CAT Questions | Indices & Surds

The topic Indices and Surds is a part of the Number System vertical of the Quantitative Aptitude section in the MBA entrance exam. Although we can observe from the trend that the frequency of occurrence of questions in this topic has decreased, we cannot ignore this topic entirely as we can always expect 1-2 questions on this topic in many MBA exams.

Exams which use contain this topic:

Many exams ask questions on Indices and Surds. These may range from 1-2 questions which are usually assigned easy to moderate level of difficulty. Hence, it is wise to cover this topic to score well.

 

ExamYearNo of QuestionsLevel of Difficulty
CAT
20181Moderate
20181Easy
NMAT
20191Moderate
20181Easy
SNAP20181Easy

 

List of concepts for Indices and Surds:

Indices: The base ‘a’ raised to power ‘b’ is equal to the multiplication of a, b times a = a × a… × a b times. Where a is the base and b is the indices.

Examples

2^1 = 2

2^2 = 2*2 = 4

2^3 = 2*2*2 = 8

Surds: Numbers that can be written as √a + √b, where a and b are not perfect squares and natural numbers. Hence, the numbers in the form of √5, 5√7, ……. x√y

Rules and Properties of Indices and Surds

Name of the Rule

Conversion

Division

am/ an = am-n

an / bn = (a / b)n

Multiplication

an am = am+n

an  bn = (a b)n

Power

(an)m = anm

anm = a(nm)

m√(an) = a n/m

n√a = a1/n

a-n = 1 / an

Important points to Remember:

1) Surd nx can be simplified if the factor of x is a perfect square
2)Any number raised to the power zero always equals one. (Eg: x 0 = 1)
3) The conjugate of (x√a + y√b) is (x√a – y√b)
4) If the denominator in a fraction has a surd, then rationalize the denominator by multiplying both numerator and denominator by a conjugate surd
5) Different expressions can be simplified by rationalizing the denominator and eliminating the surd
6) Every surd is an irrational number.
 

Some Questions from Previous Papers

CAT 2019 Slot 1 – If m and n are integers such that (√2)^19 * 3^4 * 4^2 * 9^m * 8^n = 3^n * 16^m (4√64) then m is?

1. -20

2. -24

3. -16

4. -12 

Answer – 12

 Explanation:

Given, √2^19 3^4 4^2 9^m 8^n=3^n 16^m ∜64

Or 2^(19/2)×3^4×2^4×3^2m×2^3n= 3^n×2^4m×2^(6/4)

2^(19/2+4+3n)×3^(4+2m)=3^n×2^((4m+6/4) )

Comparing both sides,

n = 4+2m

19/2 +4 + 3n = 4m + 6/4

Or (19 + 8)/2 + 3(4+2m) = 4m + 3/2

27/2 + 12 + 6m = 4m + 3/2

6m -4m = 3/2 – 27/2 -12

2m = -24

Thus m = -12

 

If 17x = 4913, find the value of 22x-1.

a) 16

b) 32

c) 64

d) 128

17x = 4913

⇒17x = 4913

⇒17x = (17)3

⇒x = 3

 

Value of 22x-1 ⇒ 22.3-1⇒ 25 = 32

 

If 2x × 8(1/4) = 2(1/4) then find the value of x

As bases are not equal we cannot add the indices, hence first convert all the numbers with the same base.

2x × (23)(1/8) = 2(1/4)

 Hint:

Law of Indices (xm)n = xmn

 2x × 2(3/4) = 2(1/4)

 2[x + (3/4)] = 2(1/4)

If 4 (x – y) = 64 and 4 (x + y) = 1024, then find the value of x.

a. 3

b. 1

c. 6

d. 4 

4 (x – y) = 64

4 (x – y) = 64 = 43

Equation 1) x – y = 3

 

4 (x + y) = 1024 = 45

Equation 2) x + y = 5

Solving equation (1) and (2), we get

x = 4 and y = 1

 

Crosscheck the answers by substituting the values of x and y in the given expression.

4 (4 – 1) = 43 = 64 and 4 (4 + 1) = 45 = 1024

Hence, the answers x = 4 and y = 1 are correct.

 

If a and b are whole numbers such that ab = 121, then find the value of (a – 1)b + 1

a. 0

b. 10

c. 102

d. 103

121 = 112 , hence value of a = 11 and b = 2 can be considered.

Therefore, the value of (a – 1)b + 1 = (11 – 1) 2 + 1= 103

How to deal with that topic preparation

Preparing for Indices and Surds will require a basic understanding of the key concepts and speedy calculation along with hard work and dedication. Here are some Level-wise preparatory guidelines to follow:

Level – 1

  1. Learn all the basic concepts of indices and surds and their rules and properties.
  2. Learn Speed calculation: For an effective and quick calculation, be thorough with tables till 20, memorize squares till 30, and cubes till 15.
  3. Memorize the properties of the log.
  4. Practice beginner-level questions.

