Question: A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
Hey there!
I can see that most of the responses have used a formulaic approach using an unknown variable.
I would
NOT suggest the same.
GMAT is a test of logic and not usage of equations & formulas!
Lets try to use the logical
STRATEGY of BACKSOLVING! What is the Strategy of Back-solving in GMAT?Its a powerful and effective strategy that can help you
eliminate multiple incorrect answer choices and involves working backwards from the answer choices to determine which one is correct. It helps you to narrow down the options.
On GMAT, the answer choices are in ascending or descending order and hence it makes sense to start with option C and eliminate extreme options A,B or D,E depending on the constraints.
Lets try to use this strategy instead of conventional equations!
GMAT Track of thought 1 The area of the rectangular photograph that measures 8 inches by 10 inches = 8 * 10 =80 square inches
All the 5 answer choices represent the width of the border, in inches
GMAT Track of thought 2 Area of the border = 144 and hence the area of the photograph along with the border = 144 + 80 =224 square inches
GMAT Track of thought 3 Begin with option(C) which is 6
If the width was 6 units the length would be 10 + 6 + 6 =22 units and the breadth 8 +6 +6 =20 units and hence the area of the photograph along with the border = 22 * 20 = 440 square inches. Its way greater than 224 square inches which is the area of the photograph along with the border as calculated above.
GMAT Track of thought 4 All values greater than 6 will result in area values even greater than 440.
So eliminate C,D & E
Use the same strategy of testing on option B now that provides 4 inches as the width of the border.
Then the length would be 10 + 4 + 4 =18 inches and breadth would be 8 + 4 +4 = 16 inches and hence the area of the photograph along with the border = 18 * 16 =288 and this is greater than 224 square inches.
That leaves us with
option(A) as the answer.
You can go ahead and mark A without further calculations but if you do check with calculation,you would observe that if the width was 3 as mentioned in option A, the length would be 10 + 3 +3 =16 inches and the breadth would be 8 + 3 + 3 = 14 inchess.
and hence the area of the photograph along with the border = 16 * 14 = 224 square inches!!
BINGO!Hope you learnt something new here and would apply it ahead.
Devmitra Sen
GMAT Mentor _________________
Crackverbal Prep Team
www.crackverbal.com