The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for **Free**) head out here: **CAT Official Question Mocks**. In CAT 2017 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: **CAT Question Bank**

Question 13 : If a and b are integers of opposite signs such that (a + 3)^{2} : b^{2} = 9 : 1 and (a - 1)^{2} : (b - 1)^{2} = 4 : 1, then the ratio a^{2} : b^{2} is :

- 9 : 4
- 81 : 4
- 1 : 4
- 25 : 4

Buy CAT'21 95-99 Booster Course for just

Valid until 19th Sep

Online Batches Available Now!

Let us consider the two ratios given to us.

For (a + 3)^{2} : b^{2} = 9 : 1

⟹ \\frac{(a + 3)^2}{b^2}) = 9

⟹ \\frac{(a + 3)}{b}) = ± 3 ------- (1)

Similarly, we can say that, (a - 1)^{2} : (b - 1)^{2} = 4 : 1,

⟹ \\frac{(a - 1)^2}{(b - 1)^2}) = 4

⟹ \\frac{(a - 1)}{(b - 1)}) = ± 2 ------(2)

From (1), we can say that, a + 3 = ± 3b, So

a = 3b – 3 ------- (3) Or,

a = -3b – 3 ------- (4)

Sub (3) in (2)

⟹ (a – 1) = 2(b – 1) or (a – 1) = -2(b – 1)

⟹ (3b – 4) = 2b – 2 or (3b – 4) = -2b + 2

⟹ b = 2 or b = \\frac{6}{5})

⟹ a = 3 or a = \\frac{3}{5})

Both these cases are not possible since a and b are said to be of opposite signs.

Let’s try condition (4).

Sub (4) in (2), we get

⟹ (a – 1) = 2(b – 1) or (a – 1) = -2(b – 1)

⟹ (-3b – 4) = 2b – 2 or (-3b – 4) = -2b + 2

⟹ b = -\\frac{2}{5}) or b = – 6

⟹ a = -\\frac{9}{5}) or a = 15

Here a = 15 and b = – 6 are possible.

Let’s find a^{2} : b^{2}

⟹ \\frac{a^2}{b^2}) = \\frac{15^2}{-6^2})

⟹ \\frac{a^2}{b^2}) = \\frac{225}{36})

⟹ \\frac{a^2}{b^2}) = \\frac{25}{4})

Hence a^{2} : b^{2} is equal to 25 : 4

The question is **"If a and b are integers of opposite signs such that (a + 3) ^{2} : b^{2} = 9 : 1 and (a - 1)^{2} : (b - 1)^{2} = 4 : 1, then the ratio a^{2} : b^{2} is :" **

Choice D is the correct answer.

CAT 2021

Enroll at

44,000/-

Online Classroom Batches Starting Now!

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com