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14 Jul 2026, 06:08
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An integer divided by 4 gives 0, 1, 2 or 3 as remainder
An integer divided by 11 gives 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 as remainder
If they must be equal, then remainder is (0, 1, 2, 3)
remainder=0 when the integer is multiple of 4 and 11 and less than 100: (0, 44, 88)
remainder=1 when the integer is (multiple of 4 and 11)+1 and less than 100: (1, 45, 89)
remainder=2 when the integer is (multiple of 4 and 11)+2 and less than 100: (2, 46, 90)
remainder=3 when the integer is (multiple of 4 and 11)+3 and less than 100: (3, 47, 91)
But we want only positive integers: (1, 2, 3, 44, 45, 46, 47, 88, 89, 90, 91), 11 integers
Answer D
An integer divided by 11 gives 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 as remainder
If they must be equal, then remainder is (0, 1, 2, 3)
remainder=0 when the integer is multiple of 4 and 11 and less than 100: (0, 44, 88)
remainder=1 when the integer is (multiple of 4 and 11)+1 and less than 100: (1, 45, 89)
remainder=2 when the integer is (multiple of 4 and 11)+2 and less than 100: (2, 46, 90)
remainder=3 when the integer is (multiple of 4 and 11)+3 and less than 100: (3, 47, 91)
But we want only positive integers: (1, 2, 3, 44, 45, 46, 47, 88, 89, 90, 91), 11 integers
Answer D
14 Jul 2026, 06:29
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remainder <4
So r = 1, 2, 3 or 0
n is congruent to r at mod 4 & n is congruent to r when mod is 11
so n is congruent to r 4*11
which 44
44k + 0 = 44, 88
44k + 1 = 1, 45 , 89
44k + 2 =2,46, 90
44k +3 = 3, 47, 91
2+3+3+3 = 11
D
So r = 1, 2, 3 or 0
n is congruent to r at mod 4 & n is congruent to r when mod is 11
so n is congruent to r 4*11
which 44
44k + 0 = 44, 88
44k + 1 = 1, 45 , 89
44k + 2 =2,46, 90
44k +3 = 3, 47, 91
2+3+3+3 = 11
D
Bunuel
14 Jul 2026, 06:33
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Common remainders upon division by 4 and upon division by 11 are 0,1,2,3
To give 0 as remainder the integer must be multiple of 4 and multiple of 11: 4*11*n = 44n
The integer must be less than 100, integer is 0, 44 or 88
Add 1 to the integers whose division by 4 and 11 gives 0 and the remainder will be 1: 1, 45 or 89
Add 2 to the integers whose division by 4 and 11 gives 0 and the remainder will be 2: 2, 46 or 90
Add 3 to the integers whose division by 4 and 11 gives 0 and the remainder will be 3: 3, 47 or 91
12 integers but only 11 positives. 11 is the answer.
The answer is D
To give 0 as remainder the integer must be multiple of 4 and multiple of 11: 4*11*n = 44n
The integer must be less than 100, integer is 0, 44 or 88
Add 1 to the integers whose division by 4 and 11 gives 0 and the remainder will be 1: 1, 45 or 89
Add 2 to the integers whose division by 4 and 11 gives 0 and the remainder will be 2: 2, 46 or 90
Add 3 to the integers whose division by 4 and 11 gives 0 and the remainder will be 3: 3, 47 or 91
12 integers but only 11 positives. 11 is the answer.
The answer is D
