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Factor primes of 450. 5, 5, 2, 3, 3. Three numbers could be 25, 9, 2. Check to see if LCM of these three is 450. Yep. Check the inequality expression. Yep. Range of these numbers = 23â€¦

a,b and c are positive integers such that abc= 450 and a+4<b+2<c. If T is the set of all possible values of a+b+c, what is the range of T?

(A) 50 (B) 54 (C) 60 (D) 68 (E) 72

We are told that a,b,c are integers abc=450 and that a+2<b<c-2, In other words a<b<c and at least two integers are between a and b and at least integers are between b and c.

How can we maximize a+b+c? By having a,b, and c as disperse as possible, so that c is really big. 450=2*3^2*5^2, so if a=1, b=5, c=90 we get a+b+c=96.

How can we mimimize a+b+c? By having a,b and c as close together as possible!

Can a=5? b*c would then be 2*3^2*5 The lowest possible value of b (remember b>a+2) would be 9. However in that case c would be 10, which is not possible, as c>b+2.

Can a=3? b*c would then be 2*3*5^2 b could be 6 and c would then be 25 (a+b+c=34) or b could be 10 and c would then be 15 (a+b+c=28).

If a=2 , b*c=3^2*5^2, every possible (b,c) for a=2 would yield a value of a+b+c>28.

So, the mimimum and maximum values of a+b+c will be 28 and 96 respectively and so the range of T is 68. Sorry for the trouble I had in getting the question written properly, but I think it was worth the wait. I daresay this is one of my better questions. Do you agree?

Yes. They're for a book I'm putting together, albeit slowly. Contributions are most welcome, as my creativity comes in spurts. I have 250 questions so far, and IÂ´d like 500 to make a really good book. Do you think such a book would have a market?

Yes, I think so especially if explanations are clear within it, if concepts are well isolated and applicable to real GMAT questions and if questions are ordered in level of difficulties like inside the OG.

An hard part is how to market it Such new book needs to have enough of credibility to compete other big names After all, why not trough GMATClub members... It could be

For the book to sell, it would have to be relevant to a GMAT test taker. So if conceptually it covers most of the things that are tested on the GMAT then it would do well. For mass appeal it should probably have a graded level of difficulty, starting from easier problems and then moving on to tougher ones.

Need not be a GMAT book at all! These are lovely questions, and there are lots of math freaks and students out there.

Heck, I'd buy one for my kid

Luv your problems. And let us know when the book is out.
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

Graded difficulty is a double-edged sword. I sometimes think that prior knowledge of the difficulty conditions how we think (especially for DS). Yet for others, it helps to use their time more wisely.