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MartyMurray
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Juan bought some paperback books that cost $8 each and some 11 May 2024, 09:03
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sayan640
I did not consider the total to be exactly 260 ; It is actually less than 260.
8p +25h < 260
MartyMurray

sayan640
KarishmaB Can you please share the link where you discussed this question ? The previous link is no longer available.
MartyMurray , IanStewart Can you please help too ?­
Using statement , if I start plugging in values into this inequality
8p + 25h < 260
for h = 4 , 8p <260 -100
p<20 
So h=4 satisfies while no other value of h gives an integer value of p where p = number of paper back books and h = number of hardcover books.
I am finding  a single solution from this inequality  i.e 8p + 25h < 260 . Number of books cant be fraction.
Why is B not the answer ? Where am I making mistakes ? ­
­You lost track of what you were doing.

You're working with an inequality, but you're treating it as an equation.

Keeping track of what you're doing and executing well is key for getting GMAT Quant questions correct. In other words, it's one thing to understand the math concepts and set things up. You also have to be logical in each step you take.

In this case, the fact that you are dealing with an inequality means that the total doesn't have to be exactly 260.
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­So, then, there are multiple different values that work, right?

The total could be 235, 210, 202, or 185 and still satisfy the inequality. So, h doesn't have to be 4.
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Juan bought some paperback books that cost $8 each and some Updated on: 11 May 2024, 09:19
Originally posted by sayan640 on 11 May 2024, 09:06.
Last edited by sayan640 on 11 May 2024, 09:19, edited 1 time in total.
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I dint think about that possibility...I kept myself focussed only on one value.. marty . But in those cases mentioned  by you , p is coming as not an integer but a decimal. How can the number of paper back books be a decimal  value? It has to be integer.­
Can you please cite a pair of values 'p' and 'h' which satisfy this inequality ? Sorry  if I am asking you stupid questions.. Request you to help.­
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I dint think about that possibility...I kept myself focussed only on one value.. marty . But in those cases mentioned  by you , p is coming as not an integer but a decimal. How can the number of paper back books be a decimal  value? It has to be integer.­
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­235 = 8 * 20 + 25 * 3

210 = 8 * 20 + 25 * 2

202 = 8 * 19 + 25 * 2
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Juan bought some paperback books that cost $8 each and some Updated on: 11 May 2024, 09:45
Originally posted by sayan640 on 11 May 2024, 09:27.
Last edited by sayan640 on 11 May 2024, 09:45, edited 1 time in total.
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Thank you marty . It clarified my doubt. Actually in my sub conscious mind , I was using that one number 260 only and was trying to crunch values .
How do I get good with numbers so that all these possibilities start appearing in front of eyes naturally ? Any tips to think of these scenarios ?
May be I should never consider an inequality to give me two certain values of the variables in it . Right ?

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An equation can give me two definite values of variables in it.
But an inequality in all probability will not get me two definite values of the variables in it. It will always get me multiple values . Please advise marty

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Thank you marty once again and sorry for troubling you with stupid questions.

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KarishmaB Can you please share the link where you discussed this question ? The previous link is no longer available.
MartyMurray , IanStewart Can you please help too ?­
Using statement , if I start plugging in values into this inequality
8p + 25h < 260
for h = 4 , 8p <260 -100
p<20 
So h=4 satisfies while no other value of h gives an integer value of p where p = number of paper back books and h = number of hardcover books.
I am finding  a single solution from this inequality  i.e 8p + 25h < 260 . Number of books cant be fraction.
Why is B not the answer ? Where am I making mistakes ? ­
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­Have edited the link above. I don't have the same post but a question similar to this is discussed here:https://anaprep.com/algebra-equations-or-inequalities-a-lesson-in-active-passive/

Statement 2 alone is not sufficient.
8p + 25h < 260
If h = 4, p < 20 
If h = 3, p < 23
If h = 2, p < 26
etc.
So lots of cases are possible.

Why should h be 4 only without statement 1?

 
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Thank you KarishmaB , I got my doubts cleared .
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