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Macy

Guest

Help me with algebra- Thank you -

1. Three numbers p, q, r are all prime numbers less than 50 with property that p + q = r. How many values of r are possible?

2. A two-digit number n has the property that the sum of the digits of n is the same as the sum of the digits of 6n. How many such numbers are there?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Help me with algebra- Thank you -

1. One of p and q must be 2. (If they were both odd, their sum would be an even number greater than 2.) Then it’s a matter of finding pairs of twin primes less than 50. There are 6 of them.

2. n would have to be a multiple of 9. (6n is divisible by 3, so the sum of the digits of 6n is divisible by 3. Hence the sum of the digits of n is divisible by 3; ∴ n itself must be divisible by 3. This means 6n is divisible by 9. Therefore the sum of the digits of 6n is divisible by 9; hence the sum of the digits of n is divisible by 9; ∴ n itself must be divisible by 9.)

There are 10 2-digit multiples of 9. Checking these in turn, we find that all of them except 63 and 81 have the given property. Hence there are 8 such numbers n.

Last edited by JaneFairfax (2008-09-13 11:34:46)

macy

Guest

Re: Help me with algebra- Thank you -

Thanks Jane, That's great answer!