Data Sufficiency

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

)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.

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

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