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XAT 2021 — Decision Making Question 9

Ratio, Proportion & VariationEasy
Passage / Data

Read the following scenario and answer the three questions that follow.
The following plot describes the height (in cm), weight (in kg), age (in years) and gender (F for female, M for male) of 20 patients visiting a hospital.

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A person’s body mass index (BMI) is calculated as weight (in kg) divided by squared height (measured in square metres). For example, a person weighing 100 kg and of height 100 cm (1m) will have a BMI of 100. A person with BMI less than or equal to 18.5 is considered as underweight, above 18.5 but less than or equal to 25 as normal weight, above 25 but less than or equal to 30 as overweight, and above 30 as obese.

The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?

Answer & solution

  • A

    (3 + √3) : (1 + √3) : 1

  • B

    (3 - √3) : 1 : (√3 - 1)

  • C

    1 : 1 : 1

  • (3 - √3) : (√3 - 1) : 1

  • E

    (√3 - 1) : 1 : (3 - √3)

Solution

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Let ED = √3x

In triangle CDE, tan 30 = CD3x ⇒ CD = x

In triangle BDE, tan 45 = BD3x ⇒ BD = 3x ⇒ BC = 3x - x

In triangle ÖDE, tan 60 = AD3x ⇒ AD = 3x ⇒ AB = 3x - 3x

AB : BC : CD = (3 - √3) : (√3 - 1) : 1

XAT 2021 Decision Making Q9: The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The p — Solution | TheCATExam