This set of Aptitude Questions and Answers (MCQs) focuses on “Real Numbers and BODMAS Simplification”.

1. Find the rational number lying between √7 and √8.

a) 12/5

b) 14/5

c) 22/9

d) 23/9

View Answer

Explanation: We have, √7 = 2.64575… and √8 = 2.82842…

From options, 12/5 = 2.4

14/5 = 2.8

22/9 = 2.444…

23/9 = 2.555…

Clearly 2.8 i.e., 14/5 lies between √7 and √8.

2. What is the value of x, if x is real and |\(\frac{7-x}{5}\)|<2?

a) 0<x<17

b) -17<x<17

c) -3<x<17

d) x<17

View Answer

Explanation: As, |\(\frac{7-x}{5}\)|<2

\(\frac{7-x}{5}\)<2 or \(\frac{(7-x)}{5}\)<2

x > -3 or x < 17

Hence, -3 < x < 17

3. Given that, 1^{2}+3^{2}+5^{2}+7^{2}+9^{2}=165, then what is the value of 3^{2}+9^{2}+15^{2}+21^{2}+27^{2}?

a) 1485

b) 1385

c) 990

d) 495

View Answer

Explanation: = 3

^{2}+9

^{2}+15

^{2}+21

^{2}+27

^{2}

= 3

^{2}* (1

^{2}+3

^{2}+5

^{2}+7

^{2}+9

^{2}) = 9*165 = 1485

4. If m is a positive integer, then in which of the following form every square integer is represented?

a) 4m

b) 4m+1 or 4m+3

c) 4m or 4m+3

d) 4m or 4m+1

View Answer

Explanation: If m is a positive integer, then every square integer is of the form 4m or 4m+1, as every number is either a multiple of 4 or exceeds multiple of 4 by unity.

5. If x and y are natural number, not necessarily distinct. For all values of x and y, which of the following is also a natural number?

a) x + y

b) x – y

c) x/y

d) logx – logy

View Answer

Explanation: x – y can be negative, if y is greater than x. Hence, it cannot be natural number.

x/y and logx-logy can sometimes be in fractions and are not natural numbers.

x+y always represents natural number, when x and y are natural numbers.

6. If \(\frac{a}{5}\)=\(\frac{b}{6}\)=\(\frac{c}{9}\), then what is the value of \(\frac{a+b+c}{a}\)?

a) 4

b) 5

c) 3

d) 6

View Answer

Explanation: Let \(\frac{a}{5}\)=\(\frac{b}{6}\)=\(\frac{c}{9}\)=k

i.e., a = 5k, b = 6k, c = 9k

\(\frac{a+b+c}{a}=\frac{5k+6k+9k}{5k}\)=4

7. If m is a negative real number, then which of the following is true?

a) |m| = m

b) |m| = -m

c) |m| = -1/m

d) |m| = 1/m

View Answer

Explanation: Clearly, by the definition of modulus function |m| = -m, when m<0 i.e., when m is negative real number.

8. If x, y and z are real numbers such that x < y and z < 0, then which of the following statement is true?

a) (x/z) < (y/z)

b) (z/a) > (z/y)

c) xz > yz

d) xz < yz

View Answer

Explanation: Given that, x < y and z < 0 i.e., z is negative real number.

On multiplying a negative number to any inequality, we must flip the inequality sign.

Therefore, xz > yz

9. If \(\frac{m}{n}=\frac{5}{8}\), then what is the value of \(\frac{m-n}{m+n}\)?

a) 3/13

b) 13/3

c) -3/13

d) -13/3

View Answer

Explanation: \(\frac{m-n}{m+n}=\frac{\frac{m}{n}-1}{\frac{m}{n}+1}=\frac{\frac{5}{8}-1}{\frac{5}{8}+1}=\frac{5-8}{5+8}=\frac{-3}{13}\)

10. If m is positive even integer and n is negative odd integer, then which of the following real number is the solution of m^{n}?

a) Odd integer

b) Even integer

c) Rational number

d) Irrational number

View Answer

Explanation: If m is positive even integer and n is negative odd integer, then m

^{n}is rational number.

Consider m=8 and n=-5, then 8

^{-5}= 1/(32768), which is rational number.

11. Find the value of (125+216)-\(\frac{1750}{5^3}\)+15.

a) 329

b) 342

c) 392

d) 344

View Answer

Explanation: = (125+216)-\(\frac{1750}{5^3}\)+15

= (341)-\(\frac{1750}{125}\)+15

= 341- 14+15 = 342.

To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.