Basically this arrangements will give us all numbers less than 10,000 in which sum of the digits (sum of 5 d’s=5) equals 5. Hence the answer is . Answer: C (56).
How many positive integer less than 10,000 are such that the product of their digits is 210?
54 positive numbers
∴ There are 54 positive numbers less than 10,000 are such that the product of their digits is 210.
How many positive integers less than or equal to 1000 are not divisible by any of 2/3 or 5?
Hence exactly 772 of the numbers between 1 and 1000 are divisible by at least one of 2, 3, 5 and 7. Therefore the number of integers which are not divisible by any of these is given by 1000 – 772 = 228.
How many positive integers less than 1000 A are divisible by 7 B are divisible by 7 but not by 11 C are divisible by both 7 and 11 d are divisible by either 7 or 11 e are divisible by exactly one of 7 and 11 F are divisible?
Ans: 28 = 256. the set of integers less than 1000 divisible by 7 and B the integers less than 1000 divisible by 11.). Answer: [1000]+[10001 – 11000] = 142 +90 – 12 = 220.
How many numbers less than 10,000 have an even number of factors?
The number 10,000 can be divided by 25 positive divisors (out of which 20 are even, and 5 are odd).
How many positive integers are there?
Hence k can be 0, 1, 2, 3……., 34 or 35. You gotta consider 0 because, at k=0, 28k+10 =10 is a positive integer. 10, 38,…….., 990 are in arithmetic progression(difference between subsequent terms is constant(28). Both ways are one and the same thing tho.
How many positive integers of at most 3 3 digits are there such that the product of their digits is 30 30?
So the answer is that there are 204 three-digit integers whose digits are either increasing or decreasing.
How many positive numbers less than 1000 are divisible by 6 but not 5?
Step 1: Count the numbers under 1000 which are divisible by 6. 1000 mod 6 = 166. Step 2: Remove those numbers which are divisible by 5. LCM of 5 and 6 = 30 => every multiple of 30 is divisible by 6 as well as 5.
How many numbers from 1 to 1000 are divisible by both 3 and 5?
467 unique numbers between 1 and 1000 which are divisible by 3 or 5.
Why is the sum of all positive integers greater than n?
It’s true for all n > 2. The reason is that if k ∈ { 1, …, n − 1 } is relatively prime to n, so is n − k, so the integers that you’re adding can be combined into φ ( n) 2 pairs whose members sum to n. If n > 2, n 2 is never relatively prime to n, so you really do get pairs { k, n − k }.
How many integers less than 1, 000, 000 have the sum of digit?
Note – 1,000,000 has sum of digit = 1. Then we are concerned with numbers between 1 – 999,999. Let us assign an alphabet for every digit. Now, any one u, v, w, x, y, z can be more than 10.
Which is the sum of consecutive integers from n 1 to n 2?
The sum of consecutive positive integers from n 1 to n 2 is equal to: n 1 + (n 1 + 1) + + n 2 = n 2 (n 2 + 1) / 2 – n 1 (n 1 – 1) / 2.
Can you find the sum of the positive odd integers less than 100?
We are asked to find the difference between the sum of the positive even integers less than or equal to 100 and the sum of the positive odd integers less than 100. (1) Can you solve a simpler problem?
