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# Joe, Bob and Dan worked in the ratio of 1:2:4 hours, respectively. How

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Math Expert
Joined: 02 Sep 2009
Posts: 43901
Joe, Bob and Dan worked in the ratio of 1:2:4 hours, respectively. How [#permalink]

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07 Oct 2014, 07:55
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79% (00:45) correct 21% (00:47) wrong based on 216 sessions

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Tough and Tricky questions: Ratios

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
[Reveal] Spoiler: OA

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Re: Joe, Bob and Dan worked in the ratio of 1:2:4 hours, respectively. How [#permalink]

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07 Oct 2014, 08:05
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KUDOS
ok, 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 to find the answer to our question, we need to find out either total hours worked, or X.
(1) tells us the total number of hours worked by Joe, Bob and Dan. Thus, we can solve for X.
49 = 7x
x = 49/7
x = 7
Bob worked 2x => he worked 7*2 = 14 h. sufficient.

(2) 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 = 14 h. sufficient.

Of course, for DS, we do not need to do all the calculations, just to check if we can solve for X or not.
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Re: Joe, Bob and Dan worked in the ratio of 1:2:4 hours, respectively. How [#permalink]

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07 Oct 2014, 08:44
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Bunuel wrote:

Tough and Tricky questions: Ratios

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

That was a sitter -

Ratio = 1: 2: 4 = X : 2X : 4X

1 - Total work by J B and D = 49 hrs. = we can calculate the number of hours each worked
2 - D worked 21 hours more than J = 4X - X = 21 - This will also give the value of B's work

Ans - D
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Joined: 07 Mar 2014
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Location: India
Joe, Bob and Dan worked in the ratio of 1:2:4 hours, respectively. How [#permalink]

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12 Nov 2014, 02:29
the ratio of work done by Joe, Bob and Dan = $$1:2:4$$

how many hours Bob work??

Statement 1:

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

Statement 2

Dan work 21 hours more than Joe

therefore, $$4x-1x =21$$
$$3x= 21$$
$$x= 7$$

so, work done by Bob = $$2 * 7 = 14 hours$$

Sufficient

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Re: Joe, Bob and Dan worked in the ratio of 1:2:4 hours, respectively. How [#permalink]

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12 Apr 2017, 04:35
Hello from the GMAT Club BumpBot!

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Re: Joe, Bob and Dan worked in the ratio of 1:2:4 hours, respectively. How   [#permalink] 12 Apr 2017, 04:35
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