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XAT 2014 — QA & DI Question 9

Simple EquationsEasy

Consider four natural numbers: x, y, x + y, and x – y. Two statements are provided below:

  1. All four numbers are prime numbers.
  2. The arithmetic mean of the numbers is greater than 4.

Which of the following statements would be sufficient to determine the sum of the four numbers?

Answer & solution

Correct answer: Statement I.

  • Statement I.

  • B

    Statement II.

  • C

    Statement I and Statement II.

  • D

    Neither Statement I nor Statement II.

  • E

    Either Statement I or Statement II.

Solution

Considering Statement I:

Since this is the only possible solution, statement I is sufficient.
Considering Statement II:

​​​​​​​

Since no unique solution is possible, statement II is not sufficient.

Hence, option (a).

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XAT 2014 QA & DI Q9: Consider four natural numbers: x, y, x + y, and x – y. Two statements are provided below: All four numbe — Solution | TheCATExam