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The number N is 5,2H4, where H represents the ten's digit. If N is div

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Bunuel
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The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink] New post   25 Jun 2019, 03:48
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The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
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D
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Re: The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink] New post   25 Jun 2019, 03:55
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Bunuel wrote:
The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


According to divisibility rule, the sum of the digits of number should be divisible by 9, hence, 5+2+H+4= 11+H hence need 7 which can bring the total to 18, which is divisible by 9. IMO the answer is D.

Correct me if I am wrong.
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Re: The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink] New post   25 Jun 2019, 05:34
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Bunuel wrote:
The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9



Divisibility rule of 9 --> sum of all digits should be a multiple of 9
--> 5 + 2 + H + 4 = 9k, for any positive integer k
--> 11 + H = 9 or 18 or 27 . . . .

H = 7 only satisfies

IMO Option D

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Re: The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink] New post   25 Jun 2019, 07:04
Bunuel wrote:
The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

The divisibility rules for 9 is that the sum of digits must be a multiple of 9. 5+2+4=11; So 11+H must add up to multiple of 9 so H=7 ; IMO D.
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Re: The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink] New post   26 Jun 2019, 08:21
Bunuel wrote:
The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


sum of the digits should be divisible by 9 ; so 5+2+h+4 ; 11+h out of given options h = 7 11+7 ; 18 ; 9
IMO D
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Re: The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink] New post   28 Jun 2019, 00:08
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Solution



Given:
    • N = 5,2H4, where H represents the tens digit.
      o N is divisible by 9.

To find:
    • Value of H

Approach and Working:
    • N is divisible by 9.
      o Hence, the sum of digits of N is divisible by 9.
      o Sum of digits of N = 11 +H
         Sine H is a single digit non-negative integer,0 ≤ H ≤ 9

    • 11 ≤ 11 + H ≤ 20
    • However, 11+H is a multiple of 9. Hence, 11 +H = 18
      o H = 7

Hence, the correct answer is option D.

Answer: D
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Re: The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink] New post   28 Jun 2019, 00:43
as we know, for a number to be divisible by 9 its digits need to add upto 9 or multiple of 9 and hence 5+4+2+H=11+H

therefore H=7 making the above total 18
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Re: The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink] New post   01 Jul 2019, 17:15
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Bunuel wrote:
The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9


We use the rule for divisibility by 9: if the sum of the digits of the number is divisible by 9, then the number itself is divisible by 9. Since we know that n is divisible by 9, then 5 + 2 + H + 4 = 11 + H must be a multiple of 9, so H is 7.

Answer: D
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Re: The number N is 5,2H4, where H represents the ten's digit. If N is div [#permalink]
01 Jul 2019, 17:15
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