What is the ratio of 2a to b?

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Mon Jul 02, 2018 1:10 am

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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?

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Source: Beat The GMAT — Data Sufficiency | Mon Jul 02, 2018 1:10 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Mon Jul 02, 2018 3:02 am

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>

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 02, 2018 5:10 am

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

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

Target question: What is the ratio of 2a to b?
In other words, What is the value of 2a/b?

Statement 1: a/b = 2
Take: a/b = 2
Multiply both sides by 2 to get: 2a/b = 4
So, the answer to the target question is 2a/b = 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a + b = 5
Let's test some values.
There are several values of a and b that satisfy statement 2 (a + b = 5). Here are two:
Case a: a = 1 and b = 4. In this case, the answer to the target question is 2a/b = 2(1)/4 = 2/4 = 1/2
Case b: a = 2 and b = 3. In this case, the answer to the target question is 2a/b = 2(2)/3 = 4/3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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