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18 Oct 2009, 10:50
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If anyone has their OG 12 book handy, I'd like to know if there is a shortcut to solving any problem related to #148 in the Problem Solving section (page 173).
I get about half-way through the simplification/factoring of the initial equation given, but then the "official answer" explains further steps to take that I simply/honestly never would have thought of - especially in a 2-minute time allotment.
In other words, how can I tackle such questions that give you three variables,...then tack on a "x < y" expression....and then list integers as the answers?
Many thanks....
I get about half-way through the simplification/factoring of the initial equation given, but then the "official answer" explains further steps to take that I simply/honestly never would have thought of - especially in a 2-minute time allotment.
In other words, how can I tackle such questions that give you three variables,...then tack on a "x < y" expression....and then list integers as the answers?
Many thanks....
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
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18 Oct 2009, 13:16
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Like you, I got to the k = 10 + 10y/(x+y) step of the simplification and never would have thought to use the inequality algebraically!
If you run across such a problem in PS form, you can always rely on the answers at that point. Since x and y are positive, 10y/(x+y) is positive and the value of k must be greater than 10. Eliminate A.
Likewise, if x < y, then the denominator (x + y) < 2y, so 10y/(x+y) > 10y/2y = 5. Thus, k > 15. Eliminate B and C.
Then ask, could 10y/(x+y) equal 8 or 20? (answers D and E are this much greater than 10, respectively.)
Test D:
10y/(x+y) = 8?
10y=8x+8y?
2y=8x?
(1/4) y = x, which implies that x < y since both are positive.
Therefore, 18 is a possible value of k.
Test E:
10y/(x+y) = 20?
10y=20x+20y?
-10y=20x?
Impossible, since both x and y are positive.
Therefore, 20 is NOT a possible value of k.
Actually, you could test all five answer choices this way, but I just happened to notice the properties that eliminate A, B and C first.
18 Oct 2009, 14:04
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I appreciate your time in the response... I finally figured it out (after reviewing your explanation).... however, this is exactly where I differ from the way GMAC would have me calculate these problems....
I skip this whole part of the process and jump right to pugging-in #'s. It may/may not use up more time, but once I get to the equation:
k -10 = 10y/(x+y)
...given x<y....I just don't think of (x+y) < 2y so 10y/(x+y) > 10y/2y.... etc...etc...
Thanks again!
