The top surface area of a square tabletop was changed so that one of

Because x1 = -9 is not valid, the dimension must be positive

Option D.
S1:Let initial side of square=a
After changes,area=(a-1)*(a+2)=70
Now there is a difference of 3 between (a-1) & (a+2) and 70=7*10
So a-1=7=> a=8
Suff

S2:a+2=a+25% of a
We can calculate a to find out area of square.Suff

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Given:

shape : square,
one dimension increased by 1 inch and second dimension increased by 2 inches, which makes new rectangle shape.

assume dimension variable d.

Statement I:

Area of new shape is 70 sq inches.
i.e \(70 = (d + 1) * (d + 2)\)
Value of dimension d could be determine, hence statement I is sufficient.

Statement II:

Area of new shape increase by 25%

\(1.25*d^2 = (d + 1) * (d + 2)\)

Again value of dimension d could be determine, hence alone statement II is also sufficient.

Correct answer is D.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?

(1) After the changes were made, the surface area was 70 square inches.
(2) There was a 25 percent increase in one of the dimensions.

In the original condition, suppose one side is x. There is 1 variable(x), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
In 1), from (x-1)(x+2)=70, x^2+x-72=0, (x-8)(x+9)=0, x is 8, which is unique and sufficient.
In 2), from 2=0.25x, x is 8, which is unique and sufficient. Therefore, the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Statement 1 is sufficient
Can be solved using properties of a square and quadratics
dimensions before increase were X and X (since square)
Dimension after = (x-1) and (x+2)

Statement 2
Can be solved by realising we are told the side that increased (x+2)
(New- Old)/Old
((x+2)-x)/x = 1/4
2/x =1/4
x=8
sufficient

Statement 1:
(x-1)(x+2)=70
or, x^2+x-2=70
or, x^2+x-72=0
So, x=-9 or x=8
Since the side of a square can not be negative, x=8. So, the area of the square=64

Sufficient.

Statement 2: x*25%=2 or x=8. Sufficient.
D

[quote="MathRevolution"]Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

The surface area of a square tabletop was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?

(1) After the changes were made, the surface area was 70 square inches.
(2) There was a 25 percent increase in one of the dimensions.

In the original condition, suppose one side is x. There is 1 variable(x), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
In 1), from (x-1)(x+2)=70, x^2+x-72=0, (x-8)(x+9)=0, x is 8, which is unique and sufficient.
In 2), from 2=0.25x, x is 8, which is unique and sufficient. Therefore, the answer is D.



Hi,

Thank You providing the solution.

I was not able to solve the question since I did not understand the question. The question states that one of the dimensions was reduced by 1 and the another one was increased by 2.

How do we know that the transformed figure is a square. I mean it could so happen that the 2 sides of the square are as it is and the other two are changed. In which case we get a very irregular figure.

Can you please help me understand the question ?


Thank you
Sonal

sonalchhajed2019 : A square/rectangle has only two dimensions(length and breadth). I think you are confused because you are trying to relate "dimension" with "side".

“The top surface area of a square tabletop was changed” makes me think that a cube’s or rectangular solid’s top surface was changed.

What is exactly “The top surface area of a square tabletop”? How can 2 dimensional square has “top surface area”?

Posted from my mobile device

Statement 1:
Original square dimensions --> new rectangular dimensions (decrease by 1 inch, increase by 2 inches)
Case 1: 9*9 --> 8*11 = 88
Case 2: 8*8 --> 7*10 = 70
Case 3: 7*7 --> 6*9 = 63
Only Case 2 yields a rectangle with an area of 70.
In Case 2, the area of the original square = 8*8 = 64
SUFFICIENT.

Statement 2:
Only in Case 2 above is the increase (2 inches) equal to 25% of the original dimension (8 inches).
In Case 2, the area of the original square = 8*8 = 64
SUFFICIENT.

The top of the table is always two dimensional. It can be square, rectangle, circle and so on.
Here it is given it is a square. Now the top of the table will have some width and so the total surface area will be the top+bottom+sides(width).

Here we are talking of top surface area of square table top, and the wordings do convey it correctly.

Can someone help to explain why Statement 2 is sufficient?

Statement 2: There was a 25 percent increase in one of the dimensions.

We must look at the statement 2 independently. Thus it can be any dimension.
Cannt 1.25x = x+1 , thus x=4
Why does it necessarily have to be 1.25x = x+2, thus x=8 , IMO insufficient.

Posted from my mobile device

The question stem says that there is an increase of 2 inch and decrease of 1 inch, while the statement II says there is an increase of 25%.
So we have to relate this 25% to the increase, which is 2 inches

Assume initial side as "x", after change dimension will be= (x-1) & (x-2)

S1. (x-1)(x-2) = 70, x= -9 & 8
Sufficient as -9 will be eliminated. Hence sufficient

S2. 25% increase, it means (x-2) is increased 25%. Sufficient

Hence D answer

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