Amount of air inside cuboid ?

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vaibhavjha: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Thu Aug 19, 2010 7:26 am; Thanked: 1 times

by vaibhavjha » Fri Nov 12, 2010 12:59 pm

Q) What is the amount of air inside an empty rectangular cuboid ?
(1) Areas of the two faces of the rectangular cuboid are 10 and 25.
(2) One of the dimension of the rectangular cuboid is 5 units

OA : E

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Source: Beat The GMAT — Data Sufficiency | Fri Nov 12, 2010 12:59 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Nov 12, 2010 9:04 pm

vaibhavjha wrote:Q) What is the amount of air inside an empty rectangular cuboid ?
(1) Areas of the two faces of the rectangular cuboid are 10 and 25.
(2) One of the dimension of the rectangular cuboid is 5 units

OA : E

Statement 1: Areas of the two faces of the rectangular cuboid are 10 and 25. Only from this we can't determine the volume of the cuboid.

Not sufficient.

Statement 2: One of the dimension of the rectangular cuboid is 5 units. But we don't know about the other two dimensions.

Not sufficient.

1 & 2 Together: Different combinations are possible as any of the 3 dimensions (length, breadth, width) may be equal to 5 units. This will result in different volume.

Not sufficient.

The correct answer is E.

Rahul Lakhani
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ymach3: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Mon Jul 13, 2009 4:25 pm; Thanked: 1 times

by ymach3 » Tue Nov 16, 2010 2:08 am

)please corrcet my approach

(1) has 2 face areas= 10 and 25

possible dimensions: l*b=10*1
b*h=1*25...Therefore l*b*h=10*1*25=250

also, l*b=2*5
b*h=5*5....and volume=l*b*h=2*5*5=50 ... Two different answers, hence (1) is INSUFFICIENT..

(2) is clearly Insufficient.

Both (1) & (2)

has 2 faces with areas =10, 25

and one of the lengths is 5 ..

--> l*b=2*5 =10 and
b*h=5*5=25
or

----l> l*h=2*5 and
h*b=5*5

As we are asked to find volume of the cube, i think we may not require specific values of l,b and h.

Volume=l*b*h=2*5*5=50 c.units.

Hence (c) ....

Please correct me and let me know where did i commit a mistake.

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Tue Nov 16, 2010 3:49 am

ymach3 wrote:)please corrcet my approach
...
Both (1) & (2)

has 2 faces with areas =10, 25

and one of the lengths is 5 ..

--> l*b=2*5 =10 and
b*h=5*5=25
or

----l> l*h=2*5 and
h*b=5*5

As we are asked to find volume of the cube, i think we may not require specific values of l,b and h.

Volume=l*b*h=2*5*5=50 c.units.

Hence (c) ....

Please correct me and let me know where did i commit a mistake.

You missed several possibilities.
In your 1st case, it may be possible that l = 5 => b = 2 and h = 12.5 => Volume = 125
In your 2nd case, it may be possible that l = 5 => h = 2 and b = 12.5 => Volume = 125

And there is also a case 3 which you missed.
In which case, l*b = 10 and l*h = 25 with same two possibilities. On of which will result in volume = 50 and in another volume = 125.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

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rishab1988: Master | Next Rank: 500 Posts; Posts: 332; Joined: Tue Feb 09, 2010 3:50 pmFollowed by: 7 members; Thanked: 41 times; GMAT Score:720

by rishab1988 » Tue Nov 16, 2010 8:06 am

the prompt is what is lbh=?

1) gives areas of 2 surfaces. we know that surface area of rect cuboid = 2(lb+bh+hl).If we choose lb and bh ,b is common and the 2 diff sides are l and h; if we choose bh and lb, b is common and l and h are different; finally, if we choose lb and hl, h is the common side and b and h are different.

So, this shows that if we choose any 2 sides, they have atleast one side common and 2 sides that are different.

now we are given that the 2 surface areas are 10 and 25. Since these 2 areas are different we can be sure that these 2 surfaces are different; also, these surfaces could be lb and bh; bh and hl; lb and hl;

now if 10=5*2 , 25=5*5 or 2*12.5 (because we don't know which side is common to both) . vol= 5*2*5=50 or 5*2*12.5=250

we get 2 values for volume so insufficient. Eliminate A and D; answer could be B,C, or E.

2) one of the sides =5. Clearly, this information is insufficient, as the volume could be 5*1*2=5 or 5*2*100=1000; In other words we need the other 2 sides,without which we can't find a definitive value for volume of the cuboid.

Eliminate B.Answer could be C or E.

Now, combining 1 and 2.

We know from 2 that one of the sides is 5. so 10=5*2 and 25=either 2*12.5 or 5*5 ( same reason as given in A);

volume = 5*2*5=50 or 5*2* 12.5 =125.

Since we get 2 different values for volume, both taken together are also insufficient. Eliminate C

Answer E

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ymach3: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Mon Jul 13, 2009 4:25 pm; Thanked: 1 times

by ymach3 » Wed Nov 17, 2010 9:36 pm

Yes, i was considering only integers... Thanks Rahul.

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