Multiple choice

Directions: The following problem consists of a question and two statements numbered I and II. You have to decide whether the data provided in the statements is sufficient to answer the question and then mark according to the codes given below: (a) Statement I alone is sufficient, but statement II alone is not sufficient. (b) Statement II alone is sufficient, but statement I alone is not sufficient. (c) Either statement I or statement II alone is sufficient. (d) Statements I and II even together are not sufficient. (e) Statements I and II together are sufficient. What is the value of a and b? Statement I: a2 + b2 = 169 Statement II: ab = 90

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From statement I, a^2 + b^2 = 169. From statement II, ab = 90. Using (a+b)^2 = a^2 + b^2 + 2ab, we get (a+b)^2 = 169 + 180 = 349, so a+b = sqrt(349). Using (a-b)^2 = a^2 + b^2 - 2ab, we get (a-b)^2 = 169 - 180 = -11. Since the square of a real number cannot be negative, there is no real solution for a and b. Even if complex numbers are allowed, the system provides multiple possible values for a and b, so the statements together are not sufficient to determine unique values.

Keep practicing — related questions