A Palindrome Is a Number That Reads

A palindrome is a number that reads the aforementioned forward and backward. For case, 2442 and 111 are palindromes...

This topic has expert replies

Timer

Your Reply

Global Stats

GMAT Prep

A palindrome is a number that reads the aforementioned forrad and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using ane or more of the digits i, two, 3, how many such palindromes are possible?

A. 12
B. 15
C. 18
D. 28
E. 27

OA E

GMATGuruNY: GMAT Teacher; Posts: 15536; Joined: 25 May 2010; Location: New York, NY; Thanked: 13060 times; Followed by:1901 members; GMAT Score:790

AAPL wrote: ↑
Mon Feb 22, 2022 ten:13 am
GMAT Prep

A palindrome is a number that reads the same frontward and astern. For instance, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits i, 2, 3, how many such palindromes are possible?

A. 12
B. 15
C. 18
D. 28
Eastward. 27

To read the same forrard and backward, the 5-digit integer must expect equally follows:
ABCBA.
The ten-thousands digit and the units digit must be THE Aforementioned.
The thousands digit and the tens digit must as well be THE SAME.

Number of options for the ten-thousands digit = iii. (1, 2, or 3)
Number of options for the units digit = 1. (Must be the aforementioned as the ten-thousands digit)
Number of options for the thousands digit = iii. (1, 2, or three)
Number of options for the tens digit = 1. (Must be the same as the thousands digit)
Number of options for the hundreds digit = three. (ane, 2, or 3)
To combine these options, we multiply:
3*three*3*1*1 = 27.

The right answer is E.

AAPL wrote: ↑
Monday February 22, 2022 10:13 am
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. fifteen
C. 18
D. 28
E. 27

OA E

Solution:

We accept three options for the outset digit, three options for the 2d, 3 options for the 3rd, 1 option for the quaternary (since it has to be the aforementioned equally the 2d), and ane option for the 5th (since it has to exist the same as the first). Thus, there are 3 x 3 x three = 27 possible palindromes.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Run into why Target Examination Prep is rated five out of five stars on Beat the GMAT. Read our reviews

AAPL wrote: ↑
Monday Feb 22, 2022 10:xiii am
GMAT Prep

A palindrome is a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If v-digit palindromes are formed using i or more of the digits i, 2, iii, how many such palindromes are possible?

A. 12
B. 15
C. 18
D. 28
Due east. 27

OA E

Accept the task of creating a 5-digit palindrome and pause it into stages.

Stage 1: Select a digit for the offset position.
We tin can choose 1, two or three, so we can consummate stage 1 in iii ways

Stage 2: Select a digit for the second position.
We can choose 1, 2 or iii, so we can complete stage 2 in 3 ways

Stage 3: Select a digit for the third position.
We can choose 1, 2 or three, so we tin can consummate stage 3 in three ways

Stage 4: Select a digit for the fourth position.
Of import: In lodge to create a palindrome, the 4th digit must exist the same as the second digit.
For case, if the first 3 digits are 213, so fourth digit must be one, and the fifth digit must be 2 to get the 5-digit palindrome 21312
Since the fourth digit must be the same as the 2nd digit, we can complete stage 4 in i manner

Stage 5: Select a digit for the 5th position.
Since the fifth digit must be the same equally the first digit, we can complete stage 5 in ane way

By the Fundamental Counting Principle (FCP), nosotros can complete all 5 stages (and thus create a 5-digit palindrome) in (iii)(3)(3)(1)(1) ways (= 27 ways)

Answer: East

danielspoxim2000.blogspot.com

Source: https://www.beatthegmat.com/a-palindrome-is-a-number-that-reads-the-same-forward-and-backward-for-example-2442-and-111-are-palindromes-t321442.html

A Palindrome Is a Number That Reads