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, 12+32+52+72+92=165, then what is the value of 32+92+152+212+272?
a) 1485
b) 1385
c) 990
d) 495
View Answer
Explanation: = 32+92+152+212+272
= 32 * (12+32+52+72+92) = 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 mn?
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 mn 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”.
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