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CAT Questions – number system (digits) with VIDEO Solution

QUESTION 1
Find the sum of digits of smallest number which is divisible by all single digit prime numbers but no digit of the number is prime.
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QUESTION 2
What is the sum of all the digits of the smallest three digit number $N$ such that all the digits of $3 \times N$ are even.
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QUESTION 3
Let ABCDE be a five digit number where A, B, C, D, and E are the digits. If $ABCDE\times 9=1AAA0E$ , what is the value of A+B+C+D+E?
1. 12
2. 15
3. 18
4. 21
Option: 2
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QUESTION 4
Let a be a number (in base 10) which has m number of digits and ${{a}^{3}}$ has n number of digits. Which of the following CANNOT be the value of m+n?
1. 3000
2. 3001
3. 3002
4. 3003
Option: 2
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QUESTION 5
There are positive integers with leading digits being 6 and upon removing this leading digit, the resulting integer is $\cfrac{1}{{25}}$ of the original value. Determine the least of such positive integers.