If \(4a = 7b = 21c,\) what is the value of \(b?\)

[Vincen]

If \(4a = 7b = 21c,\) what is the value of \(b?\)

(1) \(a = \dfrac74\)

(2) \(c = \dfrac13\)

Answer: D

Source: Princeton Review

[deloitte247]

If 4a = 7b = 21c, what is the value of b?

Statement 1: a = 7/4
From the question stem, 4a = 7b
$$b=\frac{4a}{7}=\frac{\frac{7}{4}\cdot\frac{4}{1}}{7}=1$$
The exact value of b=1, so, therefore, statement 1 is SUFFICIENT.

Statement 2: c = 1/3
From the question stem, 7b = 21c
$$b=\frac{21c}{7}=\frac{21\cdot\frac{1}{3}}{7}=\frac{7}{7}=1$$
The exact value of b=1, so, therefore, statement 2 is SUFFICIENT.

Since each statement is SUFFICIENT alone, then, the correct answer is option D.