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A palindrome is a number that reads the same forward or backward. If t
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23 Sep 2021, 09:28
23 Sep 2021, 09:28
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A palindrome is a number that reads the same forward or backward. If the first two digits of a four digit palindrome form a multiple of the last two digits, how many such four digit palindromes are there?
A. 0
B. 6
C. 9
D. 12
E. 18
A. 0
B. 6
C. 9
D. 12
E. 18
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Re: A palindrome is a number that reads the same forward or backward. If t
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23 Sep 2021, 09:33
23 Sep 2021, 09:33
1
Carcass wrote:
A palindrome is a number that reads the same forward or backward. If the first two digits of a four digit palindrome form a multiple of the last two digits, how many such four digit palindromes are there?
A. 0
B. 6
C. 9
D. 12
E. 18
A. 0
B. 6
C. 9
D. 12
E. 18
Given that the answer choices are relatively small, we might consider the strategy of listing and counting
To begin, if all 4 digits are the same, then the first two digits of a four digit palindrome form a multiple of the last two digits
For example, in the number 2222, the first two digits (22) is multiple of the last two digits (22)
So, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999 all work.
At this point, we've already listed 9 possible palindromes.
So, we can ELIMINATE A and B
What else is there?
Well, numbers in the form n00n also work, since n0 must be a multiple of n
For example, in the number 2002, the first two digits (20) is multiple of the last two digits (02)
So, 1001, 2002, 3003, 4004, 5005, 6006, 7007, 8008, 9009 all work.
We now have a TOTAL of 18 possible palindromes.
Since 18 is the greatest answer choice, we can be certain that no more palindromes exist.
Answer: E
Cheers,
Brent
gmatclubot
Re: A palindrome is a number that reads the same forward or backward. If t [#permalink]
23 Sep 2021, 09:33
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