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A
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23%
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A number that is a palindrome reads the same way forwards and backwards. For example, 3113 and 7447 are palindromes. Let n be the product of all 4-digit palindromes. What is the unit’s digit of n?
A. 0
B. 2
C. 4
D. 5
E. 8
A. 0
B. 2
C. 4
D. 5
E. 8
27 Nov 2019, 04:57
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Bunuel
A number that is a palindrome reads the same way forwards and backwards. For example, 3113 and 7447 are palindromes. Let n be the product of all 4-digit palindromes. What is the unit’s digit of n?
A. 0
B. 2
C. 4
D. 5
E. 8
A. 0
B. 2
C. 4
D. 5
E. 8
A 4-digit palindrome can end in all the digits from 1-9 and NOT in 0 (E.g: 0550 is not a 4-digit number!)
Last digits of palindromes = (1, 2, 3, 4, 5, 6, 7, 8, 9}
Product will ALWAYS end in 0 (Since 5 & even numbers 2,4 are there etc.)
IMO Option A
13 Apr 2020, 06:48
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Bunuel
A number that is a palindrome reads the same way forwards and backwards. For example, 3113 and 7447 are palindromes. Let n be the product of all 4-digit palindromes. What is the unit’s digit of n?
A. 0
B. 2
C. 4
D. 5
E. 8
A. 0
B. 2
C. 4
D. 5
E. 8
There are many 4-digit palindrome numbers. Included among these palindrome numbers are 5005 and 2002 (and many others)
If n = the product of all 4-digit palindrome numbers, ....
...then n = (5005)(2002)(#)(#)(#)(#)(#)(#)....
= (10020010)(#)(#)(#)(#)(#)(#)....
Since 10020010 has units digit 0, we know that the entire product (aka n) will have units digit 0
Answer: A
Cheers,
Brent
