Quantitative Aptitude
Number System and Simplification
548 Questions
Number system and simplification questions assess mathematical proficiency in handling fractions, decimals, and complex algebraic expressions. Test takers must simplify surds, calculate reciprocals, and solve intricate number pattern equations. This foundational quantitative aptitude topic is critical for achieving high scores in SSC and banking exams.
Fraction simplificationDecimal operationsSurds and indicesPercentage calculationsComplex number algebra
Number System and Simplification Questions
E
Correct answer
Explanation
To find the fraction with the lowest denominator, compare the bottom numbers: 6, 7, 9, 4, and 3. The smallest is 3, so 7/3 (Option E) has the lowest denominator. This is a straightforward comparison task.
Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit.
$f_1 = \Sigma m(4, 5, 6, 7, 8)$
$f_3 = \Sigma m(1, 6, 15)$
$f = \Sigma m(1, 6, 8, 15)$
Then f2 is
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$\Sigma m(4, 6)$
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$\Sigma m(4, 8)$
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$\Sigma m(6, 8)$
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$\Sigma m(4, 6, 8)$
Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit.
$f_1 = \Sigma m(4, 5, 6, 7, 8)$
$f_3 = \Sigma m(1, 6, 15)$
$f = \Sigma m(1, 6, 8, 15)$
Then f2 is
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$\Sigma m(4, 6)$
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$\Sigma m(4, 8)$
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$\Sigma m(6, 8)$
-
$\Sigma m(4, 6, 8)$
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100 marbles
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90 marbles
-
82 marbles
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72 marbles
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42 marbles
D
Correct answer
Explanation
After receiving marbles from Privartan, total marbles with Mohit = 422.
Hence, Mohit will have 422 - 350 = 72 marbles more than Sachin.
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80 marbles
-
99 marbles
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149 marbles
-
145 marbles
-
100 marbles
B
Correct answer
Explanation
Marbles required by Pritish to have as many marbles as Mohit = 200 - 101 = 99.
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27 runs
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100 runs
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15 runs
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25 runs
-
35 runs
A
Correct answer
Explanation
Manish required 100 - 73 = 27 more runs to make a century.
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1/20
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1/5, 1/20, 1/5
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1/20, 1/10
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1/4, 1/5
-
B
Correct answer
Explanation
As given 3/8 is 1/4 and 1/8
means 1/4 + 1/8 = (2+1) / 8 = 3/8
so if we add,we get
1/5 + 1/20 + 1/5 = (4+1+4)/20 = 9/20
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mixed fraction
-
proper fraction
-
improper fraction
-
equivalent fraction
B
Correct answer
Explanation
A proper fraction is a fraction where the numerator is less than the denominator (e.g., 3/4, 2/5). An improper fraction has a numerator greater than or equal to the denominator. A mixed fraction is a whole number plus a proper fraction. Equivalent fractions are different fractions representing the same value.
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1/2
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2
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-2
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-1/2
-
None of these
C
Correct answer
Explanation
It is the reciprocal as it is written in - b/a for -a/b. Hence, this option is correct.
C
Correct answer
Explanation
If two or more fractions will have the same value, then it is called as an equivalent fraction.
The value of the fraction does not change, if the numerator and denominator are multiplied by a same natural number.
Here 12/36 = 1/3 ..........[After dividing by 12 on both numerator and denominator]
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-1
-
$\frac{7}{2}$
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$\frac{5}{3}$
-
$\frac{5}{2}$
D
Correct answer
Explanation
$\frac{7x^2 + 2x + 5}{x+5}$ = $\frac{7(-1)^2 + 2(-1) + 5}{(-1)+5} = \frac{7-2 + 5}{4}$= $\frac{5}{2}$.
D
Correct answer
Explanation
$\frac{7x^2y + 2xy^2 + 3}{(x+4)^3}$ = $\frac{7(1)^2 2 + 2(1)(2)^2 + 3}{(1+4)^3}$= $\frac{14+8+3}{125} = \frac{1}{5}$
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$\frac{9}{2}$
-
- $\frac{9}{2}$
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$\frac{7}{2}$
-
$\frac{-7}{2}$
B
Correct answer
Explanation
$\frac{x+4}{x+2} = \frac{1}{5}$
5 (x + 4) = x + 2
5x + 20 = x + 2
5x – x = 2 – 20
4x = –18
x = $\frac{-18}{4}$
x =$\frac{-9}{2}$
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y = 3x + 2
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3y = 2 + 3x
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x + 3y = 2
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None of these
A
Correct answer
Explanation
Denominator is 2 more than thrice its numerator, y = 2 + 3x
B
Correct answer
Explanation
$\frac{8(x)^3 + 3(x)^2y + 2y}{x+y}$
= $\frac{8(-1)^3 + 3(-1)^2y + 2y}{-1+y}$
= $\frac{8(-1)^3 + 3(-1)^2 2 + 2(2)}{-1+2}$
= $\frac{8(-1) + 6 + 4}{1}$
= – 8 + 6 + 4 = 2
