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Inequality 2

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by DanaJ » Tue Feb 03, 2009 3:45 am
1. This doesn't help much. This statement is equivalent to 120 < 4^x - 4^(x -1). So you are looking for the difference between two consecutive powers of 4. Just picture this: 4^4 = 256, while 4^3 = 64. The difference between the two is obviously greater than 120 and this gets bigger with bigger powers.

2. x^2 = 36 has two solutions:
a.x = -6
b. x = 6
We cannot tell from 2 alone what is the value of x.

Now, if we put both statements together, what do we get?
Well, let's see:
a. For x = -6, x -1 = -7. 4^(-6) = 1/(4^6) is smth greater than 0 but smaller than 1 and so is 4^(-7) = 1/(4^7). So the difference between these two numbers is obviously not greater than 120.
b. x = 6 is consistent with all the constraints, since 4^6 - 4^5 will be greater than 120.

Answer C.
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by sacx » Tue Feb 03, 2009 4:42 am
where am I going wrong

2. x^2 = 36
x is either -6 or 6
3x will then either be -18 or 18, which are both less than 500

I agree with Dana if the question was asking for the value of x, but the question is asking is 3x <500

Should answer be not B
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by Ian Stewart » Tue Feb 03, 2009 5:18 am
sacx wrote:where am I going wrong

2. x^2 = 36
x is either -6 or 6
3x will then either be -18 or 18, which are both less than 500

I agree with Dana if the question was asking for the value of x, but the question is asking is 3x <500

Should answer be not B
Yes, as the question is written, the answer should be B, for the reasons you mention. I've seen several similar questions, and seeing that the OA is C in the original post, I expect there's a typo in the first post above - it probably should ask "Is 3^x less than 500". If x is indeed intended to be an exponent, then the answer would be C; with both statements you would know that 3^x must be greater than 500, so you would know with certainty that the answer to the question is 'no'. But if the question is actually about 3x, the answer is B.
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by sanju09 » Tue Feb 03, 2009 5:19 am
sacx wrote:where am I going wrong

2. x^2 = 36
x is either -6 or 6
3x will then either be -18 or 18, which are both less than 500

I agree with Dana if the question was asking for the value of x, but the question is asking is 3x <500

Should answer be not B
:roll: IMO B

And I agree with sacx's explanation.
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by DanaJ » Tue Feb 03, 2009 6:58 am
ooops.... Sorry, I was in a hurry... Yes guys you're right...
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by cjb » Wed Feb 04, 2009 12:17 pm
This is how I tackled it (assuming it's about 3^x, not 3x):

From the question:
3^x < 500
implies
x < 6

So we're checking to see if we know that x< 6.


From 1:
4^(x-1) + 120 < 4^x
120 < 3 * 4^(x-1)
40 < 4^(x-1)
x > 2
Insufficient


From 2:
x^2 = 36
x = 6 or x = -6
Insufficient


Combining 1 and 2:
Only x = 6 satisfies both constraints. So it is definitely not the case that x < 6.

Answer C.
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