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How long would it take Sue to paint the room?

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Math Expert
Joined: 02 Sep 2009
Posts: 46297
How long would it take Sue to paint the room? [#permalink]

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24 Jan 2016, 05:38
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Difficulty:

5% (low)

Question Stats:

89% (00:21) correct 11% (00:36) wrong based on 196 sessions

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How long would it take Sue to paint the room?

(1) Working with Bob, the project would last 2 hours.
(2) Bob could accomplish the painting alone in 31⁄4 hours.

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Manager
Joined: 03 May 2015
Posts: 236
Location: South Africa
GPA: 3.49
WE: Web Development (Insurance)
Re: How long would it take Sue to paint the room? [#permalink]

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24 Jan 2016, 05:41
2 variables, so both the equations are required.
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Kudos if I helped

SVP
Joined: 26 Mar 2013
Posts: 1677
How long would it take Sue to paint the room? [#permalink]

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25 Jan 2016, 01:30
Bunuel wrote:
How long would it take Sue to paint the room?

(1) Working with Bob, the project would last 2 hours.
(2) Bob could accomplish the painting alone in 31⁄4 hours.

Total time (T) = (X) (Y)/(X+Y) where X= Sue time alone & Y= Bob time alone & T= combined time

2) Only Bob time= Y.... Ins

1)only Combined time= T.......Ins

Combine 1 & 2......... we can solve for X=sue time

Manager
Joined: 03 Jan 2015
Posts: 84
Re: How long would it take Sue to paint the room? [#permalink]

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28 Jan 2016, 12:29

(1) Working with Bob, the project would last 2 hours.

S + B = 2
One equation, two variables. Not sufficient

(2) Bob could accomplish the painting alone in 31⁄4 hours.

B = 31⁄4 hours. Does not say anything about Sue. Not sufficient

Together, you have two distinct equations and two variables. Combined, both are sufficient. Answer C.
Intern
Joined: 22 Oct 2015
Posts: 17
Re: How long would it take Sue to paint the room? [#permalink]

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04 Feb 2016, 10:23
Could someone actually go through the problem and solve it?
Manager
Joined: 03 Jan 2015
Posts: 84
Re: How long would it take Sue to paint the room? [#permalink]

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04 Feb 2016, 11:01
2
ZaydenBond wrote:
Could someone actually go through the problem and solve it?

Sure. I am not sure if statement 2 says 3 1/4 hours or 31/4 hours but I am assuming 31/4 hours

Anyway here is how I would do it:

Given:
$$S + B = 2$$
$$B = 31/4$$

$$\frac{1}{S} + \frac{1}{31/4} = \frac{1}{2}$$

$$\frac{1}{S} + \frac{4}{31} = \frac{1}{2}$$

$$\frac{1}{S} = \frac{1}{2} - \frac{4}{31}$$

$$\frac{1}{S} = \frac{31}{62} - \frac{8}{62}$$

$$\frac{1}{S} = \frac{23}{62}$$

$$S = \frac{62}{23}$$

Would statement 2 say that Bob could accomplish the painting alone in 3 1/4 hours instead of 31/4 hours than the answer would of course change but you can still use the same steps.

Hope this helps.
Intern
Joined: 22 Oct 2015
Posts: 17
Re: How long would it take Sue to paint the room? [#permalink]

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04 Feb 2016, 11:08
saiesta wrote:
ZaydenBond wrote:
Could someone actually go through the problem and solve it?

Sure. I am not sure if statement 2 says 3 1/4 hours or 31/4 hours but I am assuming 31/4 hours

Anyway here is how I would do it:

Given:
$$S + B = 2$$
$$B = 31/4$$

$$\frac{1}{S} + \frac{1}{31/4} = \frac{1}{2}$$

$$\frac{1}{S} + \frac{4}{31} = \frac{1}{2}$$

$$\frac{1}{S} = \frac{1}{2} - \frac{4}{31}$$

$$\frac{1}{S} = \frac{31}{62} - \frac{8}{62}$$

$$\frac{1}{S} = \frac{23}{62}$$

$$S = \frac{62}{23}$$

Would statement 2 say that Bob could accomplish the painting alone in 3 1/4 hours instead of 31/4 hours than the answer would of course change but you can still use the same steps.

Hope this helps.

Thank you very much! I had the same exact process and answer, but was doubting myself. Kudos!
Director
Joined: 24 Nov 2015
Posts: 562
Location: United States (LA)
Re: How long would it take Sue to paint the room? [#permalink]

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28 Jul 2016, 04:19
We are asked how long will Sue take to paint the room
basically for solving this question we need to find time required by Sue to complete the task
Statement 1 tells us that working with Bob the task would require 2 hrs
if we consider time required by Bob to complete the task be B hrs and time required by Sue to complete the task be S hrs then
B + S = 2hrs
we don't anything about their individual rate of working so clearly insufficient
Statement 2 tells us Bob alone can complete the task of painting in 31/4 hrs
we don't have info regarding Sue's rate of working so clearly insufficient

Combining both Statements and if we consider time required by Bob to complete the task be B hrs and time required by Sue to complete the task be S hrs then
B + S = 2hrs
B = 31/4 hrs
we can solve this 2 equations(although the time is given you get the idea of solving these 2 equations using principles of time and work)
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Joined: 09 Sep 2013
Posts: 7045
Re: How long would it take Sue to paint the room? [#permalink]

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29 Aug 2017, 15:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How long would it take Sue to paint the room?   [#permalink] 29 Aug 2017, 15:12
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