Thread: Value of w + z

If the product of the integers, w, x, y, and y is 770, and
1 < w < x < y < z, what is the value of w + z?

1. The book tells me to find the prime factorization of 770.

I found that to be 2 * 5 * 7 * 11.

2. The book tells me to let w = 2, x = 5, y = 7, and z = 11.

Thus, 1 < 2 < 5 < 7 < 11 is a true statement.

3. From step 2, I figured out that w + z = 2 + 11 or 13.

Question:

What information in this problem indicates that prime factorization is needed as step one?

The prime factorization isn't necessary...for example:

$\displaystyle (w,x,y,z)=(1,7,10,11)$

will also work. Then you get a different value for the sum:

$\displaystyle w+z$

I think only if the book had restricted the factors to being integers greater than 1 would the prime factorization have been your only choice.

Originally Posted by MarkFL

The prime factorization isn't necessary...for example:

$\displaystyle (w,x,y,z)=(1,7,10,11)$

will also work. Then you get a different value for the sum:

$\displaystyle w+z$

I think only if the book had restricted the factors to being integers greater than 1 would the prime factorization have been your only choice.

But we given that $1<w$.

Originally Posted by Plato

But we given that $1<w$.

Yes, thanks - I missed that the first time around.

Thank you everyone.