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Re: Absolute Value PS [#permalink]
09 Jan 2013, 09:33

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sambam wrote:

Given that w = |x| and x = 2^b – (8^30 + 8^5), which of the following values for b yields the lowest value for w?

(A) 35 (B) 90 (C) 91 (D) 95 (E) 105

The w=|x| implies that we are not bothered about the sign. The expression can be rewritten as x=2^b - (2^{90} + 2^{15})

Now pick up the available answer choices. For b=35, x=2^{35} - (2^{90} + 2^{15}) or x=2^{35} - 2^{90}- 2^{15} or x= 2^{15} (2^{20} -2^{70} -1). Since 1 is too less if compared to other available values, hence we neglect it. Now the expression becomes x=2^{15}(2^{20}-2^{70}) or x=2^{15} * 2^{20} * (-2^{50})

For b=90, Same approach is applied and x comes out to be as -2^{15}.

For b=91, Same approach is applied and x comes out as 2^{15} * 2^{75}

For remaining answer choices, x would be even more. Hence if b=90, we have the smallest value of |w|. hence +1B _________________

Look at the answer choices. Eliminate all except those that are close to 2^90

You only have B and C: b=90 or 91

Now look again at the question: is says w = |x|. Coincidence? Never!

In fact you can have here a negative number because you have |x|.

Therefore bewteen 2^(15) (in fact it is - 2^(15) but as I said you are dealing with absolute value here so it is 2^(15)) and 2^(91) - 2^90 + 2^(15) which is the smallest?

2^(15) for sure (there is a huge difference here)!