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22 Apr 2025, 00:30
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E
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Difficulty:
25%
(medium)
Question Stats:
82% (01:28) correct
18%
(01:39)
wrong
based on 115
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Take a four-digit number and reverse its digits. The difference between the original number and the new number must be divisible by which of the following?
A) 2
B) 4
C) 5
D) 6
E) 9
A) 2
B) 4
C) 5
D) 6
E) 9
22 Apr 2025, 00:53
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Bunuel
let Number = abcd
Reversed number = dcba
abcd = 1000a+100b+10c+d
dcba = 1000d+100c+10b+a
abcd-dcba = 999a +90b - 90c - 999d = 9*(111a+10b-10c-111d)
Answer: Option E
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22 Apr 2025, 06:52
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Take a four-digit number and reverse its digits. The difference between the original number and the new number must be divisible by which of the following?
A) 2
B) 4
C) 5
D) 6
E) 9
Let’s just say that we have the number : 4 a b 3, then its reverse would be 3 a b 4
When we subtract them, we know that even - odd will yield an odd number, meaning that it can’t be divisible by 2, 4 or 6
(While it could be divisible by them if the thousands and units digits were both either even or odd, it wouldn’t ALWAYS be divisible as not all four digit numbers have their thousands and units digits both either even or odd)
We know it can’t ALWAYS be 5 as seen in the first example ( units digit = 9) , meaning that this leaves us with 9.
Answer = 9 = E
We can also solve this by taking a random 4 digit number and reversing then subtracting , this will still give us 9 as the answer.
A) 2
B) 4
C) 5
D) 6
E) 9
Let’s just say that we have the number : 4 a b 3, then its reverse would be 3 a b 4
When we subtract them, we know that even - odd will yield an odd number, meaning that it can’t be divisible by 2, 4 or 6
(While it could be divisible by them if the thousands and units digits were both either even or odd, it wouldn’t ALWAYS be divisible as not all four digit numbers have their thousands and units digits both either even or odd)
We know it can’t ALWAYS be 5 as seen in the first example ( units digit = 9) , meaning that this leaves us with 9.
Answer = 9 = E
We can also solve this by taking a random 4 digit number and reversing then subtracting , this will still give us 9 as the answer.
