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The four-digit number 3,58Q is divisible by 9. What is the value of Q?
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16 Feb 2022, 07:00
16 Feb 2022, 07:00
Expert Reply
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Question Stats:
100% (00:45) correct
0% (00:00) wrong based on 12 sessions
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Q represents the units digit of the four-digit integer 358Q. If 358Q is divisible by 9, what is the value of Q?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
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Re: The four-digit number 3,58Q is divisible by 9. What is the value of Q?
[#permalink]
16 Feb 2022, 07:45
16 Feb 2022, 07:45
1
Carcass wrote:
Q represents the units digit of the four-digit integer 358Q. If 358Q is divisible by 9, what is the value of Q?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Key property: If an integer is divisible by 9, then the sum of its digits must be divisible by 9.
So it must be the case that: 3 + 5 + 8 + Q is divisible by 9
In other words: 16 + Q is divisible by 9
Since Q = 2 is the only digit that meets this condition, the correct answer is B.
Re: The four-digit number 3,58Q is divisible by 9. What is the value of Q?
[#permalink]
16 Feb 2022, 10:39
16 Feb 2022, 10:39
1
Carcass wrote:
Q represents the units digit of the four-digit integer 358Q. If 358Q is divisible by 9, what is the value of Q?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
4 digit int to be divisible by need all individual digit's sum to be divisible by 9
So, 3+5+8+Q => 16+Q. Lets see no. divisible by 9 i.e. 9, 18, 27, 36 etc
So if Q is 2, sum of digit becomes divisible by 9. 2nd nearest no. is going to be 11 and will not be correct
So ans is B
