# CAT Practice : Number System

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The following topics are covered in the CAT quant section from Number system. Detailed explanatory answers, solution videos and slide decks are also provided.
1. ### Product of digits

How many numbers with distinct digits are possible product of whose digits is 28?

1. 6
2. 4
3. 8
4. 12
2. ### Sum of first n natural numbers

A page is torn from a novel. The sum of the remaining page numbers is 10000. What is the sum of the two page-numbers on the torn page of this novel?

1. 77 and 78
2. 33 and 34
3. 8 and 9
4. None of these
3. ### Perfect Square

A 4-digit number of the form aabb is a perfect square. What is the value of a - b?

1. 3
2. 2
3. 4
4. 1
4. ### Last two digits

What are the last two digits of the number 745?

1. 07
2. 23
3. 49
4. 43
5. ### Multiples

n2 + 5n + 6 is a multiple of 6. n is natural number less than 100. How many values can n take?

1. 33
2. 65
3. 66
4. 67
6. ### Greatest integer function

[x] is the greatest integer less than or equal to x. Find the number of positive integers n such that $\left[ {{{\rm{n}} \over {{\rm{11}}}}} \right]{\rm{ = }}\left[ {{{\rm{n}} \over {{\rm{13}}}}} \right]$.

1. 31
2. 25
3. 35
4. 40
35
• Greatest integer function
• Medium
7. ### Medians, Number

Positive numbers 1 to 55, inclusive are placed in 5 groups of 11 numbers each. What is the maximum possible average of the medians of the 5 groups?

1. 34
2. 28
3. 35
4. 38
8. ### 44th digit of a number

N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit?

1. 5
2. 6
3. 1
4. 2
9. ### Divisibility of powers

A number 416 + 1 is divisible by x. Which among the following is also divisible by x?

1. 496 + 1
2. 432 + 1
3. 48 + 1
4. 448 + 1
448 + 1
• Divisibility of powers
• Medium
10. ### Test of Divisibility

Which among the following is the smallest 7 digit number that is exactly divisible by 43?

1. 1000043
2. 1000008
3. 1000006
4. 1000002
11. ### Three digit number combinations

How many 3-digit positive integers, with digits a, b and c exist such that a < b and c < b? Assume that a is in hundred's place, b is in ten's place, c is in unit's place and a is a non-zero digit.

1. 450
2. 240
3. 364
4. 648
• Three digit number combinations
• Medium

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