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The surface area of a square tabletop was changed so that on

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The surface area of a square tabletop was changed so that on [#permalink]

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New post 07 Sep 2009, 06:41
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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.
[Reveal] Spoiler: OA

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Re: Surface Area/Percent [#permalink]

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New post 07 Sep 2009, 06:58
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1)sufficient
(x-1).(x+2)=70
x^2+x-1-70=0
so we can find x^2
2)sufficient
we know one side increased by 25% and the increase is 2.
so side was 8. So we can find the area.
D

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Re: Surface Area/Percent [#permalink]

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New post 08 Sep 2009, 07:34
maliyeci wrote:
1)sufficient
(x-1).(x+2)=70
x^2+x-1-70=0
so we can find x^2
2)sufficient
we know one side increased by 25% and the increase is 2.
so side was 8. So we can find the area.
D


Ok but look (x-1)(x+2) = 70
\(x^2+x-2=70\)
\(x^2+a-72=0\)
\((x+9)(x-8) =0\)
\(x1 =-9\)
\(x2=8\)

I see that the are two answers. Why does A answer the question?

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Re: Surface Area/Percent [#permalink]

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New post 08 Sep 2009, 08:55
Because x1 = -9 is not valid, the dimension must be positive

TheRob wrote:
maliyeci wrote:
1)sufficient
(x-1).(x+2)=70
x^2+x-1-70=0
so we can find x^2
2)sufficient
we know one side increased by 25% and the increase is 2.
so side was 8. So we can find the area.
D


Ok but look (x-1)(x+2) = 70
\(x^2+x-2=70\)
\(x^2+a-72=0\)
\((x+9)(x-8) =0\)
\(x1 =-9\)
\(x2=8\)

I see that the are two answers. Why does A answer the question?

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Re: The surface area of a square tabletop was change so that one [#permalink]

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New post 14 Mar 2014, 07:00
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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Ryerson (Ted Rogers) Thread Master
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Re: Data Sufficiency and Geomatry problem - Source: GMAT Plus, Q25, P53 [#permalink]

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New post 20 Dec 2015, 16:43
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.
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Re: The surface area of a square tabletop was changed so that on [#permalink]

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New post 21 Dec 2015, 22:41
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.
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Re: The surface area of a square tabletop was changed so that on [#permalink]

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Re: The surface area of a square tabletop was changed so that on   [#permalink] 20 Sep 2017, 02:36
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