Cost of painting

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Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members; Location: International Space Station; Thanked: 11 times

by Aman verma » Wed Oct 05, 2011 8:43 am

Q: An open box is made of wood 2cm thick. It's internal length is 86 cm , breadth 46 cm and height is 38 cm. The cost of painting the outer surface of the box at $ 10 per square meter is:

a) $ 8.65

b) $ 10.00

c) $ 11.65

d) $ 17.50

e) $ 18.50

[spoiler][/spoiler]OA[spoiler]c) $ 11.65[/spoiler]

800. Arjun's-Bird-Eye

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Source: Beat The GMAT — Problem Solving | Wed Oct 05, 2011 8:43 am

sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Wed Oct 05, 2011 9:19 am

External length = 90 cm
External breadth = 50 cm
External height = 38 cm

The rectangular box has 6 sides. One side is open

2 sides will have area 2*(50*38) = 3800 cm^2
2 sides will have area 2*(90*38) = 6840 cm^2
1 side will have area 90*50 = 4500 cm^2

In square meters it is 1.5140
Cost of painting the box is $10/square meter. Total cost = $15.14

I don't seem to be getting the desired answer

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gmatclubmember: Master | Next Rank: 500 Posts; Posts: 158; Joined: Sat Sep 03, 2011 10:31 amFollowed by: 2 members; Thanked: 29 times

by gmatclubmember » Wed Oct 05, 2011 9:22 am

sl750 wrote:External length = 90 cm
External breadth = 50 cm
External height = 38 cm

The rectangular box has 6 sides. One side is open

2 sides will have area 2*(50*38) = 3800 cm^2
2 sides will have area 2*(90*38) = 6840 cm^2
1 side will have area 90*50 = 4500 cm^2

In square meters it is 1.5140
Cost of painting the box is $10/square meter. Total cost = $15.14

I don't seem to be getting the desired answer

The area to be painted would be 2*h(l+b) = 2*38(90+50)
and this will give the answer as 11.64 which is C.

a lil' Thank note goes a long way

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Wed Oct 05, 2011 9:41 am

gmatclubmember wrote:
sl750 wrote:External length = 90 cm
External breadth = 50 cm
External height = 38 cm

The rectangular box has 6 sides. One side is open

2 sides will have area 2*(50*38) = 3800 cm^2
2 sides will have area 2*(90*38) = 6840 cm^2
1 side will have area 90*50 = 4500 cm^2

In square meters it is 1.5140
Cost of painting the box is $10/square meter. Total cost = $15.14

I don't seem to be getting the desired answer
The area to be painted would be 2*h(l+b) = 2*38(90+50)
and this will give the answer as 11.64 which is C.

Well, I did consider the possibility that the problem might be ignoring the base as well, nevertheless, the cost comes to $10.64

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Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members; Location: International Space Station; Thanked: 11 times

by Aman verma » Thu Oct 06, 2011 8:02 am

Thanks guys for answering and raising doubt, even as per my calculation the answer comes to be $ 15.70 . But I think the answer provided by Gmatclubmeber has some merit. Normally nobody paints the bottom of a box and I am still not clear about the outer surface mentioned in the question. I have consulted with the source but they are pretty insistent about the answer to be c)11.65. Though, I am still in doubt. I thought the height to be 40. I would like to have other's suggestion on this.

800. Arjun's-Bird-Eye

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Thu Oct 06, 2011 8:17 am

As I mentioned in my earlier post, even if you exclude the base, the cost equals $10.64 and not $11.64.
The height won't change.

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Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members; Location: International Space Station; Thanked: 11 times

by Aman verma » Thu Oct 06, 2011 9:08 am

sl750 wrote:As I mentioned in my earlier post, even if you exclude the base, the cost equals $10.64 and not $11.64.
The height won't change.

But please explain why the height won't change. Shouldn't the wood of the base extend 2 cm beneath the sides

800. Arjun's-Bird-Eye

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Thu Oct 06, 2011 9:30 am

The extension is only along the x and y axes, not the z axes. The only way to see this is if you can draw a box or visualize it

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parveen110: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Fri Jan 17, 2014 7:34 am; Thanked: 7 times

by parveen110 » Sun Mar 09, 2014 5:26 am

I tried visualising. But I still don't understand why height won't change?? If internal height is 38cm then the external height would include the height of the base i.e. 2 cm more.

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parveen110: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Fri Jan 17, 2014 7:34 am; Thanked: 7 times

by parveen110 » Sun Mar 09, 2014 5:27 am

I tried visualising. But I still don't understand why height won't change. If internal height is 38cm then the external height would include the height of the base i.e. 2 cm more.

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by [email protected] » Sun Mar 09, 2014 8:38 pm

Hi parveen110,

Don't worry about this question. It's written in something of an ambiguous fashion. Since the prompt refers to the cost of painting the "outer surface", it stands to reason that the "bottom" of the box should also be painted (but apparently the solution doesn't include it). The question also states that the box is made of wood that is 2cm thick; the proper visualization would be to add 2cm to each of the dimensions TWICE (but the solution doesn't do that either; it assumes that the "outside height" and the "inside height" of the box are the same).

GMAT writers create (and vet) questions to a significant degree; the test would not include an active question (that counted) that was written in this fashion. It is possible that this might, in some rare set of circumstances, show up as an experimental question, but I'll bet that you'll never see anything written in this odd style on your GMAT. You'll be tested on the basic geometry formulas behind this question though.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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