What is the volume of rectangular box R?

We need to find volume = L*B*H, so we need the values of 3 variables, which means we need atleast 3 distinct equations.

Stmt 1: Total Surface Area = 2(L*B + B*H + L*H) = 12, we have 1 equation and 3 variables, cannot be solved. Hence Insufficient. Eliminate A,D

Stmt 2: H = 50 cm, 1 equation and 3 variables, cannot be solved. Hence Insufficient. Eliminate B.

Combined: We still have only 2 equations and 3 variables, cannot be solved. Hence Insufficient. Eliminate C.

Hence Option E.

Question: Volume of Rectangular Box R = l*b*h = ?

Statement 1: The total surface area of R is 12 square meters.
Total Surface Area of Box = 2*(lb+bh+lh) = 12
i.e. lb+bh+lh = 6
Since l, b and h can NOT be deduced hence
NOT SUFFICIENT

Statement 2: The height of R is 50 centimeters = 0.5 meters (1 meter = 10 centimeters)
there is no information about l and b hence
NOT SUFFICIENT

Combining the two statements

lb+bh+lh = 6 and h = 0.5

i.e. lb+0.5(l+b) = 6

Still l and b are unknown hence
NOT SUFFICIENT

Answer: Option E

To calculate : l x b x h

(1) Applying the formula:
2(lb+ bh + hl) = 12
(lb+ bh + hl) = 6
Insufficient

(2) h = 50 cm = 1/2 m
Insufficient

(1)+(2); lb+ (1/2)b + (1/2)l = 6
Insufficient

E is correct

(1) 2(LB+BH+LH) = 12 or LB+BH+LH=6. But without knowing the values of L, B, and H, we cannot determine the volume (LBH). Insufficient.

(2) H = 0.5, gives us no clue about the other two dimensions L and B. Insufficient.

Combining the two statements:
LB+BH+LH=6 and H=0.5
LB+(0.5)*(L+B)=6
2LB+L+B=12
However, we still can't determine the values of L and B from here.
For ex: B=1, L=11/3 and LB=11/3
For ex: B=2, L=2, and LB=4

Therefore, option E.

Hi, I took a lot of time in this question because I thought (lb+bh+lh)=6 can have UNIQUE values of l,b and h. How do I know when I should not be looking for unique values and waste my time and when I should find unique values. I get stuck in such questions.

Please help Bunuel MartyTargetTestPrep KarishmaB

An equation with two or more variables can have a unique solution in cases there are some constraints on it (for example, the values should be integers etc). Here, the question stem does not put any constraints on the values of l, b and h except that they must be positive. The dimensions could easily be fractions. In that case we know that the variables could take many different values.

To be sure you should try to figure out 2 different sets of values that will work and that's it. Assume two variables as 1 each and then get the third. Then assume two variables as 2 each and get the third etc.

Be mindful that you are asked the value of the volume i.e. lbh, not of each dimension individually. In such cases, you may need lesser data hence confirm by getting 2 different values.