Advanced Gmat quant - chapter 4, question 9 - CONFUSING

[ozlen_bilen]

Hi,

I do not understand the explanation given in your book for the following data sufficiency question.

If a ≠ 0, is 1/a > a/b4+3
(1) a2 = b2
(2) a2 = b4

In the book it is said that the 1st answer choice is sufficient because b2 must be positive, so a is positive. I do not understand this part, why a should be positive and not negative.
Also, in the 2nd answer choice, this is the case; a2 = b4 can be true with positive or negative values of a.
So I do not understand why in first choice a must be absolutely positIve while it can be negative in the 2nd one.

Thank you for your clarification.

[StaceyKoprince]

It's helpful if you can give us the page number, too - just makes it easier to look up the problem. Thanks!

When typing things with exponents, use this symbol to indicate the exponent: ^

So the problem reads:
If a ≠ 0, is 1/a > a/[(b^4)+3]
(1) a^2 = b^2
(2) a^2 = b^4

Okay, now here's the answer to your question. There's a typo in the problem! The first statement is supposed to say "a = b^2" NOT "a^2 = b^2."

Does that make more sense now? :)

You can find the full error list here:
http://www.manhattangmat.com/errata-adv-quant-4th.cfm

And sorry for the error! It was probably driving you crazy.

[MariaK176]

Hi, I also wanted to ask a question about the explanation.

I don't understand why if a>0, then 1/a > a/(b^4 + 3) -> b^4 +3 >a^2. I feel like it is related to P. 113 #4 that says that inequalities involving a variable in the denominator have two possibilities. When plugging in, it makes a bit more sense- given 1/y <x. If y<0, say -1/2 and x=1, -2<1, but if y>0, it must be that y=2, and x=1 for the inequality to hold. But I can't quite figure out why that makes sense in this problem.


Thank you in advance!

[RonPurewal]

you are correct to be concerned in general with the signs of the denominators -- but, IN THAT EXAMPLE, both denominators must be positive.

• b^4 is 0 or greater, since it's an even power. (think about how squares behave -- squares can't be negative. for the same reason, other even powers can't be negative, either.)
thus, b^4 + 3 is at least 3, so it's positive.

• you are given that a > 0, so, a is positive.

thus there are no other cases to consider.