What is the range of values of b for which 1 - b^8

Question

What is the range of values of b for which 1 - b^8 < 0 ?

(A) b < -1 or b > 1
(B) -1 <= b <= 1
(C) b > 1
(D) b < -1
(E) 0 <= b <= 1

Which answer choices complement one another--meaning they aggregately describe the entire range of numbers?

Solution

Show Spoiler

Answer choices (A) and (B) cover the whole range of numbers. The significance of this is that the GMAT questions tend to be answered by one of the complementary answers.

In this particular case, answer (A) is correct.

Occasionally, some answer choices combine to describe all the numbers that a solution could contain. Knowing that the GMAT typically makes one of these answers the correct one can save time.

A similar phenomenon occurs frequently with probability problems, percent problems and proportion problems. When answers on these problems add up to 1 or 100% often times one of those answers is the correct one.

Show Answer

Official Answer

A

gmat1220 · Answer

Stem can be rephrased as -
b^8 - 1 > 0

Hence b > 1 or b < -1

subhashghosh · Answer

The answer is A, because b^8 > 1 for this to be true. Clearly, only A fulfils this.

IanStewart · Answer

I often read prep books recommend certain guessing strategies, but they rarely provide any evidence that these strategies actually work. I did a test - it doesn't take long, so you may wish to replicate it - where I went through every PS question in both OG12 and the new Quant Review book. I identified every question which had 'twin' answer choices, that is:

* a pair of answers which add to 100% or to 1 in a ratio/percent/probability question
* an answer choice which was the negative of another answer choice
* an answer choice which was the reciprocal of another answer choice

For questions with answer choices like the following:

A) 20%
B) 40%
C) 50%
D) 60%
E) 80%

where answer C is its own 'twin', I assumed the test taker who is looking for twin answers will choose one of the other more obvious twins, though if I considered C to be a twin, it wouldn't materially affect my findings. I then worked out how many right answers someone would get if they always guessed one of the twin answer choices. For example, if there were 2 twins, and one of them was correct, the test taker could expect to get the question right 1/2 = 0.5 times. If, however, there were 2 twins and neither was correct, the test taker guessing one of the twin choices will never get the question right. I then added up the number of correct answer one would get by always guessing one of the twins choices, and how many questions one would get right by guessing purely randomly.

So, of the 406 PS questions in the two official guides, 54 have 'twin' answer choices. It isn't all that common in the first place to encounter twins, so it's debatable whether it matters if a test taker has a guessing strategy for such questions; on an average GMAT, one will only encounter two or three questions with twin choices. More importantly, if you were to guess randomly at those 54 questions, you'd expect to get 10.8 correct answers. If you always guess one of the 'twin' choices, you'd get 10.75 correct answers. So identifying twin choices as a basis for a GMAT guessing strategy is completely pointless; it's no better than guessing at random. For every question like Q223 in OG12 where it seems useful to guess a 'twin, there are questions like Q220 or Q187 where the twins are all wrong answers.

GMAT question designers are fully aware of the simplistic guessing strategies recommended by prep books, and they go to great lengths to ensure that test takers are not rewarded simply for reading one prep book instead of another. If you have no understanding of a GMAT question, there is no strategy based on looking at the answer choices alone that will make any meaningful difference.

gmat1220 · Answer

I have been advised strictly to think critically and calculate less. But that does not condone random guessing. So see Ian's point.

I am big fan of guessing - in fact guessed a lot in my undergrad classes and never rewarded for that strategy. However GMAT allows some kind of "educated guessing". And I employ that based on question. If I know I am not gonna make the time in 120 secs lap - I prefer using critical thinking than math. Relying on intuition is best when you know the answer - somehow cannot explain why or what. And intuition pays off. But guessing has drawbacks too ;-)

Temurkhon · Answer

b^8>1
|b|>1, bec. 8 is even
b>1 or b<-1

A

bumpbot · Answer

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What is the range of values of b for which 1 - b^8 < 0 ?

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