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# Is x negative? (1) n*n*n(1-x*x) < 0 (2) x*x-1 < 0 The

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Is x negative? (1) n*n*n(1-x*x) < 0 (2) x*x-1 < 0 The [#permalink]  19 Sep 2003, 07:36
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1. Is x negative?

(1) n*n*n(1-x*x) < 0
(2) x*x-1 < 0

2. What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.

Thanks:)[/code][/quote]
CEO
Joined: 15 Aug 2003
Posts: 3469
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Joviest wrote:

(1) n*n*n(1-x*x) < 0

Here (1-x^2) can be greater than or less than 0

So cant say

(2) x*x-1 < 0

x^2 -1 < 0

x^2 < 1

Gives x >-1 or x<1 again cant say yes or no

Combine, we now know from 2 that 1-x^2 > 0

So that means x^2 <1 which means x>-1 and x<1

2. What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.

Thanks:)[/code]
[/quote]

Its a bit confusing the way you have written the powers ...

(1) n*n*n(1-x*x) < 0

Here (1-x^2) can be greater than or less than 0

So cant say

(2) x*x-1 < 0

x^2 -1 < 0

x^2 < 1

Gives x >-1 or x<1 again cant say yes or no..insufficient

Combine, we now know from 2 that 1-x^2 > 0

but that still doesnt give the answer

I think E

2. What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively.

you can take any set lb,bh,lh ..it will get you the same answer

b*h = 15
l*h = 24

not sufficient three unknowns ,two equations.

(2) Each of two opposite faces of the solid has area 40.

l*b = 40

Not sufficient

Combine , three unknowns, three equations, sufficient...C
Intern
Joined: 19 Sep 2003
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Location: NYC
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I think the answer to the second question is C because...

If sides are adjacent, it means they share the length value of one side.
If sides are 15 and 24, the only common denominators are 3 and 1.

If the common leg is 3....
8 x 3 (24=area)
5 x 3 (15=area)
VOLUME = 8 x 3 x 5 = 120

if the common leg is 1...
24 x 1 (24=area)
15 x 1 (15=area)
VOLUME = 24 x 1 x 15= 360

A tells you it's either 120 or 360.

B tells you an area of a side is 40. That's impossible under the 2nd A scenario. The first A scenario fits right in.

you have side areas of
24 3x8
15 3x5
40 8x5

I'm not sure yet about #1
Intern
Joined: 13 Sep 2003
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agree with praet on the first one..ans is E.
consider the value of x=-1/2 and x= 1/2.

in both cases x2 < 1.
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