Data Sufficiency

What is the ratio of 2a to b?

(1) a/b = 2
(2) a + b = 5

The OA is A.

How can I find the ratio without knowing the value of a and b? And why is not sufficient the second statement?

M7MBA wrote:What is the ratio of 2a to b?

(1) a/b = 2
(2) a + b = 5

The OA is A.

How can I find the ratio without knowing the value of a and b? And why is not sufficient the second statement?

Hello M7MBA.

Let's take a look at your question.

We need to find the quotient $$\frac{2a}{b}=?$$

First statement

(1) a/b = 2

Here, we can multiply by 2 and we get $$2\cdot\frac{a}{b}=2\cdot2\ \ \ \Rightarrow\ \ \ \frac{2a}{b}=4.$$ So, this statement is sufficient.

Second statement

(2) a + b = 5

Here, if we suppose that "a" and "b" are integers then we could get different cases:

- a=1, b=4 and then $$\frac{2a}{b}=\frac{2\cdot1}{4}=\frac{2}{4}=\frac{1}{2}.$$
- a=4, b=1 and then $$\frac{2a}{b}=\frac{2\cdot4}{1}=\frac{8}{1}=8.$$ Since we get different answers, we conclude that this statement is not sufficient.

Therefore, the correct answer is the option A.

I hope it helps you. <i class="em em-smiley"></i>