Number Properties - 4th Edition - Chapter 8 - pg. 100

[geoffrey.baszczuk]

The example given on page 100 of the 4th edition of the Number Properties guide states the following:

If n is an integer and n^3 is between 1 and 100, inclusive, what is the value of n?

(1) n=2k + 1, where k is an integer.
(2) n is a prime number.

Why is statement 1, alone, not sufficient?

The initial question states that n is an integer, and that n^3 is between 1 and 100. Therefore, as the book states, we can have 1, 2, 3, or 4.

Because n has to be an odd number (because of the 2(variable) + 1 statement) in statement 1, that leaves us with 1 or 3 to work with. Taking the smallest integer for k (1), it would be impossible to have n = 1. The only answer is 3, taking what we have from the original question and the information placed in statement 1.

Am I missing something? To me, statement 1 is sufficient.

[gokul_nair1984]

You are absolutely right, if this is what is printed in the book , then this is erroneous!

I would like to further elaborate on the stem:

n is an integer and n^3 is between 1 and 100.

This means n can be only 2, 3 or 4. ( 1 is out of consideration because n^3 has to be between 1&100)

First statement clearly states that n has to be odd. Thus 3 is the only option. Hence A is correct

[tim]

geoffrey, you are absolutely wrong when you state that the smallest integer is 1. k could be 0, leaving us with n=1..

gokul, you are wrong because you ignored the fact that the problem includes the word "inclusive"..

try to pay more attention, guys.. :)

[gokul_nair1984]

Oops! Thank you

[tim]

no problem!