rectangle area

srivathsan wrote:If the dimensions of a rectangular box are 5x6x7, which of the following cant be total surface area of two sides of the box?

a.60
b.84
c.70
d.77
e.90.

Options a,b,c are not possible..But how to select between options d. and e.

Kindly help me..

(5x6)+(5x6)=60
(6x7)+(6x7)=84
(5x7)+(5x7)=70
If 7 is common (6x7)+(5x7)=77

Ans is E

P.S: If 6 is common (6x7)+(5x6)=72
If 5 is common (5x7)+(5x6)=75

Area of the first side = 5*6 = 30 square units
Area of the second side = 6*7 = 42 square units
Area of the third side = 5*7 = 35 square units

Possibilities:
Area of the first side + Area of the first side = 30 + 30 = 60 [Option A is eliminated]
Area of the first side + Area of the second side = 30 + 42 = 72
Area of the first side + Area of the third side = 30 + 35 = 65
Area of the second side + Area of the second side = 42 + 42 = 84 [Option B is eliminated]
Area of the second side + Area of the first side = 42 + 30 = 72
Area of the second side + Area of the third side = 42 + 35 = 77 [Option D is eliminated]
Area of the third side + Area of the third side = 35 + 35 = 70 [Option C is eliminated]
Area of the third side + Area of the first side = 35 + 30 = 65 [Need not calculate]
Area of the third side + Area of the second side = 35 + 42 = 77 {need not calculate]

Option E is the only one left out and that is the answer.

The GMAT way:

Area of the first side = 5*6 = 30 square units
Area of the second side = 6*7 = 42 square units
Area of the third side = 5*7 = 35 square units

Since 42 square units is the maximum area of a side, the maximum value when areas of two different sides are added is 42 + 42 = 84. and 90 > 84. So, 90 can never be the answer.