Dilnur Y.

Software Developer at Dreamy Stars Ltd.

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SAT

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Question:

if 2x-y=4, what is the value of 9^x/3^y?

Dilnur Y.

Answer:

9^x/3^y = (3^2x)/(3^y) = 3^(2x-y) We know that 2x-y=4, so: 3^(2x-y) = 3^4 = 81

Number Theory

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Question:

How can we compute the number of divisors of number n? Explain your answer step by step, and give an example.

Dilnur Y.

Answer:

First, we will have to get its prime factorization. Let's say it looks like this: n = (p1^a1) * (p2^a2)......* (pk^ak), where p1, p2....pk are relatively prime. Then, we should be able to see that, n divides every variation of its prime divisor's degree. In other words, a1 can be 0, 1, ....ak, and n will still divide each and every variation of the new number. This is true for a2,.....ak. Now, we are going to dive into the world of Combinatorics. There are (ai+1) variations of ai, starting from zero up until ai. To put it into perspective, we can get (ai+1) new divisors by changing the pi's degree from 0 until ai, where 1 <= i <= k. We use the multiplication principle to get the total number of divisors of n. So, the total number of divisors of n is (a1+1)*(a2+1).......(ak+1). Example: n=12. 1) primer factorization 12= (2^2)*3 2) Degrees a1=2, a2=1 3) Number of divisors is: (a1+1)*(a2+1) = (2+1)*(1+1) = 6 Indeed, 12 has six divisors: 1, 2, 3, 4, 6, 12

C++ Programming

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Question:

class Record{ public: Record(string date); }; class Book: public Record{ public: Book(string date, string title); // } In Java, we can access the superclass constructor of class Book with a keyword 'super'. In constructor Book, for instance, in Java, we could just say: Book(string date, string title){ super(date); } How can we achieve something similar in C++?

Dilnur Y.

Answer:

C++ does not let us access superclass methods with keywords, such as 'super'. Nonetheless, in C++, we can access the superclass by calling it by name, followed by two colons. So, we would access Record's constructor as such: Book(string date, string title){ Record::Record(date); }

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