# Thread: two questions about: Let x,y,z be distinct, non-zero, one-digit numbers.

1. ## two questions about: Let x,y,z be distinct, non-zero, one-digit numbers.

This simple problem is from a series of review problems:
problem.jpg

Here is the book's solution:
solution.PNG

Here is what I did:
my solution.jpg

Question 1) Where did the author get the 4? The two largest numbers are 5 and 7 and the difference can only be 2 or -2.

Question 2) Is there a way to solve this problem using algebra? Or is that even expected here?

2. Originally Posted by allegansveritatem
This simple problem is from a series of review problems:
problem.jpg

Here is the book's solution:
solution.PNG
Here is what I did:
my solution.jpg
Question 1) Where did the author get the 4? The two largest numbers are 5 and 7 and the difference can only be 2 or -2.
Question 2) Is there a way to solve this problem using algebra? Or is that even expected here?
There are four one digit prime numbers: $2,~3,~5,~\&~7$
Read again carefully the wording. Then repost.


3. Originally Posted by allegansveritatem
This simple problem is from a series of review problems:
problem.jpg

Here is the book's solution:
solution.PNG

Here is what I did:
my solution.jpg

Question 1) Where did the author get the 4? The two largest numbers are 5 and 7 and the difference can only be 2 or -2.

Question 2) Is there a way to solve this problem using algebra? Or is that even expected here?
This is not an algebra problem. I'd say it's just testing general reasoning skills.

You can't assume the numbers are 2, 5, 7. What other possibilities are there for the three numbers?

4. Originally Posted by Dr.Peterson
This is not an algebra problem. I'd say it's just testing general reasoning skills.

You can't assume the numbers are 2, 5, 7. What other possibilities are there for the three numbers?
I'm afraid I ASSUMED that the two digits, the ones other than 2, had to be contiguous. Don't ask me why. I suppose it is because there is a category of word problem where we are asked to find contiguous even or odd digits that have such and such addends and/or subtrahends. A good motto when dealing with word problems: Assume nothing!

5. Originally Posted by pka
There are four one digit prime numbers: $2,~3,~5,~\&~7$
Read again carefully the wording. Then repost.

I catch your drift. I assumed certain conditions that did not warrant assumption.

6. Originally Posted by allegansveritatem
I catch your drift. I assumed certain conditions that did not warrant assumption.
Each of the three numbers is prime & one is even.
Thus the selection is $\{2,3,5\},~\{2,3,7\},\text{ or }\{2,5,7\}$

$7-3=4,\text{ or }7-5=2$

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