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Difficulty:
5%
(low)
Question Stats:
87% (01:06) correct
13%
(01:13)
wrong
based on 126
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If a, b, and c are positive and \(a= \frac{b}{\sqrt{c}}\), what is the value of c ?
(1) \(c > a + b\)
(2) \(\frac{a}{b}\)= \(\frac{1}{4}\)
(1) \(c > a + b\)
(2) \(\frac{a}{b}\)= \(\frac{1}{4}\)
21 Jul 2014, 22:19
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If a, b, and c are positive and a= b/\sqrt{c} ,what is the value of c ?
1) c > a + b
2) \frac{a}{b}= \frac{1}{4}
Here's how I address this question:
First start with statement 1 by itself. Does it answer "what is the value of C?" Well let's try plugging in some numbers. If C > a+b, all three are positive, and a = b/\sqrt{c}, then I'm going to try to plug in: b = 10; a = 1. The statement shows that c = 100. Now I'm going to try a = 1; b = 100. The statement shows that c = 10,000. Since we don't have a consistent answer for what is the value of C, we know that statement one is not sufficient. If we know that statement one is not sufficient, we can rule out answer choices A and D.
Now let's do statement 2 by itself. If we know that \frac{a}{b}= \frac{1}{4}; then we know there is a fixed ratio between a and b. In our previous plugging in, we didn't follow this. I like to take the simplest plug in value to start: a = 1; b = 4. If that is true, then c = 16. That works. Now to see if we can disprove it. If we make a = 2; b = 8, then c = 16. Okay, so c stayed the same. Let's try one more. a=3; b=12, then c = 16. Okay, it looks like no matter what we do, c = 16, so statement 2 by itself is sufficient to answer the question.
The correct answer is therefore B.
1) c > a + b
2) \frac{a}{b}= \frac{1}{4}
Here's how I address this question:
First start with statement 1 by itself. Does it answer "what is the value of C?" Well let's try plugging in some numbers. If C > a+b, all three are positive, and a = b/\sqrt{c}, then I'm going to try to plug in: b = 10; a = 1. The statement shows that c = 100. Now I'm going to try a = 1; b = 100. The statement shows that c = 10,000. Since we don't have a consistent answer for what is the value of C, we know that statement one is not sufficient. If we know that statement one is not sufficient, we can rule out answer choices A and D.
Now let's do statement 2 by itself. If we know that \frac{a}{b}= \frac{1}{4}; then we know there is a fixed ratio between a and b. In our previous plugging in, we didn't follow this. I like to take the simplest plug in value to start: a = 1; b = 4. If that is true, then c = 16. That works. Now to see if we can disprove it. If we make a = 2; b = 8, then c = 16. Okay, so c stayed the same. Let's try one more. a=3; b=12, then c = 16. Okay, it looks like no matter what we do, c = 16, so statement 2 by itself is sufficient to answer the question.
The correct answer is therefore B.
22 Jul 2014, 03:13
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Bookmarks
If a, b, and c are positive and \(a= \frac{b}{\sqrt{c}}\), what is the value of c ?
\(a= \frac{b}{\sqrt{c}}\) --> \(\sqrt{c}=\frac{b}{a}\) --> \(c=(\frac{b}{a})^2\)
(1) \(c > a + b\) --> we cannot get the ratio of b to a from this. Not sufficient.
(2) \(\frac{a}{b}\)= \(\frac{1}{4}\) --> b/a = 4. Sufficient.
Answer: B.
\(a= \frac{b}{\sqrt{c}}\) --> \(\sqrt{c}=\frac{b}{a}\) --> \(c=(\frac{b}{a})^2\)
(1) \(c > a + b\) --> we cannot get the ratio of b to a from this. Not sufficient.
(2) \(\frac{a}{b}\)= \(\frac{1}{4}\) --> b/a = 4. Sufficient.
Answer: B.
