OG 12 Qn-122

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rah_pandey: Master | Next Rank: 500 Posts; Posts: 122; Joined: Fri May 22, 2009 10:38 pm; Thanked: 8 times; GMAT Score:700

OG 12 Qn-122

by rah_pandey » Thu Jun 18, 2009 10:20 am

What is the volume of the rectangular solid?
(1) two adjacent sides have areas 15 and 24 respectively?
(2) each of two opposite faces of the solid has area 40? what does this statement mean?

According to me it means area of each of the face is 40. Am i missing something

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Source: Beat The GMAT — Data Sufficiency | Thu Jun 18, 2009 10:20 am

shashank.mehra: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Mon Jun 15, 2009 8:59 pm

Re: OG 12 Qn-122

by shashank.mehra » Thu Jun 18, 2009 10:34 am

rah_pandey wrote:What is the volume of the rectangular solid?
(1) two adjacent sides have areas 15 and 24 respectively?
(2) each of two opposite faces of the solid has area 40? what does this statement mean?

According to me it means area of each of the face is 40. Am i missing something

Statement 1) Two adjacent sides will have at least one side comman. Therefore possible edges of two adjacent faces are 3*5 & 3* 8 OR 1* 15 and 1*24. So one cannot decide what are the dimensions of the adjacent phases. Hence 1 is not suff

2) Each of two oppositve faces have an area of 40. Therefore all phases have area as 40. Therefore it's a cube. a^2 = 40 --------> a = 2 (10) ^ 1/2.

Now statement one and statement 2 both give different dimensions of the phases. Hence neither of the two statements are sufficient.

IMO E

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muna_m: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Fri Mar 06, 2009 3:36 pm

by muna_m » Thu Jun 18, 2009 10:55 am

If u consider it to be a cube, with area of face = 40
then like you said a = Sqrt(40)

But answer would be B because you can find the volume of a cube when you know one side.

If statement two does not mean its a cube but a cuboid, then I would say E.

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chintanjadwani: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Tue Feb 24, 2009 3:12 am; Thanked: 3 times; GMAT Score:730

answer

by chintanjadwani » Thu Jun 18, 2009 11:22 am

Please note while doing the above question that in GMAT data sufficiency, both statement when taken to be true should give same answers.

So when the first statement says two adjacents sides have area 15 and 24. Accept it as true.

2) Each opposite side has area 40. This doesnt mean that all sides have area 40. Note here that assuming this would prove false the 1st statement, which can never happen.

How to solve this question:-

First of all a rectangular solid has 3 sides so let them be a, b and c.

we need the volume i.e a*b*c

1) a*b=15
b*c=24

a*b^2*c = 24*15....however we need a*b*c , not b^2 ...INSUFFICIENT

2) other opposite sides have area 40.
A rectangular solid has 6 surfaces, wherein opposite sides are equal.

so here we have the third area , i.e. a*c=40

INUSFICIENT

both taken together

(a*b)*(b*c)*(c*a) = 15*24*40

a^2 * b^2 * c^2 = 15*24*40

taking square root of both sides, we get the answer..
Hence, answer is C...!!

hope this helps ...

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: OG 12 Qn-122

by Stuart@KaplanGMAT » Thu Jun 18, 2009 11:32 am

rah_pandey wrote:What is the volume of the rectangular solid?
(1) two adjacent sides have areas 15 and 24 respectively?
(2) each of two opposite faces of the solid has area 40? what does this statement mean?

According to me it means area of each of the face is 40. Am i missing something

As noted by the previous poster, it's impossible for DS statements to contradict each other. Therefore, if by your interpretation/artithmetic they do contradict, you have made a mistake.

Let's attack this our favourite way - quick and easy with minimal math.

Q: What's the volume of a rectangular box?

1) We know the area of 2 adjacent sides, which means we know the area of 4/6 total sides (since for a rectangular solid, opposite sides are identical). Does every rectangular solid with 2 of the same sides have the same 3rd side? Definitely not: insufficient.

2) "each of two opposite faces has area 40" means that there's at least ONE pair of sides with area of 40 each. No information about the other 4 sides, however: insufficient.

Together: We know the area of each of the 6 sides (2*15, 2*24, 2*40). If we know the 6 sides, we have a unique box and, if we have a unique box, there must be some way to figure out the volume: sufficient, choose (C).

* * *

As an aside, if we wanted to calculate volume (which we definitely don't need to do in this case, since it's a DS question), we can set up 3 equations for our 3 unknowns:

lw = 15
wh = 24
lh = 40

and then solve the system. If this were abstract algebra we'd actually get more than 1 solution (since our equations are non-linear), but since it's geometry we can ignore all negative solutions.