Question

If the number from \[1\] to \[45\]which are exactly divisible by \[3\]are arranged in ascending order, minimum number being on the top, which would come at the ninth place from the top?
A. \[18\]
B.\[21\]
C.\[\;24\]
D.\[27\]

Answer 1

Hint: First we have to define what the terms we need to solve the problem are. Ascending order is nothing but arranging the numbers from small to big. Find the number divisible \[3\] by between \[1\] to\[45\] and arrange them in ascending order. And then find the value of the ninth term. It is occurred by the condition followed by the first three terms of the sequence

Complete answer:
It is given that to find the number divisible \[3\] by between \[1\] to\[45\].
We know that the given number from \[1\] to \[45\]which is exactly divisible by \[3\] are arranged in ascending order:
\[3{\text{ }} < {\text{ }}6{\text{ }} < {\text{ }}9{\text{ }} < 12{\text{ }} < {\text{ }}15{\text{ }} < 18{\text{ }} < 21{\text{ }} < {\text{ }}24{\text{ }} < {\text{ }}27 < \;30{\text{ }} < 33{\text{ }} < 36{\text{ }} < 39{\text{ }} < 42{\text{ }} < 45\]
Then we find the minimum number is \[3\] , Therefore it is at the top.
We already know that the number is divisible by \[3\]is a multiple of\[3\].
The number in the first place is \[1 \times 3 = 3\]
The number in second place is \[2 \times 3 = 6\]
The number in third place is \[3 \times 3 = 9\]
By this condition,
we moving to ninth place,
The number in ninth place is \[9 \times 3 = 27\]
The ninth place from the top will be\[27\].

Hence the correct option is D)\[27\].

Note:
If the sum of the digits in a number is multiple of \[3\],it is divisible by\[3\].
A divisible rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division.
The number is said to be divisible by another number if the remainder is\[0\].
If it has a common difference among sequences it is in Arithmetic progression. If it has common ratio among sequence it is in Geometric progression.