XAT 2021Decision Making Question 3

Lines & AnglesEasy
Passage / Data

Read the following scenario and answer the three questions that follow.
A quick survey at the end of a purchase at buyagain.com asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)
3. How satisfied are you? (HAPPY, NEUTRAL or UNHAPPY)

240 shoppers answer the survey, among whom 65 are first time shoppers. Furthermore:
i. The ratio of the numbers of male to female shoppers is 1 : 2 while the ratio of the numbers of unhappy, happy and neutral shoppers is 3 : 4 : 5
ii. The ratio of the numbers of happy first-time male shoppers, happy returning male shoppers, unhappy female shoppers, neutral male shoppers, neutral female shoppers and happy female shoppers is 1 : 1 : 4 : 4 : 6 : 6
iii. Among the first-time shoppers, the ratio of the numbers of happy male, neutral male, unhappy female and the remaining female shoppers is 1 : 1 : 1 : 2, while the number of happy first-time female shoppers is equal to the number of unhappy first-time male shoppers

ABC is a triangle with integer-valued sides AB = 1, BC >1, and CA >1. If D is the mid-point of AB, then, which of the following options is the closest to the maximum possible value of the angle ACD (in degrees)?

Answer & solution

  • 15

  • B

    30

  • C

    45

  • D

    75

  • E

    60

Solution

Given, AB = 1, AC > 1 and BC > 1
If ABC was an equilateral triangle i.e if AB = AC = BC = 1, ACD would have been 30°.
As C moves away from A and B, the angle decreases, hence the angle should be less than 30 and among the given options only 15 is less than 30.

XAT 2021 Decision Making Q3: ABC is a triangle with integer-valued sides AB = 1, BC >1, and CA >1. If D is the mid-point of AB, then, which — Solution | TheCATExam