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13 Mar 2022, 13:53
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D
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Difficulty:
95%
(hard)
Question Stats:
42% (02:13) correct
58%
(01:56)
wrong
based on 130
sessions
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If x is a positive integer, what is the remainder when x is divided by 9?
(1) The remainder when 3x is divided by 27 is 24
(2) The remainder when 4x is divided by 18 is 14
(1) The remainder when 3x is divided by 27 is 24
(2) The remainder when 4x is divided by 18 is 14
13 Mar 2022, 20:10
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(1): Because 3x divided by 27 leaves 24
-> 3x = 27k + 24 (k is an integer)
-> x = 9k +8
-> x divided by 9 remainder 8
-> (1) can solve
(2): 4x divided by 18 leaves 14
-> 4x = 18k +14
-> 2x = 9k + 7 = 9(k-1) +16
Since 16 is even and 2x is even, 9(k-1) is even -> 9.(k-1)/2 is divisible by 9
-> x = 9.(k-1)/2 + 8
-> x divided by 9 remainder 8
-> (2) can slove
my answer is D.
-> 3x = 27k + 24 (k is an integer)
-> x = 9k +8
-> x divided by 9 remainder 8
-> (1) can solve
(2): 4x divided by 18 leaves 14
-> 4x = 18k +14
-> 2x = 9k + 7 = 9(k-1) +16
Since 16 is even and 2x is even, 9(k-1) is even -> 9.(k-1)/2 is divisible by 9
-> x = 9.(k-1)/2 + 8
-> x divided by 9 remainder 8
-> (2) can slove
my answer is D.
13 Mar 2022, 23:51
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Asked: If x is a positive integer, what is the remainder when x is divided by 9?
(1) The remainder when 3x is divided by 27 is 24
3x = 27k + 24; where k is an integer.
x = 9k + 8
The remainder when x is divided by 9 = 8
SUFFICIENT
(2) The remainder when 4x is divided by 18 is 14
4x = 18k + 14; where k is an integer.
2x = 9k + 7
Sicne 2x is even and 7 is odd, 9k is odd. x is an odd multiple of 9. Let k = 2m + 1
2x = 9(2m+1) + 7
2x = 18m + 16
x = 9m + 8
The remainder when x is divided by 9 = 8
SUFFICIENT
IMO D
(1) The remainder when 3x is divided by 27 is 24
3x = 27k + 24; where k is an integer.
x = 9k + 8
The remainder when x is divided by 9 = 8
SUFFICIENT
(2) The remainder when 4x is divided by 18 is 14
4x = 18k + 14; where k is an integer.
2x = 9k + 7
Sicne 2x is even and 7 is odd, 9k is odd. x is an odd multiple of 9. Let k = 2m + 1
2x = 9(2m+1) + 7
2x = 18m + 16
x = 9m + 8
The remainder when x is divided by 9 = 8
SUFFICIENT
IMO D
