different numbers selected from the first twenty-five counting numbers:
1, 2, 3, 4, ... , 24, 25. If M is larger than N, what is the smallest value that the expression at the right can have?

 M x N
 M - N

HSN-104)   Answer:  342
A printer has to number the pages of a book from I to 150. Suppose the printer uses a separate piece of type for each digit in each number. How many pieces of type will the printer have to use? Explain your answer in detail.

HSN-103)   Answer:  840
A jar contains a large number of pennies. The pennies can be divided into equal shares among 3, 4, 5, 6, 7, or 8 children with no pennies left over each time. What is the least number of pennies the jar could contain? Explain your answer in detail.

HSN-102)   Answer:  40
Suppose the counting numbers from 1 through 100 are written on paper. What is the total number of 3’s and 8’s that will appear on the paper? Explain your answer in detail.

HSN-101)   Answer:  198
Many whole numbers between 10 and 1,000 have 2 or 7 as the units digit. How many such numbers are there between IO and 1,000? Explain your answer in detail.

HSN-100)   Answer:  A=7,  B=8,  C=3
In the multiplication example below, each of A, B, and C stands for a different digit and each of the blank spaces represents a non-zero digit. What digits do A, B, and C each represent?  Explain your answer in detail.

  HSN-99)   Answer:  77
2, 3, 5, 7, 11, ... are examples of prime numbers; each number has only itself and I as factors. Suppose the number of units in each of the length and width of a rectangle are prime numbers and the perimeter is 36 units. What is the largest number of square units the area could have? Explain your answer in detail.

HSN-98)   Answer:  $240
A bus was rented at a fixed cost by a group of 30 people. When 10 people were added to the group, the fixed cost of the bus did not change, but the charge for each person in the original group was $2 less than before. If each person paid the same charge as each of the others, find the fixed cost of renting the bus.  Explain your answer in detail.

HSN-97)   Answer:  55
Suppose  3! means 3x2xl,  4! means 4x3x2xl,  5! means 5x4x3x2xl,  and so forth. What is the value of the expression below in simplest form?  Explain your answer in detail.

8! – 6!
3! X 5!

HSN-96)   Answer:  3980
Given the expression: 1990 x 1991 - 1989 x 1990. What counting number is equivalent to the expression?  Explain your answer in detail.

HSN-95)   Answer:  315
Find the largest factor of 2520 that is not divisible by 6.  Explain your answer in detail.

HSN-94)   Answer:  A=1,  B=8, C=5
A, B, and C represent different digits, C ¹ 0 and a blank space may represent any digit in the division problem below. What digits do A, B, and C each represent?  Explain your answer in detail.