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Number Theory: Interesting Results

Question 12In...

Question

Question 12

In the given question, out of four options, only one is correct. Write the correct answer.

If x + y + z = 6 and z is an odd digit, then the three- digit number xyz is
(a) an odd multiple of 3
(b) an odd multiple of 6
(c) an even multiple of 3
(d) an even multiple of 9

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Solution

We have, x + y + z = 6 and z is an odd digit. Since sum of the digits is divisible by 6, it will also be divisible by 2 and 3 but the unit digit is odd, so it is divisible by 3 only.
Hence, the number is an odd multiple of 3.

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Q. Question 12

In the given question, out of four options, only one is correct. Write the correct answer.

If x + y + z = 6 and z is an odd digit, then the three- digit number xyz is
(a) an odd multiple of 3
(b) an odd multiple of 6
(c) an even multiple of 3
(d) an even multiple of 9

tan (α + i β) = e^{i θ};

α, β \in R

θ \neq (2 n + 1) \frac{π}{2}, n \in Z

i = \sqrt{- 1}

Q. The sum of two odd numbers is
(a) an odd number
(b) an even number
(c) a prime number
(d) a multiple of 3

Q. Mark the correct answer in each of the following:
The negation of the statement "101 is not a multiple of 3" is
(a) 101 is a multiple of 3
(b) 101 is a multiple of 2
(c) 101 is an odd number
(d) 101 is an even number

Q. Directions:- Study the following information carefully to answer the question given below.

Two rows of numbers are given in the question. The resultant number in each row has to be worked out separately based on the following rules. The operation of numbers progresses from left to right.

Rules:-
(i) If an odd number is followed by another odd number which is a perfect square then they are to be added.
(ii) If an even number is followed by an odd number or an odd number is followed by an even number, they are to be multiplied.
(iii) If an even number is followed by another even number, the first number is to be divided by the second number.
(iv) If an even number which is a multiple of 5 is followed by an odd number which is also a multiple of 5, then the second number is to be subtracted from the first number.

18 7 6
140 85 49

What is the sum of the resultants of the two rows?

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Number Theory: Interesting Results

Standard IX Mathematics

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