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Updated on: 07 Aug 2018, 04:09
Originally posted by EgmatQuantExpert on 22 Nov 2016, 05:32.
Last edited by EgmatQuantExpert on 07 Aug 2018, 04:09, edited 5 times in total.
Last edited by EgmatQuantExpert on 07 Aug 2018, 04:09, edited 5 times in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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79% (00:44) correct
21%
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wrong
based on 842
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Exercise Question #1 Common Mistakes in Geometry Questions
ABCD is a quadrilateral as shown in the figure above. Find the area of the quadrilateral.
Answer Choices
Next Question
Detailed solution will be posted soon.
ABCD is a quadrilateral as shown in the figure above. Find the area of the quadrilateral.
- (1) The diagonals bisect each other at \(90^o\) and they are equal.
(2) The length of each diagonal is 10 cm.
Answer Choices
- A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Next Question
Detailed solution will be posted soon.
Updated on: 01 Dec 2016, 01:47
Originally posted by EgmatQuantExpert on 22 Nov 2016, 11:13.
Last edited by EgmatQuantExpert on 01 Dec 2016, 01:47, edited 2 times in total.
Last edited by EgmatQuantExpert on 01 Dec 2016, 01:47, edited 2 times in total.
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Note: This questions is related to the article on Common Errors in Geometry
Kindly go through the article once, before solving the question or going through the solution.
Official Solution
Given: ABCD is a quadrilateral.
Analysing statement 1:
The first statements states :
The diagonals bisect each other at \(90^o\) and they are equal.
From the above statement, we can conclude that the quadrilateral is a square.
But to find the area of the quadrilateral we need the length of each side, which is not given.
Hence statement 1 is not sufficient to answer the question.
Analysing statement 2:
The length of each diagonal is 10 cm.
Using only the 2nd statement, we cannot find the area of the quadrilateral, since we don't know what kind of quadrilateral it is.
Hence statement 2 is not sufficient to answer the question.
Combining statement 1 and 2:
Using both the statements, we can conclude that the quadrilateral is a square and the length of it's diagonal is 10cm.
Therefore, AB = BC = CD = AD
AC = BD = 10 (diagonals)
Since ABCD is a square angle ABC = 9\(0^o\), therefore we can infer that the diagonal(AC) is the hypotenuse and the sides AB and BC are the perpendicular and base.
Hence we can write A\(B^2\) + B\(C^2\) = A\(C^2\)
2A\(B^2\) = 1\(0^2\).............(i)
And we know the area of the square = (side\()^2\) = A\(B^2\)
We can find the value of AB from (i) and hence we can find the area of the square!
Hence combining both the statements we can find out the answer.
Correct Option : C
Thanks,
Saquib
Quant Expert
e-GMAT
Kindly go through the article once, before solving the question or going through the solution.
Official Solution
Given: ABCD is a quadrilateral.
Analysing statement 1:
The first statements states :
The diagonals bisect each other at \(90^o\) and they are equal.
From the above statement, we can conclude that the quadrilateral is a square.
But to find the area of the quadrilateral we need the length of each side, which is not given.
Hence statement 1 is not sufficient to answer the question.
Analysing statement 2:
The length of each diagonal is 10 cm.
Using only the 2nd statement, we cannot find the area of the quadrilateral, since we don't know what kind of quadrilateral it is.
Hence statement 2 is not sufficient to answer the question.
Combining statement 1 and 2:
Using both the statements, we can conclude that the quadrilateral is a square and the length of it's diagonal is 10cm.
Therefore, AB = BC = CD = AD
AC = BD = 10 (diagonals)
Since ABCD is a square angle ABC = 9\(0^o\), therefore we can infer that the diagonal(AC) is the hypotenuse and the sides AB and BC are the perpendicular and base.
Hence we can write A\(B^2\) + B\(C^2\) = A\(C^2\)
2A\(B^2\) = 1\(0^2\).............(i)
And we know the area of the square = (side\()^2\) = A\(B^2\)
We can find the value of AB from (i) and hence we can find the area of the square!
Hence combining both the statements we can find out the answer.
Correct Option : C
Thanks,
Saquib
Quant Expert
e-GMAT
22 Nov 2016, 13:15
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An interesting variant is to figure out what the answer should be if the word 'bisect' is removed from statement (1) 
