What is the volume of rectangular box R?

If the dimensions of an rectangular box are a,b & c, Then V(volume)= abc .....and.... S(Total S-area)= 2(ab+bc+ca)

(1) The total surface area of R is 12 square meters. ==> 2(ab+bc+ca)= 12 sq m or ab+bc+ca = 600 sq cm .... value of abc can not be determined - Not Sufficient
(2) The height of R is 50 centimeters. ==> one of the dimension is 50 cm , Say c=50 ........of course , value of abc can not be determined - Not Sufficient
(1+2) ab+50b+ 50a= 600 sq cm or ab+50(a+b)= 600 sq cm ....... again, value of abc can not be determined - Not Sufficient
Ans E.
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The surface area of a box is 2(lb+bh+lh) where l= length,b=bredth and h=height of the box.
From statement 1 we get surface area but since Volume=lbh and we dont get this information from above so not sufficient.
From statement 2 we know only height so again it is not sufficient.
Together we get 2(lb+bh+lh)=2(lb+.5(b+l))=12
But we wont be able to find volume from this.Not sufficient
E should be the correct choice.

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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.
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