GMAT Prep
A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?
A. 12
B. 15
C. 18
D. 24
E. 27
OA E.
A palindrome is a number that reads the same forward and
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- fskilnik@GMATH
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$$\matrix{AAPL wrote:GMAT Prep
A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?
A. 12
B. 15
C. 18
D. 24
E. 27
{\underline {{\rm{A}}\,\,{\rm{free}}} } \cr
3 \cr
} \,\,\,\matrix{
{\underline {{\rm{B}}\,\,{\rm{free}}} } \cr
3 \cr
} \,\,\,\matrix{
{\underline {{\rm{C}}\,{\rm{free}}} } \cr
3 \cr
} \,\,\,\matrix{
{\underline {{\rm{D}}\,{\rm{ = }}\,{\rm{B}}\,{\rm{copy}}} } \cr
1 \cr
} \,\,\,\matrix{
{\underline {{\rm{E}}\,{\rm{ = }}\,{\rm{A}}\,{\rm{copy}}} } \cr
1 \cr
} \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {3^3} = 27$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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Take the task of building palindromes and break it into stages.A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?
A) 12
B) 15
C) 18
D) 24
E) 27
Stage 1: Select the ten-thousands digit
We can choose 1, 2, or 3
So, we can complete stage 1 in 3 ways
Stage 2: Select the thousands digit
We can choose 1, 2, or 3
So, we can complete stage 2 in 3 ways
Stage 3: Select the hundreds digit
We can choose 1, 2, or 3
So, we can complete stage 3 in 3 ways
IMPORTANT: At this point, the remaining digits are already locked in.
Stage 4: Select the tens digit
This digit must be the SAME as the thousands digit (which we already chose in stage 2)
So, we can complete this stage in 1 way.
Stage 5: Select the units digit
This digit must be the SAME as the ten-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 5 stages (and thus build a 5-digit palindrome) in (3)(3)(3)(1)(1) ways (= 27 ways)
Answer: E
--------------------------
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Cheers,
Brent
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We have 3 options for the first digit, 3 options for the second, 3 options for the third, 1 option for the fourth (since it has to be the same as the second), and 1 option for the fifth (since it has to be the same as the first). Thus, there are 3 x 3 x 3 = 27 possible palindromes.AAPL wrote:GMAT Prep
A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?
A. 12
B. 15
C. 18
D. 24
E. 27
OA E.
Answer: E
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