The number which is exactly divisible by 99 is _____ .

3572404

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135792

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913464

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114345

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Solution

The correct option is B 114345
For a number to be divisible by $99$ it should also be divisible by all its factors, i.e by $9$ and $11$ .

Divisibility Test for $9$ :
$\to$ A number is divisible by $9$ if the sum of the digits is divisible by $9$ .

$3572404$ Sum of Digits $= 25$
$135792$ Sum of Digits $= 27$
$913464$ Sum of Digits $= 27$
$114345$ Sum of Digits $= 18$

$\Rightarrow 3572404$ isn't divisible by $99$ .

Divisibility Test for $11$ :
$\to$ Take the alternating sum of the digits in the number, read from left to right. If that is divisible by $11$ , so is the original number.

$135792$ Alternating Sum $= 1 - 3 + 5 - 7 + 9 - 2 = 3$ $\to$ Not Divisible
$913464$ Alternating Sum $= 9 - 1 + 3 - 4 + 6 - 4 = 9$ $\to$ Not Divisible
$114345$ Alternating Sum $= 1 - 1 + 4 - 3 + 4 - 5 = 0$ $\to$ Divisble

$∴ 114345$ is divisible by $99$ .

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Similar questions

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Which of the following statements are true?

(a) If a number is divisible by 3, it must be divisible by 9.

(b) If a number is divisible by 9, it must be divisible by 3.

(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.

(e) If two numbers are co-primes, at least one of them must be prime.

(f) All numbers which are divisible by 4 must also be divisible by 8.

(g) All numbers which are divisible by 8 must also be divisible by 4.

(h) If a number exactly divides two numbers separately, it must exactly divide their sum.

(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

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 divisible by both 9 and 10, it must 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 divide 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.

Question 1

Which of the following statements are true:
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) If a number is divisible by 18, it must be divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

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.

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