Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each

Question

Is Quadrilateral ABCD a Rhombus?

1) Diagonals of ABCD intersect each other at 90 degrees
2) Diagonals of ABCD are equal in dimension

Source:  https://www.GMATInsight.com

Bunuel · Answer

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amanvermagmat · Answer

Statement 1: In a quadrilateral, if diagonals intersect each other at 90 degrees, then it could be a rhombus or a square or a kite. In first two cases we can call it a rhombus only (because square is a special kind of rhombus) but if its a kite, it cannot be called a rhombus. Insufficient. 
(Please note that the statement does NOT say 'bisect each other at 90' but it says 'intersect each other at 90'.

Statement 2: Diagonals of a square, a rectangle and an isosceles trapezoid are equal in dimension. In the first case (if its a square) we can call it a rhombus (square is a special kind of rhombus) but in other two cases we cannot. Insufficient.

Combining the two statements, diagonals intersect at 90 and diagonals are also equal in dimension. This happens only in a square which is basically a rhombus only. So sufficient. answer should be C.

(OA is given to be E I don't know why)

DigitsnLetters · Answer

Diagonals of the Quadrilateral ABCD intersect each other at 90 degrees: Quadrilateral can be Rhombus or Kite. Hence, Statement-1 is insufficient.

Diagonals of the Quadrilateral ABCD are equal in dimension: Quadrilateral can be Square (note that Square is a Rhombus with each interior angle as 90 degrees) or Rectangle or a Trapezium with equal non-parallel sides. Hence, Statement-2 is insufficient.

Both statements together: Diagonals of Quadrilateral ABCD intersect each other at 90 degrees and are equal in dimension. The quadrilateral has to be a Square (which is a Rhombus with each interior angle as 90 degrees). Thus, both the statements combined give a definite answer. Hence, both the statements together are sufficient to answer the question.

Answer: C. However, OA says it's E. How? If not please modify the OA.

Kurtosis · Answer

St1: Quadrilateral is a Square, Rhombus or Kite.

St2: Quadrilateral is a Square, Rectangle or an Isosceles Trapezoid.

Combining St1 and St2: Quadrilateral is a Square. A square is a special case of Rhombus.

Answer: C

Nunuboy1994 · Answer

I don't understand why statement B uses the term "dimension"- doesn't dimension usually imply two numbers as in 5 x 5 or 7 x 11? Can someone please clarify this kudos. Initially I thought that that's what the statement meant, but then I second guessed myself and though that well if it's saying dimensions then maybe the question refers to four triangles that make up a square or rectangle for example.

C

Hero8888 · Answer

The OA is wrong. Answer is E. See attachment in which diagonals are equal and cross at 90 degree.

Hero8888 · Answer

Hi  Bunuel

Please review my answer above. If I'm correct, the OA has to be changed to E.

joydip81 · Answer

OA seems wrong. I came up with answer E, and found the last post supporting that explanation. Diagonals are intersecting and not bisecting,

NikMan · Answer

I would also concur with the previous two posts. I got E as well since the diagonals do not bisect each other.
 Bunuel  Request you to please update the OA or else correct us if we are mistaken.

Thanks

Bunuel · Answer

______________________________
Yes, it should be E. Edited. Thank you.

bumpbot · Answer

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Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each

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