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

allegansveritatem

Junior Member
Joined
Jan 10, 2018
Messages
240
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?
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,684
This simple problem is from a series of review problems:
View attachment 10597

Here is the book's solution:
View attachment 10598
Here is what I did:
View attachment 10599
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: \(\displaystyle 2,~3,~5,~\&~7\)
Read again carefully the wording. Then repost.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
2,735
This simple problem is from a series of review problems:
View attachment 10597

Here is the book's solution:
View attachment 10598

Here is what I did:
View attachment 10599

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?
 

allegansveritatem

Junior Member
Joined
Jan 10, 2018
Messages
240
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!
 

allegansveritatem

Junior Member
Joined
Jan 10, 2018
Messages
240
There are four one digit prime numbers: \(\displaystyle 2,~3,~5,~\&~7\)
Read again carefully the wording. Then repost.
I catch your drift. I assumed certain conditions that did not warrant assumption.
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,684
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 \(\displaystyle \{2,3,5\},~\{2,3,7\},\text{ or }\{2,5,7\}\)

\(\displaystyle 7-3=4,\text{ or }7-5=2\)
 
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