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How many 6-digits number are Palindromic numbers? A Palindro
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24 Aug 2020, 10:10
24 Aug 2020, 10:10
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62% (01:28) correct
37% (01:41) wrong based on 37 sessions
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How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12121.
A) 100
B) 610
C) 729
D) 900
E) 1000
A) 100
B) 610
C) 729
D) 900
E) 1000
Re: How many 6-digits number are Palindromic numbers? A Palindro
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24 Aug 2020, 10:10
24 Aug 2020, 10:10
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Re: How many 6-digits number are Palindromic numbers? A Palindro
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24 Aug 2020, 10:17
24 Aug 2020, 10:17
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Carcass wrote:
How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12121.
A) 100
B) 610
C) 729
D) 900
E) 1000
A) 100
B) 610
C) 729
D) 900
E) 1000
Take the task of building palindromes and break it into stages.
Stage 1: Select the hundred-thousands digit
We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in 9 ways
Stage 2: Select the ten-thousands digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in 10 ways
Stage 3: Select the thousands digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in 10 ways
IMPORTANT: At this point, the remaining digits are already locked in.
Stage 4: Select the hundreds digit
This digit must be the SAME as the thousands digit (which we already chose in stage 3)
So, we can complete this stage in 1 way.
Stage 5: Select the tens digit
This digit must be the SAME as the ten-thousands digit (which we already chose in stage 2)
So, we can complete this stage in 1 way.
Stage 6: Select the units digit
This digit must be the SAME as the hundred-thousands digit (which we already chose in stage 1)
So, we can complete this stage in 1 way.
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus build a 6-digit palindrome) in (9)(10)(10)(1)(1)(1) ways (= 900 ways)
Answer: D
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