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Number System - Aptitude MCQ Questions and Solutions with Explanations

Number System MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Number System with easy and logical explanations. Number System MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-1 section-7

Each section contains 100 MCQs on Number System .
1
A man engaged a servant on the condition that he would pay him Rs. 90 and a turban after service of one year. He served only for nine months and received the turban and an amount of Rs. 65. The price of turban is:
Discuss
Answer & Solution
Answer: Option C
Solution:
Let the cost of turban be Rs. x
According to the question
$$\frac{{90 + x}}{{12}} = \frac{{65 + x}}{9}$$     (per month pay)
270 + 3x = 260 + 4x
4x - 3x = 10
x = Rs. 10
2
How many composite numbers ae there from 53 to 97?
Discuss
Answer & Solution
Answer: Option A
Solution:
53 to 97 (Composite number) = 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96
Total number = 35
3
The sum of the odd divisors of 216 is:
Discuss
Answer & Solution
Answer: Option C
Solution:
216 → 23 × 33
= (20 + 21 + 22 + 23) × (30 + 31 + 32 + 33)
Sum of odd factors = 1 + 3 + 9 + 27 = 40
4
What least value which should be added to 1812 to make it divisible 7, 11 and 14?
Discuss
Answer & Solution
Answer: Option B
Solution:
7, 11, 14, LCM = 154
154k = 154 × 12 = 1848
1848 - 1812 = 36
5
For any integral value of n, 32n + 9n + 5 when divided by 3 will leave the remainder
Discuss
Answer & Solution
Answer: Option B
Solution:
32n + 9n + 5
Put n = 1
⇒ 32 × 1 + 9 × 1 + 5
⇒ 9 + 9 + 5
⇒ 23 ⇒ $$\frac{{23}}{3}$$
⇒ remainder = 2
Note: value of n can be 1, 2, 3, 4, . . . . .
6
If a certain number of two digit is divided by the sum of its digits, the quotient is 6 and the remainder is 3. If the digits are reversed and the resulting number is divided by the sum of the digits, the quotient is 4 and the remainder is 9. The sum of the digits of the number is
Discuss
Answer & Solution
Answer: Option C
Solution:
Let the number be 10x + y
Dividend = Divisor × Quotient + Remainder
∴ 10x + y = 6(x + y) + 3
⇒ 10x + y = 6x + 6y + 3
⇒ 10x - 6x + y - 6y = 3
⇒ 4x - 5y = 3 . . . . . . (i)
Again, 10y + x = 4(x + y) + 9
⇒ 10y + x = 4x + 4y + 9
⇒ 6y - 3x = 9
⇒ 2y - x = 3 . . . . . . (ii)
∴ By equation (i) + 4 × (ii),
4x - 5y = 3
8y - 4x = 12
$$\overline {3{\text{y}}\,\,\,\,\,\,\,\,\, = 15} $$
⇒ y = 5
From equation (ii)
2 × 5 - x = 3
⇒ x = 10 - 3
⇒ x = 7
∴ Sum of digits = x + y = 7 + 5 = 12
7
Product of three consecutive odd numbers is 1287. What is the largest of the three numbers?
Discuss
Answer & Solution
Answer: Option C
Solution:
Let three consecutive odd numbers be x, x + 2 & x + 4
x(x + 2)(x + 4) = 1287
Let take x = 9, x + 2 = 11 & x + 4 = 13 satisfy the equation
Therefore,
Largest number = 13
8
Arrangement of the fractions $$\frac{4}{3},\, - \frac{2}{9},\, - \frac{7}{8},\,\frac{5}{{12}}$$    into ascending order:
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & \frac{4}{3},\,\frac{{ - 2}}{9},\,\frac{{ - 7}}{8},\,\frac{5}{{12}} \cr & \frac{4}{3} = 1.33 \cr & \frac{{ - 2}}{9} = - 0.22 \cr & \frac{{ - 7}}{8} = - 0.875 \cr & \frac{5}{{12}} = 0.416 \cr & {\text{So, }}\frac{{ - 7}}{8},\,\frac{{ - 2}}{9},\,\frac{5}{{12}},\,\frac{4}{3} \cr} $$
9
Let a, b and c be the fractions such that a < b < c. If c is divided by a, the result is $$\frac{5}{2}$$, which exceeds b by $$\frac{7}{4}$$. If a + b + c = $$1\frac{{11}}{{12}}$$ , then (c - a) will be equal to:
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & \frac{c}{a} = \frac{5}{2} \cr & b = \frac{5}{2} - \frac{7}{4} \cr & b = \frac{3}{4} \cr & a + b + c = \frac{{23}}{{12}} \cr & a + c = \frac{{23}}{{12}} - \frac{3}{4} \cr & a + c = \frac{{14}}{{12}} \cr & a + c = \frac{7}{6} \cr & 2x + 5x = \frac{7}{6}\,\,\,\,\,\,\left\{ {\frac{c}{a} = \frac{{5x}}{{2x}}} \right. \cr & 7x = \frac{7}{6} \cr & x = \frac{1}{6} \cr & c - a = 3x = 3 \times \frac{1}{6} = \frac{1}{2} \cr} $$
10
The sum of the digits of the least number which when divided by 36, 72, 80 and 88 leaves the remainders 16, 52, 60 and 68, respectively, is:
Discuss
Answer & Solution
Answer: Option A
Solution:
36 - 16 = 20
72 - 52 = 20
80 - 60 = 20
88 - 68 = 20
LCM of 36, 72, 80, 88 = 7920
Least number = 7920 - 20 = 7900
Sum of the digits = 7 + 9 + 0 + 0 = 16