Level – 2

  1. Move on to more complex problems, attempt beginner and intermediate level mock on concepts of Indices and Surds.
  2. Solve previous year CAT questions on Indices and Surds and time yourself. Do not get stuck on one question and try to solve easy questions first.
  3. Keep attempting mocks to check your performance.
  4. Topic-wise mocks, provided by MBAP, can be utilized to enhance your performance.

Level – 3

  1. For advanced level preparation, start practicing questions from the book – How to Prepare for Quantitative Aptitude for the CAT, authored by Arun Sharma.
  2. Questions in Arun Sharma are categorized into Level of Difficulty (LOD), based upon your preparation level, start attempting 3 or 4 questions daily.

Details on This Page

Words From Our Students

Nihar Mehta
Nihar Mehta
Calls from IIMs, SPJIMR & MDI
Read More
I joined the classroom coaching programme at MBA Pathshala for my CAT preparation. Since the very beginning, Abhijit Sir & Haider Sir guided me in terms of the strategy & the approach required in order to fare well in the exam. They not only stressed on the academics but also pushed me to build my profile aligned with my interests. Post CAT, they gave me ample practice for my GD & PI preparations with sufficient number of mock interviews & regular feedback for improvement. I managed to get calls from IIMs, SPJIMR & MDI. A huge part in this goes to the team at MBAP and I am cannot thank them enough for their contribution.
Ishan Rathod
Ishan Rathod
Calls from IIM I, S, and all New And Baby IIM's.
Read More
MBAP is great place to preparing for MBA-CET,CAT,CMAT and faculty are unbeatable. They are very helpful best part is they give personal attention to each and every students. Most of faculty...who are alumni of IIM and JBIMS. There is more one to one interaction which helped me get better as the exams approached and helped me get calls from IIM I, S, and all New And Baby IIM's. The interview sessions proved to be of great learning helped me convert IIM S
Sanskriti Reja
Sanskriti Reja
Calls from IIMs, XLRI, XIMB
Read More
MBA Pathshala was my first choice for MBA coaching and I'm happy that joined it. The faculty here is great.. they are really good in what they do. They supported me and motivated me during my journey of clearingthe entrances. They are always available for the doubts, extra lectures. they helped me get through my GD-PIs too after the exams. I am thankful to MBAP for helping me to crack CAT and other entrance exams. I got calls from XLRI, XIMB, IIMs, among others. I have converted colleges like KJ Somaiya, TAPMI, IIM Sambalpur, IIM Sirmaur.
Parth Kanakia
Parth Kanakia
Converted SPJIMR
Read More
I joined MBAP for GD, WAT & PI preparation. Received very good training from Abhijit Singh, Haider and other MBAP faculty. Starting from very basics, good knowledge was provided. Mock interviews were conducted on regular basis. I converted SPJIMR and I would definitely recommend students to join MBAP.
Ronit jaiswal
Ronit jaiswal
Calls from IIM-A/B/C & SNAP 98.12%ile
Read More
I wanted to join a coaching where I can get personalised attention and competitive environment. I got both in MBAP. All the preparation was so rigorous that I eventually started giving my best. They conducted mock interviews/GD/WAT with anonymous panels and trust me it was such a confidence booster. I got a call from SCMHRD (SNAP-98.12) However I always wanted to go for IIM and Abhijeet sir felt that and he convinced me to try again and aim for IIM-A/B/C. Here I am back under his mentorship again. In short give your best and they will bring the best out of you. P.S- I'm a working individual. If I can do it then anybody can. Thank you for being such a great mentors.
Maitreya Khanapurkar
Maitreya Khanapurkar
Calls From IIMs
Read More
Best learning experience.Faculties are good and you will get a good support from them till you get admission into a B-School.The shortcut techniques taught will be of great help for you. Doubts will be solved anytime you want. If planning for CAT CET or any entrance exam go for MBA Pathshala. It was of tutors at MBAP I received a call from IMT Ghaziabad.
Yash Dandavate
GMAT Score - 660
Read More
I joined MBAP for GMAT prep and my experience with them was really amazing, from the first day itself the faculties gave personal attention to each student and made sure each student had their own personalised GMAT and CAT prep plans. The Verbal faculty Rohan Kulkarni Sir was amazing, I was very weak in English and verbal section, but through his guidance I scored a V38 (85th percentile) in my GMAT exam. The Quant faculties Abhijeet and Haider Sir helped me develop strategies and short cuts to approach GMAT problems and we're always available for my doubts. Overall it was a great experience and I would reccomend MBAP to everyone for GMAT and CAT prep
Previous
Next
Hello there
Signup now to get the latest news & instant updates of MBA... Subscribe below with your email Address