jmehrabi wrote:
If a,b, and c are positive integers, is b between a and c?
1) b is 3 greater than a, and b is 5 less than c
2) c is 5 greater than b, and c is 8 greater than a
I started solving this question by translating each statement
For 1 I wrote: b=3 + a and b=c-5
For 2 I wrote: c=5 + b and c=8 + a
I tried substitution but got stuck and did not know where I was going from there. What type of problem is this and if you had to guess what level? Thanks for the explanation in advance.
Don't feel obligated to use algebra in every question. Many of these 'is this number less than that number' questions can be done using the number line. Btw, the solution given above is correct and the algebraic way.
This question is quite straight forward since they have given that a, b and c are positive integers. No confusions!
'Is b between a and c?' essentially means 'does b lie between a and c on the number line?'
1) b is 3 greater than a, and b is 5 less than c
This means 'b' is 3 steps to the right of 'a' but 5 steps to the left of 'c' on the number line. It must lie between 'a' and 'c'. (draw a number line if it is not clear)
2) c is 5 greater than b, and c is 8 greater than a
'c' is 5 steps to the right of 'b' which means 'b' is 5 steps to the left of 'c'. 'c' is 8 steps to the right of 'a' which means 'a' is 8 steps to the left of 'c'. 'a' is further to the left of 'c' than 'b'. So 'b' must be between 'a' and 'c'.
So (D)