The chairs of an auditorium are to be labeled with a letter and a positive integer not exceeding 200. What is the largest number of chairs that can be labeled differently?

Q: Find the least amount of different numbers to pick from positive integers that are at most 100 to…

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Q: Suppose you had 4 red checker pieces and 5 black checker pieces. How many ways can you arrange these…

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Q: A company wants to have a 6 digit phone extension with the first digit not being zero

A: We have to make a 6- digit number. So let's assume we have 6 empty boxes to fill and form the 6-…

Q: pair of these integers with a sum equal to 9.

A: Let us take set under consideration {1,2,3,4,5,6,7,8}Possible pairs {{1,8}, {2,7}, {3,6}, {4,5}}…

Q: A license plate is to consist of 4 digits followed by 2  uppercase letters. Determine the number of…

A: Solution-: Given: A license plate is to consist of 4 digits followed by 2  uppercase letters. We…

Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6. If each number is used only…

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Q: A company wants to have 4-digit phone extensions with the first digit not being zero. How many…

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Q: From 6 female employees and 5 male employees, how many groups of 5 employees can be organized…

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Q: How many six-digit positive integers contain exactly one one, two twos and three treor? How many…

A: First note that here six digit integer can start only with 1 or 2. If it starts with 1 the remaining…

Q: On which number line is A located at -3.5? ++++++ -5 -4 -3 -2 -5 -4 -3 -2 -5 -4 -3 -2 A -5 -4 -3 -2…

A: We need to locate the point  - 3.5  on the number line. First step is to identify the exact spacing…

Q: Find the smallest integer greater than 100 that is divisible by 3 but leaves the reminder 1,5 when…

A: To find- Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder…

Q: A developer of a new subdivision wants to build homes that are all different. There are five…

A: Given, no.of interior plans=5no.of exteriors plans=7

Q: Find the number of positive integers not exceeding 1000 that are not divisible by 2 or 3 but…

A: The positive integers not exceeding 1000 that are not divisible by 2 or 3 but divisible by 5 are 5,…

Q: A boy imagined four-digit multiple of 5 with different digits. If the first digit is erased, the…

A: Suppose the number be xyzw and x,y,z,w are different numbers. Now the number is multiple of 5. so W…

Q: The door code to gain access to a super-secret underground lab is 6 digits. The first 3 digits of…

A: There are 6 digits .   Odd digits : 1,3,5,7,9  total 5 possibility   Even digits : 0,2,4,6,8  total…

Q: from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is not allowed and all the odd digits occur…

A: The biggest possible number is 975,318,642; the digit zero(0) is being excluded from the question…

Q: The pattern​ 1, 8,​ 27, 64,​ 125, ... is a cubic pattern, what is the greatest number in this…

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Q: The number of 3-digit numbers less than 400 that can be created if the last digit is either 4 or 5…

A: Solution  :

Q: What is the number of positive integers not larger than 210 and not divisible by 2, 3 or 7?…

A: Within 210, the number of integers that are divisible by 2= 210/2= 105  Within 210, the number of…

Q: What is the sum of the first 150 positive integers?

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Q: How many 3 digit numbers may be formed from the digits 0,1,2,3,4, & 5 if no digit maybe repeated?

A: The given number are 0,1,2,3,4,5.

Q: If I am creating a 5-digit number combination, how many combinations will be created if the first…

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Q: How to form the digits 2,9,6,4 and 3 from the greatest 5-digit odd number

A: To find the greatest 5-digit odd number

Q: What is the sum of the first 200 positive integers?

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Q: Suppose a license plate contains two letters followed by three distinct digits with the first digit…

A: Ans#- Given, A license plate contains two letters followed by three distinct digits with the first…

Q: Find the set of all positive integers n with the property that the set  M={n,n+1,n+2,n+3,n+4,n+5}…

A: A very good problem based on a nice application of quadratic residues

Q: How many numbers consisting of five different digits can be made from the digits (0, 1 , 2, 3, 4, 5,…

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Q: The number of positive integers not exceeding 750 that are divisible by 3. 4. and 7 is: *

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Q: A company wants to have 7-digit phone extensions with the first digit not being zero. .... How many…

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Q: If a class of children is separated into groups of 5 children, 2 children will be left over. If the…

A: Let the number of children in the class is N. 1. It is given that when the children are seperated…

Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: If two integers have the same parity, then their sum is even. (Try cases.)

A: According to the given information it is required to prove that the sum of two integers of same…

Q: What is the range of all integers greater than 40 and less than 99 that are multiples of 3

A: To find : The range of all integers greater than 40 and less than 99 that are multiples of 3

Q: What is the sum of the first 100 nonnegative integers?

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Q: What are all of the natural numbers divisible by 8 whose sum of digits is less than 10 and the…

A: Given the requirements

Q: Find the least three-digit whole number that has exactly five positive factors. The least three…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit is…

A: Number of possible arrangement can be calculated either by combination or permutation methods.…

Q: Suppose a 4-digit number will be formed from numbers 0,1,2,3,4,5,6,7,8, where each digit can only be…

A: Given, 4 digited numbers are to be formed from 0,1,2,....,8 without repetition. These numbers must…

Q: Find the largest positive integers that will divide 398, 436 and 542 leaving emainders 7, 11 and 15…

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Q: What is the smallest sum possible sum of 25 consecutive positive integers which s a perfect square?

A: Let's take the 25 consecutive positive numbers as an Arithmetic Progression with first term a.…

Q: Find the number of positive integers not exceeding 120 that are divisible by 3 or 4

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Q: “If the product of two counting numbers is an even counting number, then both of the counting…

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Q: Is it possible for two numbers to have the same least common multiple and greatest common devisor?

A: To check whether for two numbers can have the same LCM and HCF.

Q: Put a positive whole number in each of the four boxes of this table that satisfies the rule. For…

A: Prime number is a positive integer having exactly 2 factors. for example 7 is a odd prime number as…

Q: How many zeroes are at the end of 25! (= 25 factorial)?

A: The given number is 25!.  Now, we need to find the number of zeros at the end of 25!.

Q: A natural number greater than 1 that is divisible by a number other than itself and 1 is called a/an…

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Q: What is the sum of the first 9,000 positive integers

A: topic - arithmetic sequence answer is 40504500

Q: How many positive integers not exceeding 100 are divisible by 5 or 7?

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Q: The digits 5,6,7 annd 4 are to be arranged to form a 7 digit interger. How many different integers…

A: The choices for each digit is 5, 6, 7 and 4. So each digit has 4 choices.    There are total 7…

Q: Find the sum of the integers between301 and 400 inclusive that are multiples of 4.

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.