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If x and y are letters which correspond to points on the
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27 Oct 2016, 12:34
27 Oct 2016, 12:34
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If x and y are letters which correspond to points on the number line shown above, which of the following statements must be true?
A. \(x > y\)
B. \(\frac{1}{x} < \frac{1}{y}\)
C. \(\frac{1}{x}*\frac{1}{y} > 9\)
D. \(xy < \frac{1}{3}\)
E. \(x+y > 1\)
Drill 2
Question: 11
Page: 288
Question: 11
Page: 288
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Re: If x and y are letters which correspond to points on the
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27 Oct 2016, 12:38
27 Oct 2016, 12:38
Expert Reply
Explanation
Plug in values for x and y that fit the figure: Try x = \(\frac{1}{6}\) and \(\frac{2}{3}\). Now, plug these
numbers into each of the choices and use POE. Only choice D is correct:
\(\frac{1}{6}*\frac{2}{3}=\frac{2}{18}=\frac{1}{9}\), which is less than \(\frac{1}{9}\).
Hence option D is correct.
Plug in values for x and y that fit the figure: Try x = \(\frac{1}{6}\) and \(\frac{2}{3}\). Now, plug these
numbers into each of the choices and use POE. Only choice D is correct:
\(\frac{1}{6}*\frac{2}{3}=\frac{2}{18}=\frac{1}{9}\), which is less than \(\frac{1}{9}\).
Hence option D is correct.
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Re: If x and y are letters which correspond to points on the
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25 Nov 2016, 16:10
25 Nov 2016, 16:10
sandy wrote:
If x and y are letters which correspond to points on the number line shown above, which of the following statements must be true?
A. \(x > y\)
B. \(\frac{1}{x} < \frac{1}{y}\)
C. \(\frac{1}{x}*\frac{1}{y} > 9\)
D. \(xy < \frac{1}{3}\)
E. \(x+y > 1\)
Show: :: Image
Attachment:
di new.jpg
The correct answer is D. Here's why....
MAIN CONCEPT/RULE:
If I take a positive number N and multiply it by a value that is between 0 and 1, then the product will be LESS THAN N.
For example, if I take 10 and multiply it by 0.8, the product is 8 (which is less than 10)
In the question, we can see that y is between 0 and 1
Also, we can see that the value of x is between 0 and 1
So, according to the above rule, xy must be less than x (since we're multiplying x by a value that is between 0 and 1
So, we know that xy must be less than x (xy < x)
Also, from the diagram, we see that x < 1/3
So, when we combine these inequalities, we get xy < x < 1/3
So, it must be the case that xy < 1/3
Cheers,
Brent
