MHB Uncovering the Hidden Simplicity of Similar Triangles

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The discussion focuses on a common GRE exam question involving similar triangles, specifically the equation $\dfrac{800}{7000}=\dfrac{x}{1400}$. Participants highlight that the problem appears more complex than it is, emphasizing the simplification process that leads to the solution. By reducing the fractions step-by-step, they demonstrate that the answer is x=160. The conversation critiques those who overcomplicate the problem by relying on calculators instead of recognizing the simpler approach. Ultimately, the thread underscores the importance of understanding the underlying simplicity in similar triangle problems.
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This seems to be rather common GRE Exam Question
Which appears to harder that what it is
It looks like a similar triagle solution
$\dfrac{800}{7000}=\dfrac{x}{1400}$
 
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karush said:
This seems to be rather common GRE Exam Question
Which appears to harder that what it is
It looks like a similar triagle solution
$\dfrac{800}{7000}=\dfrac{x}{1400}$

800/7000 = x/1400

It's a little bit of smoke.

80/700 = x/1400

8/70 = x/1400

8/7 = x/140

8/1 = x/20

Look easier?

Anyone whose first move is to produce 112,000 = 700x simply isn't paying attention.
 
"Anyone whose first move is to produce 112,000 = 700x" solves problems like this by immediately plugging numbers into a calculator!​
 
tkhunny said:
800/7000 = x/1400

It's a little bit of smoke.

80/700 = x/1400

8/70 = x/1400

8/7 = x/140

8/1 = x/20

Look easier?

Anyone whose first move is to produce 112,000 = 700x simply isn't paying attention.
actually the answer is
x=160
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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