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CAT 2007 — QA Question 17

Number TheoryEasy

Each question is followed by two statements A and B. Answer each question using the following instructions.
Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone.
Mark (4) if the question cannot be answered on the basis of the two statements.

Consider integers x, y and z. What is the minimum possible value of x2 + y2 + z2 ?

A. x + y + z  = 89
B. Among x, y, z two are equal.

Answer & solution

Correct answer: 1

  • 1

  • B

    2

  • C

    3

  • D

    4

  • E

    5

Solution

Statement A:

x + y + z = 89

x2 + y2 + z2 will be minimum when x = y = z = 89/3

But 89/3 is a non-integer.  ∴ We consider integer values of x, y, z which are as close as possible to 89/3.

We get two cases

1.  x, y, z = 30, 30, 29

x2 + y2 + z2 = 2641

2.  x, y, z = 31, 29, 29

x2 + y2 + z2 = 2643

Minimum possible value of x2 + y2 + z2 is 2641. Thus statement A is sufficient to get the answer. Though statement B states a fact related to the minimum value, it is not necessary to arrive at the minimum value.

Hence, option (a).

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CAT 2007 QA Q17: Each question is followed by two statements A and B. Answer each question using the following instructions. Ma — Solution | TheCATExam