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If a = 3b, b^2 = 2c, 9c = d, then a^2/d =
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17 May 2019, 01:58
17 May 2019, 01:58
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If \(a = 3b\), \(b^2 = 2c\), \(9c = d\), then \(\frac{a^2}{d} =\)
(A) \(\frac{1}{2}\)
(B) \(2\)
(C) \(\frac{10}{3}\)
(D) \(5\)
(E) \(6\)
(A) \(\frac{1}{2}\)
(B) \(2\)
(C) \(\frac{10}{3}\)
(D) \(5\)
(E) \(6\)
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Posts: 186
Given Kudos: 5
Location: United States
GMAT 1: 770 Q51 V44
GRE 1: Q169 V168
WE:Education (Education)
Re: If a = 3b, b^2 = 2c, 9c = d, then a^2/d =
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17 May 2019, 08:07
17 May 2019, 08:07
1
Expert Reply
Quote:
If \(a = 3b\), \(b^2 = 2c\), \(9c = d\), then \(\frac{a^2}{d} =\)
With this many variables in the problem, consider plugging in your own easy value for the foundation variable, if the algebra seems unnecessarily complex. In this case, look to plug in for the non-lonely variable or the only letter that never sits by itself on one side of an = sign. Here, c is the only variable that is never lonely, so pick a number for c that will make the math easy such as 8.
If c = 8, then b^2 = 2(8). So, b^2 = 16.
Now, we'll ignore that in theory this problem doesn't work for one solution since b could be +4 or -4, and assume that the problem is sticking to the positive value since each of the choices is > 0. So, b = 4.
Then, if b = 4, a = 3(4) = 12.
Then, 9c = d. So, 9(8) = d = 72.
Finally, solve for the a^2/d value the problem seeks. So, 12^2/72 = 144/72 = 2. Select Choice B.
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Re: If a = 3b, b^2 = 2c, 9c = d, then a^2/d =
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21 May 2019, 07:13
21 May 2019, 07:13
1
Carcass wrote:
If \(a = 3b\), \(b^2 = 2c\), \(9c = d\), then \(\frac{a^2}{d} =\)
(A) \(\frac{1}{2}\)
(B) \(2\)
(C) \(\frac{10}{3}\)
(D) \(5\)
(E) \(6\)
(A) \(\frac{1}{2}\)
(B) \(2\)
(C) \(\frac{10}{3}\)
(D) \(5\)
(E) \(6\)
Here's an algebraic approach.
If \(a = 3b\), then \(a^2 = (3b)^2 = 9b^2\)
So, we can replace \(a^2\)with \(9b^2\)
Also, since we're told that \(9c = d\), we can replace \(d\) with \(9c\)
We get: \(\frac{a^2}{d} = \frac{9b^2}{9c} = \frac{b^2}{c}\)
Now let's replace that c (in the denominator) with something USEFUL.
We're told that \(b^2 = 2c\), but I'd rather not solve that equation for c (and get a fraction) and then replace the c in the denominator.
Instead, we can make things easier by taking our existing fraction, \(\frac{b^2}{c}\), and multiplying top and bottom by 2 to get an EQUIVALENT fraction \(\frac{2b^2}{2c}\)
Now I can easily replace \(2c\) with \(b^2\) to get: \(\frac{2b^2}{b^2}\), which equals 2
Answer: B
Cheers,
Brent
