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A palindrome is a number that reads the same when read from either end. For example, 12321 is a palindrome. A set consists of all the 3-digit palindromes whose product of digits has 1 as the unit digit. Select for Minimum the minimum possible value of the tens digit of any of the numbers in the set, and select for Maximum the maximum possible value of the tens digit of any of the numbers in the set. Make only two selections, one in each column.
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| Minimum | Maximum | |
| 0 | ||
| 1 | ||
| 3 | ||
| 5 | ||
| 7 | ||
| 9 |
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Official Answer
Minimum: 1
Maximum: 9
19 Jul 2024, 07:05
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Bunuel
GMAT Club Official Explanation:
The inference is that all digits in the palindrome are odd, and why is that so?Because if the product of digits ends in 1, which is odd, then all the digits involved in the product have to be odd.
The number, thus, is of the form ABA, and we are looking for the value of B, where both A and B are odd digits.
1 * 1 * 1 or 9 * 9 * 1 or 7 * 7 * 9 or 3 * 3 * 9, etc., will give numbers like 111, 919, and so on. We do not have to calculate all numbers but check for the values that we seek to establish.
Min: We know B is odd, and 1 is the least possible value. Can we have a number A1A, that is A * A ends in 1? 111 and 919 are two examples. Hence, the answer is 1.
Max: We know B is odd, and 9 is the largest possible value. We can have a number A9A, that is A * A ends in 9 as (A * A) * 9 will have a units digit of 1. 393 and 797 are such two numbers because 9 * X9 results in 1 in the units digit, such as 49 * 9 or 9 * 9. Hence, the answer is 9.
