skamal7 wrote:

Is ABCD rectangular?

(1) Angle ABC and BCD are right angle

(2) Two diagonal have the same length.

The best approach to tackle statement questions in DS is as follows:

Step 1: Convert all the alphabetical statements in algebraic statements

Step 2: Reduce the number of variable to minimum

Step 3: Check how many variables are left. You may probably need that many statements to solve the questions but you might need lesser number of statements to answer the question.

Caution: Don't waste your time in solving the question. You have to analyse the data sufficiency and not solve the question.

Lets solve this using the approach given above:

Step 1: Is ABCD rectangular? can be reduced to the fact that angle ABC, BCD, CDA, and DAB are all right angles. If we deduce this, we can be assured that it is a reactangle.

Step 2: If 3 angles are 90 degrees, the fourth angle automatically becomes 90 degree. Hence, we need to know only 3 angles. Further look, even a group of opposite angle if each 90 degree, even then we can say it is a rectangle.

Step 3:

(1) Angle ABC and BCD are right angle.

ABC and BCD are consecutive angles, and not opposite angles, thus, we can't say about other two angles. Hence, it is not sufficient.

(2) Two diagonal have the same length

This statement does not tell anything about angles of the quadrilateral and hence not sufficient.

Now, if we take both the statements together, we know that one diagonal is AC which is a hypotenuse of AB and BC. Now, the other diagonal BD = AC as per statement 2. Since angle BCD is also a right angle, CD = AB. Now if you join AD, we get an angle ADC = 90 degree. Now we know that three angles are 90 degree and hence it is a rectangle. Option C) therefore is the right answer.

A quadrilateral is also a rectangle if any 2 angles are 90 degree and any two opposite sides are equal. Using both 1) and 2) together, we can see that ABC and BCD are 90 degree and after this we get AB = CD. Hence we can say using both the statements, we can answer the question.

Hope it helps!!!

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