Count codes when the second digit must differ

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Quantitative Reasoning

A code consists of one letter followed by two digits. The letter is chosen from $J$ , $K$ , $L$ , and $M$ . The first digit must be odd, and the second digit must differ from the first digit. Quantity A: The number of possible codes Quantity B: $180$

Compare Quantity A and Quantity B. Select one answer.

AQuantity A is greater.BQuantity B is greater.CThe two quantities are equal.DThe relationship cannot be determined from the information given.

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Answer: C (The two quantities are equal.)

For each code, there are 4 choices for the letter and 5 choices for the first digit, since the odd digits are $1$ , $3$ , $5$ , $7$ , and $9$ . After the first digit is selected, the second digit can be any of the remaining 9 digits. Therefore, the number of possible codes is $4 \times 5 \times 9 = 180$ . Thus, the two quantities are equal.

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Quantitative Reasoning

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