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

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Manager
Joined: 29 May 2008
Posts: 109
The surface area of a square tabletop was changed so that on  [#permalink]

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07 Sep 2009, 06:41
1
7
00:00

Difficulty:

75% (hard)

Question Stats:

51% (02:01) correct 49% (01:57) wrong based on 392 sessions

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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.
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Schools: UPenn, UMich, HKS, UCB, Chicago

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07 Sep 2009, 06:58
2
1
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
Manager
Joined: 29 May 2008
Posts: 109

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08 Sep 2009, 07:34
1
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?
Intern
Joined: 03 Sep 2009
Posts: 28

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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?
Manager
Joined: 20 Dec 2013
Posts: 225
Location: India
Re: The surface area of a square tabletop was change so that one  [#permalink]

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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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Re: Data Sufficiency and Geomatry problem - Source: GMAT Plus, Q25, P53  [#permalink]

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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.

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

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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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22 Dec 2018, 10:35

Project DS Butler: Day 47: Data Sufficiency (DS93)

Bumping for DS Butler project.
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Re: The surface area of a square tabletop was changed so that  [#permalink]

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30 Apr 2019, 21:51
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Re: The surface area of a square tabletop was changed so that   [#permalink] 30 Apr 2019, 21:51
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