TheCATExam
Sign in

XAT 2021 — Decision Making Question 4

Simple EquationsEasy
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

Find z, if it is known that:

a: -y2 + x2 = 20

b: y3 - 2x2 - 4z ≥ -12 and

c: x, y and z are all positive integers

Answer & solution

  • A

    Any integer greater than 0 and less than 24

  • B

    24

  • C

    We need one more equation to find z

  • D

    6

  • 1

Solution

Since x2 - y2 = 20 and x, y, z are positive integers, the only values possible are x = 6 and y = 4.

y3 - 2x2 - 4z 12 ≥ -12

Keeping the values of x and y, we get z ≤ 1
⇒ z = 1 

XAT 2021 Decision Making Q4: Find z, if it is known that: a: -y 2 + x 2 = 20 b: y 3 - 2x 2 - 4z ≥ -12 and c: x, y and z are all positive — Solution | TheCATExam