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# What is the area of square ABCD?

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Math Expert
Joined: 02 Sep 2009
Posts: 43892
What is the area of square ABCD? [#permalink]

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17 Feb 2016, 02:35
1
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Difficulty:

5% (low)

Question Stats:

93% (00:16) correct 7% (00:29) wrong based on 132 sessions

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What is the area of square ABCD?

(1) The diagonal of square ABCD is $$5\sqrt{2}$$
(2) The perimeter of square ABCD is 20

Kudos for correct solution.
[Reveal] Spoiler: OA

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Joined: 26 Mar 2013
Posts: 1441
Re: What is the area of square ABCD? [#permalink]

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18 Feb 2016, 06:58
1
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Bunuel wrote:
What is the area of square ABCD?

(1) The diagonal of square ABCD is $$5\sqrt{2}$$
(2) The perimeter of square ABCD is 20

Kudos for correct solution.

Let the length of square= L

(1) The diagonal of square ABCD is $$5\sqrt{2}$$

So L= 5........> Area =5*5=25

(2) The perimeter of square ABCD is 20..............> 4L=20...? L=5
Area= 25

Intern
Joined: 30 Aug 2015
Posts: 31
Concentration: Marketing, Finance
WE: Brand Management (Manufacturing)
Re: What is the area of square ABCD? [#permalink]

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18 Feb 2016, 15:45
1
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Let the length of square= L

(1) The diagonal of square ABCD is 52√52

So L= 5........> Area =5*5=25

(2) The perimeter of square ABCD is 20..............> 4L=20...? L=5
Area= 25
WE KNOW THAT SQUARE FORMS 45, 45, 90 TRIANGLE , SO BASIC CONCEPT IS KNOWING ANY SINGLE SIDE WE CAN CALCULATE ALL OTHER SIDES..
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4908
GPA: 3.82
Re: What is the area of square ABCD? [#permalink]

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18 Feb 2016, 18:32
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.

What is the area of square ABCD?

(1) The diagonal of square ABCD is 5 √2
(2) The perimeter of square ABCD is 20

In the original condition, there is 1 variable(one side of square: x) for square, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. In fact, it is 99% that D is the answer.
For 1), from √2(x)=5√2, x=5, which is unique and sufficient.
For 2), from 4x=20, x=5, which is unique and sufficient.

 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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Director
Joined: 24 Nov 2015
Posts: 584
Location: United States (LA)
Re: What is the area of square ABCD? [#permalink]

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04 Aug 2016, 14:26
Statement 1 gives the length of diagonal of square as 5 $$\sqrt{2}$$
so side is 5 and area =$$side^2$$ = 25
So sufficient
Statement 2 gives the perimeter as 20
perimeter = 4 * side = 20 so side is 5 and area = $$side^2$$ = 25
So sufficient
Retired Moderator
Joined: 26 Nov 2012
Posts: 597
What is the area of square ABCD? [#permalink]

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04 Aug 2016, 16:56
Bunuel wrote:
What is the area of square ABCD?

(1) The diagonal of square ABCD is $$5\sqrt{2}$$
(2) The perimeter of square ABCD is 20

Kudos for correct solution.

Took 16 secs to solve..I think it's still more..

Stat 1: $$a\sqrt{2}$$(Diagonal of a sqaure) = $$5\sqrt{2}$$.
a = 5.. Sufficient..

Stat 2: 4a = 20 , a = 5..Sufficient..

Manager
Joined: 05 Apr 2014
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Location: India
Schools: ISB '19, Fox"19
GMAT 1: 660 Q48 V33
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Re: What is the area of square ABCD? [#permalink]

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21 Feb 2017, 22:07
D
Statement 1 is sufficient
Side is 7
So area would be 49
Statement 2 is sufficient as well
Side is 7 as diagonal is sideroot2
So area 49

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Re: What is the area of square ABCD?   [#permalink] 21 Feb 2017, 22:07
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