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26 May 2025, 08:55
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (01:10) correct
0% (00:00) wrong based on 3 sessions
History
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Not Attempted Yet
If \(a > 1,\) the ratio of \(2a + 6\) to \(a^2 + 2a - 3\) is
A. \(2a\)
B. \(a + 3\)
C. \(\frac{2}{a-1}\)
D. \(\frac{2a}{3(3-a)}\)
E. \(\frac{a-1}{2}\)
A. \(2a\)
B. \(a + 3\)
C. \(\frac{2}{a-1}\)
D. \(\frac{2a}{3(3-a)}\)
E. \(\frac{a-1}{2}\)
31 May 2025, 01:56
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OE
You can simplify the process by replacing the variable a with a number in each algebraic expression. Since a has to be greater than 1, why not pick 2? Then the expression 2a + 6 becomes \(2(2) + 6, or 10.\) The expression \(a^2 + 2a - 3\) becomes \(2^2 + 2(2) - 3 = 4 + 4 - 3 = 5\)
So now the question reads, “The ratio of 10 to 5 is what?” That’s easy enough to answer: 10:5 is the same as 10/5 or 2. Now you can just eliminate any answer choice that doesn’t give a result of 2 when you substitute 2 for a. Choice (A) gives you 2(2), or 4, so discard it. Choice (B) results in 5—also not what you want. Choice (C) yields 2/1 or 2. That looks good, but you can’t stop here.
If another answer choice gives you a result of 2, you will have to pick another number for a and reevaluate the expressions in the question stem and the choices that worked when you let a = 2.
Choice (D) gives you \(\frac{2(2)}{3(3-2)}\), or \(\frac{4}{3}\) so eliminate choice (D).
Choice (E) gives you \(\frac{2-1}{2},\) or \(\frac{1}{2}\) so discard \(choice (E).\)
Fortunately, in this case, only choice (C) works out to equal 2, so it is the correct answer. But remember: when using the Picking Numbers strategy, always check every answer choice to make sure you haven’t chosen a number that works for more than one answer choice.
Answer: C
You can simplify the process by replacing the variable a with a number in each algebraic expression. Since a has to be greater than 1, why not pick 2? Then the expression 2a + 6 becomes \(2(2) + 6, or 10.\) The expression \(a^2 + 2a - 3\) becomes \(2^2 + 2(2) - 3 = 4 + 4 - 3 = 5\)
So now the question reads, “The ratio of 10 to 5 is what?” That’s easy enough to answer: 10:5 is the same as 10/5 or 2. Now you can just eliminate any answer choice that doesn’t give a result of 2 when you substitute 2 for a. Choice (A) gives you 2(2), or 4, so discard it. Choice (B) results in 5—also not what you want. Choice (C) yields 2/1 or 2. That looks good, but you can’t stop here.
If another answer choice gives you a result of 2, you will have to pick another number for a and reevaluate the expressions in the question stem and the choices that worked when you let a = 2.
Choice (D) gives you \(\frac{2(2)}{3(3-2)}\), or \(\frac{4}{3}\) so eliminate choice (D).
Choice (E) gives you \(\frac{2-1}{2},\) or \(\frac{1}{2}\) so discard \(choice (E).\)
Fortunately, in this case, only choice (C) works out to equal 2, so it is the correct answer. But remember: when using the Picking Numbers strategy, always check every answer choice to make sure you haven’t chosen a number that works for more than one answer choice.
Answer: C
