Pre calc questions

Question

1. Two of the three missing digits of the five-digit perfect square number 3, _, _, _, 9 are the same. What is the other missing digit?

2. What is the least positive multiple of 25 for which the product of its digits is also a positive multiple of 25?

3. The product of three consecutive whole numbers is 46,620. What is the mean of these three numbers?

4. What is the probability that if you multiply two randomly-selected two-digit whole numbers, the result is greater than 100 and less than 200? Express your answer as a common fraction. 

5. An integer n is a four-digit number, and 6 is a factor of n. Three of the digits of n are 1, 4 and 6. What is the greatest integer that n could be?

Answer 1

1) the number is 3 _ _ _ 9

the number has to be less than 200 because 200^2=40,000

the number has to be 1 _ 3 or 1 _ 7 in order to get the 9

start with 1 _ 7

replace the _ with 9, 8, 7, 6, 5, 4, 3, 2, 1, or 0

try 9

197 and 197²=38809, so 0 is the missing digit

 

2) 25, 2*5=10

    50, 5*0=0

    75, 7*5=35

    5*10=50, so the number is 525

 

3) factor 46,620 (you don't need all primes)

    46,620=4*9*5*7*37=(5*7)*(4*9)*(37)=35*36*37

    the numbers are 35, 36, and 37 and the mean is the middle number 36

 

5) the 4-digit number must be divisible by 2 and by 3 to be divisible by 6

    the number has to be _ 6 1 4 to be even

    6+1+4=11

    what is the greatest digit that can be added to 11 to make a multiple of 3 ?

    7 is the digit

    the number is 7614