Joe, Bob and Dan Worked in the Ratio of 1 : 2 : 4 hours, Respectively GMAT Data Sufficiency

Question: Joe, Bob and Dan worked in the ratio of 1 : 2 : 4 hours, respectively. How many hours did Bob work?

1. Together, Joe, Bob and Dan worked a total of 49 hours
2. Dan worked 21 hours more than Joe

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Solution with Explanation:
Approach Solution (1):

So knowing the ratio for each person, we can rewrite as x : 2x : 4x, where x is a factor, and the total time they worked can be written as the sum of x, 2x, and 4x. Therefore, in order t find the answer to our question, we need to find out either the total hours worked, or X.
S1 tells us the total number of hours by Joe, Bob and Dan. Thus, we can solve for x.
49 = 7x
x = 7

Bob worked 2x. Thus, he worked 7 * 2 = 14h
Sufficient

S2 Dan worked 21 hours more than Joe. We can rewrite this as 4x – x = 21
From this, we can solve for x
3x = 21
x = 7
Bob worked 7 * 2 = 14h
Sufficient

Correct Option: D

Approach Solution (2):

The ratio of work done by Joe, Bob and Dan = 1 : 2 : 4
How many hours Bob work?
S1: Work done by Joe, Bob and Dan = 49 hours
Let hour be x

Therefore, work done by Bob = \(\frac{2x*49}{1x+2x+4x}=14 hours\)

Sufficient

S2: Dan work 21 hours more than Joe
Therefore, 4x – 1x = 21
3x = 21
x = 7

So, work done by Bob = 2 * 7 = 14h
Sufficient

Correct Option: D

“Joe, Bob and Dan worked in the ratio of 1 : 2 : 4 hours, respectively. How many hours did Bob work?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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