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Kaplan Diag quiz problem

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by AA11 » Fri Jul 30, 2010 11:41 pm
If b< 1 and 2x-b=0, which of the following must be true?

A. x< -2
B. x < 3

I'm confused between these 2. The answer according to the Kaplan Diagnostic Quiz is x<3. However in that case if we take x=2, then b=4 so b is not less than 1. Shouldn't the answer be x<-2?
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by Rahul@gurome » Sat Jul 31, 2010 12:40 am
Solution:
It is given that b<1.
Since 2x - b = 0, we have 2x = b or 2x < 1 or x < 1/2.

x<1/2 does not necessarily mean that x < -2.
For example x = 1/4 is less than 1/2 but more than -2.
But x = -3 is less than 1/2 and also less than -2.
Or A. is not always true.

Now if x<1/2, x has to be less than 3.
So B. is always true.
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by sanju09 » Sat Jul 31, 2010 3:56 am
AA11 wrote:If b< 1 and 2x-b=0, which of the following must be true?

A. x< -2
B. x < 3

I'm confused between these 2. The answer according to the Kaplan Diagnostic Quiz is x<3. However in that case if we take x=2, then b=4 so b is not less than 1. Shouldn't the answer be x<-2?
You are not free to take x = 2 when b< 1 and 2x-b=0, the info-combo makes us take x < 1/2, and anything less than 1/2 isn't necessarily less than -2, but is surely less than 3, as truly said by Rahul@gurome.
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