Number System & Operations
· Mathematics-General Ability
270 Questions• 203 Mins Practice• Updated for 2026 Competitive Exams
270 MCQs
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Showing 121–140 of 270 MCQs
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270 Questions
121
How many numbers of the first 100 positive integers are divisible by 3 or 4 without a remainder? (a) 50 (b) 5 (c) 58 (d) 85
Correct Option
Option A
Explanation
We use the Principle of Inclusion-Exclusion: $N(A \cup B) = N(A) + N(B) - N(A \cap B)$.
122
Find the sum of the smallest and the largest positive numbers of 6 digits which contain only digits 0, 4, 6 and each of these digits appears at least once. (a) 666444 (b) 604604 (c) 666666 (d) 1066646
Correct Option
Option D
Explanation
**Step 1: Find the smallest 6-digit number.**
123
In a five-digit number, the digit in the hundred's place is 2 and the digit in the unit's place is twice the digit in the hundred's place. The digit at thousands place is zero. The digit in the ten thousand's place is the sum of the digit in the hundred's place and the digit in the unit's place. The digit in the ten's place is the digit in the ten thousand's place minus 1. The number is: (a) 60234 (b) 60224 (c) 60254 (d) 60264
Correct Option
Option C
Explanation
Let's build the five-digit number place by place.
124
A number when divided by 7 leaves a remainder 4. What will be the remainder when the square of the same number is divided by 7? (a) 2 (b) 4 (c) 1 (d) 3
Correct Option
Option A
Explanation
**Method 1: Using Algebra**
125
A student divided a number by 12 instead of 21 and received 35. Find the correct answer. (a) 20 (b) 15 (c) 26 (d) 25
Correct Option
Option A
Explanation
**Step 1:** Let the original number be $N$. The student performed the incorrect calculation: $N \div 12 = 35$.
126
The least number that is divisible by all the numbers from 2 to 10 is– (a) 2520 (b) 100 (c) 504 (d) 9
Correct Option
Option A
Explanation
The question asks for the Least Common Multiple (LCM) of the numbers 2, 3, 4, 5, 6, 7, 8, 9, and 10.
127
How many numbers between 1 and 99 (inclusive) have a non-zero tens digit? (a) 98 (b) 90 (c) 99 (d) 100
Correct Option
Option B
Explanation
The question is asking for the count of numbers from 1 to 99 that are 10 or greater.
128
What should be added to 135642 to get the largest six digit number? (a) 864350 (b) 863357 (c) 864357 (d) 864347
Correct Option
Option C
Explanation
**Step 1:** The largest six-digit number is 999999.
129
Which of the following numbers is divisible completely by both 9 and 11? (a) 277218 (b) 10098 (c) 12345 (d) 181998
Correct Option
Option B
Explanation
To be divisible by both 9 and 11, a number must satisfy the divisibility rules for both.
130
Which of the following numbers is divisible by 6? (a) 12378 (b) 12363 (c) 12370 (d) 12388
Correct Option
Option A
Explanation
For a number to be divisible by 6, it must be divisible by both 2 and 3.
131
If the 7-digit number $504x5y3$ is divisible by 11, then one of the values of the sum of x and y is: (a) 11 (b) 5 (c) 17 (d) 7
Correct Option
Option C
Explanation
The divisibility rule for 11 states that the difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.
132
If the largest 4–digit number is subtracted from the smallest 6-digit number, then the remainder will be: (a) 90000 (b) 99991 (c) 80001 (d) 90001
Correct Option
Option D
Explanation
- **Smallest 6-digit number:** 100,000
133
A number when divided by 280 leaves 73 as the remainder. When the same number is divided by 35, the remainder will be: (a) 4 (b) 2 (c) 3 (d) 7
Correct Option
Option C
Explanation
**Method 1: Direct Method**
134
Find the smallest four-digit number that is divisible by 47. (a) 1200 (b) 1025 (c) 1034 (d) 1360
Correct Option
Option C
Explanation
**Step 1:** The smallest four-digit number is 1000.
135
Find the two-digit number such that the sum of its digits is 8 and the digits of the number get reversed when 36 is added to it. (a) 71 (b) 35 (c) 62 (d) 26
Correct Option
Option D
Explanation
**Step 1:** Let the two-digit number be $10x + y$.
136
If n is a natural number then $n^3–n$ is always divisible by... (a) 8 (b) 6 (c) 5 (d) 4
Correct Option
Option B
Explanation
Let's factorize the given expression, $n^3 - n$.
137
Which number is divisible by 9? (a) 56112 (b) 89445 (c) 49653 (d) 58556
Correct Option
Option C
Explanation
The divisibility rule for 9 is that the sum of the digits must be divisible by 9.
138
How many times does digit 3 appear in the counting from 301 to 399? (a) 119 (b) 11 (c) 121 (d) 21
Correct Option
Option A
Explanation
Let's count the occurrences of the digit '3' in each place value from 301 to 399.
139
Which of the following numbers is divisible by 9? (a) 56765 (b) 47862 (c) 54321 (d) 87654
Correct Option
Option B
Explanation
The divisibility rule for 9 is that the sum of the digits must be divisible by 9.
140
Choose the missing digit 'x' from the options given for the number $987x54$, so that the number is completely divisible by 6. (a) 2 (b) 5 (c) 3 (d) 1
Correct Option
Option C
Explanation
For the number $987x54$ to be divisible by 6, it must be divisible by both 2 and 3.
