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13 Nov 2022, 03:33
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
67% (02:05) correct
33%
(02:02)
wrong
based on 76
sessions
History
Date
Time
Result
Not Attempted Yet
If \(abc ≠ 0\), what is the value of \(\frac{ab}{c}\)?
(1) \(\frac{a}{4} = c^2\) and \(bc = 12\)
(2) \(\frac{a}{b} = \frac{1}{3}\) and \(\frac{a}{c^2} = 4\)
(1) \(\frac{a}{4} = c^2\) and \(bc = 12\)
(2) \(\frac{a}{b} = \frac{1}{3}\) and \(\frac{a}{c^2} = 4\)
13 Nov 2022, 09:27
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Given that \(abc ≠ 0\) and we need to find the value of \(\frac{ab}{c}\)?
STAT 1: \(\frac{a}{4} = c^2\) and \(bc = 12\)
\(\frac{a}{4} = c^2\) => \(\frac{a}{c^2} = 4\) ...(1)
\(bc = 12\) ...(2)
(1) * (2) we get
\(\frac{a}{c^2} * bc = 4 * 12\)
=> \(\frac{ab}{c}\) = 48
=> SUFFICIENT
STAT 2: \(\frac{a}{b} = \frac{1}{3}\) and \(\frac{a}{c^2} = 4\)
b = 3a
and \(c^2\) = \(\frac{a}{4}\)
but when we try to find \(\frac{ab}{c}\) then we will be left with some variables
Squaring \(\frac{ab}{c}\) we get
\(\frac{a^2b^2}{c^2}\) = \(\frac{a^2b^2*4}{a}\) = \(4*ab^2\)
But b = 3a
=> = \(4*a(3a)^2\) = 36\(a^3\)
=> We don't know the value of a
=> NOT SUFFICIENT
So, Answer will be A
Hope it helps!
STAT 1: \(\frac{a}{4} = c^2\) and \(bc = 12\)
\(\frac{a}{4} = c^2\) => \(\frac{a}{c^2} = 4\) ...(1)
\(bc = 12\) ...(2)
(1) * (2) we get
\(\frac{a}{c^2} * bc = 4 * 12\)
=> \(\frac{ab}{c}\) = 48
=> SUFFICIENT
STAT 2: \(\frac{a}{b} = \frac{1}{3}\) and \(\frac{a}{c^2} = 4\)
b = 3a
and \(c^2\) = \(\frac{a}{4}\)
but when we try to find \(\frac{ab}{c}\) then we will be left with some variables
Squaring \(\frac{ab}{c}\) we get
\(\frac{a^2b^2}{c^2}\) = \(\frac{a^2b^2*4}{a}\) = \(4*ab^2\)
But b = 3a
=> = \(4*a(3a)^2\) = 36\(a^3\)
=> We don't know the value of a
=> NOT SUFFICIENT
So, Answer will be A
Hope it helps!
13 Nov 2022, 10:31
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Bunuel
Question Stem Analysis:
We are told that \(abc\neq 0\), which means neither a, nor b, nor c can equal 0. We need to determine the value of the expression ab/c.
Statement One Alone:
\(\Rightarrow\frac{a}{4} = c^2\text{ and }bc = 12\)
Thus, a = 4c^2. If we substitute a = 4c^2 in ab/c, we obtain (4c^2)b/c, which can be simplified to 4bc. Since bc = 12, the given expression is equal to 4bc = 4(12) = 48. Statement one alone is sufficient.
Eliminate answer choices B, C, and E.
Statement Two Alone:
\(\Rightarrow\frac{a}{b} = \frac{1}{3}\text{ and }\frac{a}{c^2}=4\)
If a = 4, b = 12, and c = 1, then a/b = 4/12 = 1/3, and a/c^2 = 4/1 = 4. Under these assumptions, ab/c is equal to (4 * 12)/1 = 48.
If a = 1, b = 3, and c = 1/2, then again a/b = 1/3 and a/c^2 = 1/(1/2)^2 = 1/(1/4) = 4. In this scenario, ab/c is equal to (1 * 3)/(1/2) = 6.
Since there are more than one possible values for ab/c, statement two alone is not sufficient.
Answer: A
