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If \(2 + 5a - b/2 = 3c,\) what is the value of \(b?\)

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Source: — Data Sufficiency |
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Re: If \(2 + 5a - b/2 = 3c,\) what is the value of \(b?\)

by deloitte247 » Sat Jul 25, 2020 1:08 pm

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$$2+5a-3c=\frac{b}{2}$$
$$b=2\left(2+5a-3c\right)$$
$$b=4+10a-6c$$
$$b=4+2\left(5a-3c\right)$$
Statement 1=> a + c = 13
a = 13 - c
(substituting 'a' in the question stem expression), we have
$$b=4+2\left[5\left(13-c\right)-3c\right]$$
$$b=4+2\left(65-5c-3c\right)$$
$$b=4+130-10c-6c$$
$$b=134-16c$$
Here, the value of c is unknown. So therefore, we cannot evaluate the value of B. Based on this, statement 1 is NOT SUFFICIENT.

Statement 2=> -12c = -20a + 4
Divide through by 4
-3c = -5a + 1
5a - 3c - 1 = 0 (This is equivalent to a value in the expression from the question stem).
b = 4 + 2(5a - 3c)
b = 4 + 2(1)
B = 4 + 2 = 6
Statement 2 alone is SUFFICIENT. Hence, option B is the correct answer.
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