I think this was posted in a recent thread.djsir007 wrote:3^x-3^x-1=162, then x(x-1)=
12
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81
3^(x-1) [ 3 - 1] = 162
3^(x-1) = 81 = 3^4
x-1 = 4
x(x-1) = 20
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jayhawk2001
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3^(x-1) [ 3 - 1] = 162
3^(x-1) = 81 = 3^4
x-1 = 4
x(x-1) = 20
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Cybermusings
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Scott@TargetTestPrep
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We can simplify the left side of the equation by factoring out a common 3^x from both terms, and then factor 162 as 3^4 * 2^1. Then we have:djsir007 wrote:3^x-3^x-1=162, then x(x-1)=
12
16
20
30
81
3^x - 3^x * 3^-1 = 3^4 * 2^1
3^x(1 - 3^-1) = 3^4 * 2^1
On the left side, note that the expression 1 - 3^-1 = 1 - â…“ = â…”. We now have:
3^x(2/3) = 3^4 * 2^1
3^x = (3^4 * 2)(3/2)
3^x = 3^4 *3
3^x = 3^5
x = 5
So, x(x-1) = 5(4) = 20.
Alternate Solution:
Note that 3^x = 3 * 3^(x - 1). Then the left hand side of the equation becomes:
3^x - 3^(x - 1) = 3 * 3^(x - 1) - 3^(x - 1)
Let's factor the common 3^(x - 1):
3 * 3^(x - 1) - 3^(x - 1) = 162
3^(x - 1)(3 - 1) = 162
3^(x - 1)(2) = 162
3^(x - 1) = 81
3^(x - 1) = 3^4
x - 1 = 4
x = 5
Then, x(x - 1) = 20.
Answer: C
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Hi All,
We're told that 3^(X) - 3^(X-1) = 162. We're asked for the value of then (X)(X-1). This question can be solved rather easily with a bit of 'brute force' arithmetic.
Since we're dealing with 'powers of 3', let's map out the first several values:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
We're subtracting two consecutive powers of 3 and ending up with 162. Looking at the list so far, we have an obvious 'pair' of values that fits what we're looking for:
3^5 and 3^4
243 - 81 = 162
Thus, X = 5 and the answer to the question is (5)(5-1) = 20
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that 3^(X) - 3^(X-1) = 162. We're asked for the value of then (X)(X-1). This question can be solved rather easily with a bit of 'brute force' arithmetic.
Since we're dealing with 'powers of 3', let's map out the first several values:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
We're subtracting two consecutive powers of 3 and ending up with 162. Looking at the list so far, we have an obvious 'pair' of values that fits what we're looking for:
3^5 and 3^4
243 - 81 = 162
Thus, X = 5 and the answer to the question is (5)(5-1) = 20
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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fskilnik@GMATH
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\[? = x\left( {x - 1} \right)\]djsir007 wrote:3^x-3^(x-1)=162, then x(x-1)=
12
16
20
30
81
\[\left. \begin{gathered}
{3^x} - {3^{x - 1}} = {3^{x - 1}}\left( {3 - 1} \right)\,\,\, \hfill \\
162 = 2 \cdot 81 = 2 \cdot {3^4} \hfill \\
\end{gathered} \right\}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{stem}}} \,\,\,\,\,\,\,{3^{x - 1}} = {3^4}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{3}}\,\, \notin \,\,\left\{ {0,1, - 1} \right\}} \,\,\,\,\,\,\,x - 1 = 4\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 20\,\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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