Divisibility by 3

Q.

How to find cube root by division method?

Q. In one hour, a boat goes 11 kmph along the stream and 5 kmph against the stream. Find the speed of the boat in still water (in kmph).

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Q.

Which of the following number is divisible by 99?

1. 913462

2. 135792

3. 114345

4. 3572406

Q. Give five examples of numbers, each one of which is divisible by 3 but not divisible by 9.

Q. Question 48

A five- digit number AABAA is divisible by 33. Write all the numbers of this form.

Q.

If the three digit number 24x is divisible by 9 then what is the value of x

Q.

Let $f:R\to R$ be such that for all $x\in R$, $(2^{1+x}+2^{1-x})$, $f\left(x\right)$and $(3^x+3^{-x})$ are in A.P, then the minimum value of $f\left(x\right)$is:

1. $0$

2. $4$

3. $3$

4. $2$

Q.

Add the following: ${\mathrm{l}}^2+{\mathrm{m}}^2,{\mathrm{m}}^2+{\mathrm{n}}^2,{\mathrm{n}}^2+{\mathrm{l}}^2,2\mathrm{lm}+2\mathrm{mn}+2\mathrm{nl}$

Q.

Total numbers of $4$ digit-number which are not divisible by $5$ are?

1. $7200$

2. $3600$

3. $14400$

4. $1800$

Q.

Divide and check your answer $2781$divided by $35$

Q.

If 5x6 is exactly divisible by 3, then the least value of x is

(a) 0

(b) 1

(c) 2

(d) 3

Q.

Using divisibility tests, determine if given number is divisible by $6$ :

$4335$

Q.

The value of $(1+\mathrm{i}{)}^5(1-\mathrm{i}{)}^5$

1. $-8$

2. $8\mathrm{i}$

3. $8$

4. $32$

Q.

Question 63

Find the value of k, where 31k2 is divisible by 6.

Q. For every positive integer n, prove that (7^n)-(3^n) is divisible by 4.

Q.

If x7y5 is exactly divisible by 3, then the least value of (x + y) is

(a) 6

(b) 0

(c) 4

(d) 3

Q.

A837B is divisible by 88. Find the digits A and B

Q.

Question 72

If 148101B095 is divisible by 33, find the value of B.

Q. If 20a3 is a 4-digit number and a multiple of 3, then sum of the possible values of a is

Q.

Question 62

$212x5$ is a multiple of 3 and 11. Find the value of x.

Q.

36A2 is divisible by 3 , find the value of A

1. 4 , 8

2. 2, 7 , 10

3. 1, 4 , 7

4. 2 , 3

Q.

$31x5\text{divisible by 3 ?}$

Q.

What is the probability that a number selected at random from the set of numbers $\left\{1,2,3,\dots ,100\right\}$ is a perfect cube?

1. $\frac{1}{25}$

2. $\frac{2}{25}$

3. $\frac{3}{25}$

4. $\frac{4}{25}$

Q.

Which of the following statements are true ?
(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is bivisible by both 9 and 10, ut nyst be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divede their sum exactly.
(ix) If two numbers are co-prime , at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.

Q.

Given an example of a number which is divisible by:
(i) 2 but not by 4.
(ii) 3 but not by 6.
(ii) 4 but not by 8.
(iv) both 4 and 8 but not by 32.

Q.

If 68y5 is divisible by 11, Where y is a digit, What is the value of y

Q. Test the divisibility of each of the following numers by 5:
(i) 95
(ii) 470
(iii) 1056
(iv) 2735
(v) 55053
(vi) 35790
(vii) 98765
(viii) 42658
(ix) 77990

Q.

198 is divisible by:

1. 11

2. 5
3. 8
4. 6

Q. Question 19

In the given question, fill in the blanks to make the statement true.

20x3 is a multiple of 3, if the digit x is ___ or ___ or ___.

Q.

Given that the number $\overline{35a64}$ is divisible by 3, where a is a digit, what are the possible volues of a?