CAT Quantitative Aptitude Questions | CAT Percentages Problems - Integers

CAT Questions | Percentage Questions | Percentage - Integers

The question is from CAT Percentages. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019. This question is a very interesting question on the topic percentages using the concept of golden ratios. What is the golden ratio? Go go!! Google it.

Question 5 : A is x% more than B and is x% of sum of A and B. What is the value of x?

  1. 50%
  2. 62%
  3. 75%
  4. 37%

Online CAT Coaching for CAT 2019


Signup to sample the Best CAT Online Coaching


Best CAT Coaching in Chennai


Starts Sat, Mar 16, 2019


Explanatory Answer

Method of solving this CAT Question from Percentages: Golden ratio is a wonderful concept. Go on, google it.

a = b (1 + x) => \\frac{a}{b}\\) = 1 + x
a = x (a + b), dividing by a through out
1 = x (1 + \\frac{b}{a}\\))
1 = x (1 + \\frac{1}{1/x}\\))
1 = x (\\frac{x+2}{x+1}\\))
x + 1 = x2 + 2x
=> x2 + x - 1 = 0

Now, we need to solve this equation. Using the discriminant method, when we solve this, x turns out to be \\frac{-1+√5}{2}\\).
x has to lie between 0 and 1 and there for cannot be \\frac{-1-√5}{2}\\)
So, the only solution is \\frac{-1+√5}{2}\\). This is roughly 0.62.

Or, x has to be 62% approximately. The ration 1.618 is also called the golden ratio, and is the conjugate and reciprocal of 0.618.

The golden ratio finds many mentions, from the Fibonacci series to Da Vinci. So, it is a big favourite of mathematician.

The question is " What is the value of x? "
x has to be 62% approximately.

Hence, the answer is 62%

Choice B is the correct answer.

 

Online CAT Coaching
Try it free!

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, Mar 23rd, 2019

★ CAT Coaching Info

Best CAT Coaching in Chennai

Sign up for a Free Demo of our CAT Coaching in Chennai

★ Schedule Demo


CAT Preparation Online | CAT Arithmetic Videos On YouTube


Other useful sources for Arithmetic Question | Percentages Profits SICI Sample Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com