GRE 5 lb. errata?

[franalej]

Hi,

Apparently, there are two errata in the GRE 5 lb book.

1) Chapter 9: Inequalities and Absolute Values, page 384, excercise 24:

The question states that the "x is an integer such that
-x|x|>4". However, the answer to it on page 398 assumes that "-x|x|>=4", but the question states that the inequality is only >, not >= as the answer assumes. Is there something wrong here?

2) Chapter 9: Inequatities and Absolute Values, page 384, excercise 26:

The question states that "x and y are positive numbers such that x+y+z<1 and xy=1".

Quantity A: z

Quantity B: -1

The answer to it on page 398 assumes that the positive numbers are only "integers", but the question does not mention integers, mentions "numbers". Your answer is given assuming that since only integers can be used, then the minimum value of x+y is 2 (since either x and y are both equal to 1 or they are reciprocals), and therefore the answer should be B, since z<1-2 = z<-1.

However, if the numbers assumed are also positive fractions, then x+y=1 could mean 0.1(1/0.1)=1, since xy=1, and in terms of the question, the minimum value of x+y could be 0.2 which would render z<1-0.2 or z<+0.8, which would make quantity A bigger, equal to or lower than quantity B. If this is the case, then the answer should be D, not B.

For theser two questions, is my logic correct and your book is wrong, or am I am wrong?

Thanks.

[tommywallach]

Hey Frana,

Your first example is indeed an error, though as far as I can see it doesn't change the answer. But great catch!

As for the second example, the question never assumes anything is an integer. In fact, it goes out of its way to say the numbers would be reciprocals (one is an integer, and one isn't).

Thanks!

-t

[franalej]

Thanks for the clarification Tommy Wallach. I got it that for question Chapter 9-26, either x is an interger and y is its reciprocal, or the other way around since xy=1. However, one final clarification please. For the answer to Chapter 9-26 on pages 398-399 of the GRE 5 lb book, please could you elucidate the reasoning of the following:

x<1 - (at least 2) then z< at most -1.

The relationship between "at least" 2 and then "at most" -1? Is there a number principle behind going from "at least" to "at most"?

Thanks.

Hey Frana,

Your first example is indeed an error, though as far as I can see it doesn't change the answer. But great catch!

As for the second example, the question never assumes anything is an integer. In fact, it goes out of its way to say the numbers would be reciprocals (one is an integer, and one isn't).

Thanks!

-t

[piyushagrawal4]

Hello,

Even i found an error in question 50, chapter 9.Pg 385). I agree with the answer (C), but why can't (E) also be an answer.

We get , from (C) that :
kn + lm > (mn)^2
and, (mn)^2 >= 0

so, it means that:
kn + lm > 0
i.e. kn > -lm
which is indeed (E)

Therefore, (E) is also a possible answer.

[tommywallach]

Hey Guys,

I know you're going to hate me, but could both of you repost these issues as separate threads? I hope you can understand that if we allow one thread to take on a bunch of different issues, then it stops being useful to other people (very few people will click on this thread, because they think it's just a discussion of two errors in the book). Thanks!

-t