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.
Exam | Year | No of Questions | Level of Difficulty |
CAT | 2018 | 1 | Moderate |
2018 | 1 | Easy | |
NMAT | 2019 | 1 | Moderate |
2018 | 1 | Easy | |
SNAP | 2018 | 1 | Easy |
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 | a^{m}/ a^{n} = a^{m-n} |
a^{n} / b^{n} = (a / b)^{n} | |
Multiplication | a^{n}⋅ a^{m} = a^{m+n} |
a^{n} ⋅ b^{n} = (a ⋅ b)^{n} | |
Power | (a^{n})^{m} = a^{n}^{⋅}^{m} |
_{a}n^{m} = _{a}^{(nm)} | |
^{m}√(a^{n}) = a ^{n/m} | |
^{n}√a = a^{1/n} | |
a^{-n} = 1 / a^{n} |
Important points to Remember:
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
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
Level – 2
Level – 3
Inspiring Education… Assuring Success!!
Ⓒ 2020 – All Rights Are Reserved