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XAT 2017 — QA & DI Question 27

Basics of QuadrilateralsMedium
Passage / Data

Answer the next 4 questions based on the following information:

The grid below captures relationships among seven personality dimensions: "extraversion", "true_arousal_plac", "true_arousal_caff”, "arousal_plac", "arousal_caff”, "performance_plac", and "performance caff”. The diagonal represents histograms of the seven dimensions. Left of the diagonal represents scatterplots between the dimensions while the right of the diagonal represents quantitative relationships between the dimensions. The lines in the scatterplots are closest approximation of the points. The value of the relationships to the right of the diagonal can vary from -1 to +1, with -1 being the extreme linear negative relation and +1 extreme linear positive relation. (Axes of the graph are conventionally drawn).

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ABCD is a rectangle. P, Q and R are the midpoint of BC, CD and DA. The point S lies on the line QR in such a way that SR: QS = 1:3. The ratio of the area of triangle APS to area of rectangle ABCD is

Answer & solution

  • 36/128

  • B

    39/128

  • C

    44/128

  • D

    48/128

  • E

    64/128

Solution

Let the length of the rectangle be ‘l’ and breadth be ‘b’.

The given figure is.

Let us draw a line MS parallel to DC

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∆RMS ~ ∆RDQ

∴ RM : MD = RS : SQ = 1 : 3

Let the length of the rectangle (i.e., AB = CD) ABCD be 8l and width be 8b (i.e., AD = BC).

∴ AR = 4b and RM = b

Also, MS = l and SL = 7l.

Also, PL : LC = 1 : 3 [∵ RS : SQ = 1 : 3]

Area (∆ARS) = ½ × AR × SM = 2lb

Area (∆RDQ) = ½ × RD × DQ = 8lb

Area (∆ABP) = ½ × AB × BP = 16lb

Area (PSQC) = Area (∆PSL) + Area(∆SLQC) 
                         = ½ × SL × PL + ½ × (SL + QC) × LC 
                         = 3.5lb + 16.5lb
                         = 20lb

Area of ∆ASP = Area of rectangle ABCD – [Area (∆ARS) + Area (∆RDQ) + Area (∆ABP) + Area (PSQC)]
                          = 64lb – [2lb + 8lb + 16lb + 20lb]
                          = 64lb - 46lb = 18lb

∴ Area(∆ASP)Area(ABCD) = 18lb64lb = 36128

Hence, option (a).

XAT 2017 QA & DI Q27: ABCD is a rectangle. P, Q and R are the midpoint of BC, CD and DA. The point S lies on the line QR in such a w — Solution | TheCATExam