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16 Nov 2023, 06:58
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Difficulty:
55%
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Question Stats:
68% (02:18) correct
32%
(02:19)
wrong
based on 261
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When a positive integer p is divided by 101, the quotient is q and the remainder is 10. When p is divided by 11, the remainder is 10. What is the remainder when q is divided by 11?
- (A) 0
(B) 1
(C) 2
(D) 3
(E) 4
18 Nov 2023, 10:58
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Given information:
p = 101q + 10 p = 11k + 10
Set the two expressions for p equal to each other:
101q + 10 = 11k + 10
Subtract 10 from both sides:
101q = 11k
Take both sides modulo 11:
101q ≡ 0 (mod 11)
Therefore, the remainder when q is divided by 11 is 0.
p = 101q + 10 p = 11k + 10
Set the two expressions for p equal to each other:
101q + 10 = 11k + 10
Subtract 10 from both sides:
101q = 11k
Take both sides modulo 11:
101q ≡ 0 (mod 11)
Therefore, the remainder when q is divided by 11 is 0.
18 Nov 2023, 18:17
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p = 101q + 10.
Now p is divided by 11,
11(9q) + 2q + 10 when divided by 11 gives 10 as reminder.
So 2q + 10 should also give same remainder 10
Hence 2q should be a multiple of 11, So q has to be a multiple of 11.
Remainder = 0.
Now p is divided by 11,
11(9q) + 2q + 10 when divided by 11 gives 10 as reminder.
So 2q + 10 should also give same remainder 10
Hence 2q should be a multiple of 11, So q has to be a multiple of 11.
Remainder = 0.
