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# If a, b, and c are positive integers, is b between a and c?

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Re: If a, b, and c are positive integers, is b between a and c? [#permalink]
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Thanks Karishma. I felt good answering this particular question correctly because when I first read the question I said to myself, "Hold on! This question doesn't need any calculations at all! Just visualize the points on the number line and you are done!"
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Re: If a, b, and c are positive integers, is b between a and c? [#permalink]
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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.

check this out:

stmt1: b= a+3, b= c-8
now place them in order a,b,c in terms of b => b-3, b , b+8 sufficient => B, C, E ruled out
Stmt2: c= B+5, c = a+8 equate them a+3 = b now again write them all in terms of A

a, a+3,a+8 again suff, so D as A is ruled out

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Re: If a, b, and c are positive integers, is b between a and c? [#permalink]
VeritasPrepKarishma wrote:
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)

Your explanations are ALWAYS Awesome - Gold Standard! Thanks Karishma
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Re: If a, b, and c are positive integers, is b between a and c? [#permalink]
VeritasPrepKarishma wrote:

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!

Hi Karishma,
The stem requires that a, b, and c are positive integers, but that info isn't used much, is it? Even if the they are not, the correct answer will still be D. Is that right?

I drew a number line for this question and found that it doesn't matter whether a, b, and c are positive integers or not. Is my reasoning correct? Thank you very much!
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Re: If a, b, and c are positive integers, is b between a and c? [#permalink]
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truongynhi wrote:
VeritasPrepKarishma wrote:

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!

Hi Karishma,
The stem requires that a, b, and c are positive integers, but that info isn't used much, is it? Even if the they are not, the correct answer will still be D. Is that right?

I drew a number line for this question and found that it doesn't matter whether a, b, and c are positive integers or not. Is my reasoning correct? Thank you very much!

Yes, it doesn't matter at all. Where exactly then numbers are on the number line is immaterial. All we care about is the relative placement of the numbers. But when we solve questions using algebra, we need to ensure that negative numbers/fractions etc will not affect our solution. A question with "positive integers" puts us at ease immediately.
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Re: If a, b, and c are positive integers, is b between a and c? [#permalink]
The Best approach to solve these kind of questions is plot the number line and then mark the positions as additional data is being provided.
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Re: If a, b, and c are positive integers, is b between a and c? [#permalink]
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Re: If a, b, and c are positive integers, is b between a and c? [#permalink]
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