If a, b,n are integers and a^2 + b^2 = n, then the remainder of n upon division by 4 is not 3.

Q: a 4 digit number is selected from the number {1,2,3,4,5,6} where the digits are selected without…

A: Given that  there are digits {1, 2, 3, 4, 5, 6} we have to find number of 4-digits numbers those are…

Q: A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees pläntec…

A: Given 24 trees per row1235 trees to plant

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

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

A: Let x be the required number. The number is divisible by 3, so it leaves the remainder 0 when it is…

Q: How many three digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible…

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Q: When a carton of apples were packed into bags of 4, there would be 3 apples left over. When the same…

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Q: When four positive integers are added three at a time the sums are 1551, 1659, 1720 and 1736. The…

A: when four positive integers are added three at a time the sums are 1551, 1659 ,1720 and 1736. we…

Q: If 17th term of an AP exceeds its 10th term by 7 , Find the common differenc

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Q: If 6th  term of GP is 9375 and its 4th term is 375.Find its 9th term

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Q: A and B can do a piece of work in 3 days, B and C in 4 days, while A and C in 2.5 days. In how many…

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Q: Show that if any eight positive integers are chosen, two of them will have the same remainder when…

A: Pigeonhole Principle- If n items are assigned to m containers, and m<n,then at least one…

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

A: Solution  :

Q: How many EVEN 5-digit numbers can be made from the digits 2, 4, 5, 6, 7, 8, and 9?

A: Fundamental Counting Principle The Fundamental Counting Principle is a method used to determine the…

Q: A certain number is doubled and then divided by 8. If after subtracting 4 from this result, one gets…

A: The statements involving algebraic operations and expression namely addition , subtraction ,…

Q: How many 4 digit numbers can be formed from the digits 0,1,2,3,4,5, and 6 if each digit can be used…

A: 1. we will first find how many 4 digits numbers can be formed. To formed 4 digit numbers from…

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

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Q: When 32 is divided by an integer, the remainder is 4. When 51 is divided by the same integer, the…

A: We can use concept of HCF to solve the problem

Q: Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

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Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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Q: How many 5 digit numbers can be formed if each one uses all the digits 0,1,2,3,4 without repetition?

A: We have 5 digits 0,1,2,3,4

Q: Multiply three consecutive integers together and then add the second integer to that product. Use…

A: Consider three consecutive numbers x, (x+1), (x+2). Take a product of these numbers we get,…

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: How many odd 4-digit numbers greater than 3000 can be formed from the digits 1, 5, 6, 7, 8 if no…

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Q: How many 9 digit numbers are there that use each of the digits 1,2,3,4,5,6,7,8,9 exactly once?

A: To form a 9 digit number We know that each 9 digit places are must be one of the 9…

Q: how many 6 digit numbers can be formed, if at the place of hundred thousand there are allowed two…

A: Yes your step is right.Hundredth thousand place can be chosen in 2 ways. And hundredth place can be…

Q: Show A and Show B are two of the most popular television shows of all time. The number of episodes…

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Q: Suppose that 6 machines can complete a certain task in 9 days. If there are 18 machines, how many…

A: Concept: If number of machine increase then number of work completion day will decrease . Hence Both…

Q: Two integers, a and b, have a product of 48. What is the least possible sum of a and b? The least…

A: Answer is a+b= -49. Explanation is given below...

Q: How many 4-digit numbers can be formed from 1,2,3,4 and 5 if no digit is repeated?

A: Given digits 1,2,3,4,5 Repeatation not allowed

Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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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: How many five digit numbers containing each of the digits 1,2,3,4,5 exactly once are divisible by…

A: * SOLUTION :-  From the given information the calculation as follows .

Q: How many even three digits numbers can be found from the digits 3,2,5,6 and 9 if each digits can be…

A: Given, s={3,2,5,6,9}

Q: How many distinct integers do we have to pick in order to have two that have the same remainder when…

A: To find - How many distinct integers do we have to pick in order to have two that have the same…

Q: How many even 4 digit numbers can be formed from the digits 1, 7, 2, 4, 6, 9, 3, and 0 if the…

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Q: The digits 1,2,3,4 and 5 are to used to form a five-digit number. How many different numbers can be…

A: Given data: Digits  to use = 1,2,3,4 and 5 to form five digit number  To find: The number must be…

Q: The sum of an integer and 4 less than that integer is even.

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Q: If the sum of the digits is divisible by 2, then the number is divisible by 2. true or false

A: If the sum of the digits is divisible by 2, then the number is divisible by 2.

Q: Suppose you have 1000 blocks, each of which is 1.0 cm on a side. If all 1000 of these blocks are…

A: First consider the case of 1000 blocks stacked to give a cube 10 cm on a side. The block which have…

Q: How many 4-digit numbers are there that are divisible by 10 and the sum of whose digits is 10?

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Q: Suppose you have 13 juniors and 11 seniors. How many different draws of 6 names would contain…

A: Given that, We have 13 juniors and 11 seniors. We should select 3 juniors from 13 and 3 seniors from…

Q: How many even three-digit numbers can be formed from the digits 1,2,3,5,6,8 and 9 if each digit can…

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Q: Number 332 – 1 has exactly two divisors greater than 75 and less than 85. What is their product?

A: We need to find two divisors of 332-1 between 75 and 85.  Now, we can use the identity a2-b2=a-ba+b…

Q: many even four-digit numbers can be formed from the digits 0, 1, 2, 5, 6, and 9 if each digit can be…

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Q: the student noticed that if he writes a multiplication sign between the second and third digit of…

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Q: What 2 nonnegative numbers with a sum of 23 have the largest possible product?

A: Given information: The two non negative numbers with a sum of 23.  Calculation: Consider x and y are…