Question

a 4-oz prescription bottle.
a 2-oz prescription bottle.
a 16-oz prescription bottle.

question 30
1 point
which of the following dea numbers is valid?
ab1234563
aj2468135
bm4567892
ac1357928

Explanation:

To determine a valid DEA number, we use the checksum method:

Step 1: Recall DEA Number Structure

A DEA number has 2 letters (first 2), followed by 7 digits, and a check digit (last digit). The formula for validation is:

• Sum of the 1st, 3rd, 5th digits (let’s call this \( S_1 \)).
• Sum of the 2nd, 4th, 6th digits (let’s call this \( S_2 \)), then multiply by 2 (\( 2 \times S_2 \)).
• Add \( S_1 + 2 \times S_2 \). The last digit of this sum should match the check digit (7th digit of the number, or the 9th character overall).

Analyze Each Option:

Option 1: \( \boldsymbol{AB1234563} \)

Digits: \( 1, 2, 3, 4, 5, 6 \) (positions 3–8), check digit: \( 3 \) (position 9).

• \( S_1 = 1 + 3 + 5 = 9 \)
• \( S_2 = 2 + 4 + 6 = 12 \); \( 2 \times S_2 = 24 \)
• Total: \( 9 + 24 = 33 \). Last digit of \( 33 \) is \( 3 \), which matches the check digit \( 3 \).

Option 2: \( \boldsymbol{AJ2468135} \)

Digits: \( 2, 4, 6, 8, 1, 3 \), check digit: \( 5 \).

• \( S_1 = 2 + 6 + 1 = 9 \)
• \( S_2 = 4 + 8 + 3 = 15 \); \( 2 \times S_2 = 30 \)
• Total: \( 9 + 30 = 39 \). Last digit \( 9

eq 5 \) (check digit). Invalid.

Option 3: \( \boldsymbol{BM4567892} \)

Digits: \( 4, 5, 6, 7, 8, 9 \), check digit: \( 2 \).

• \( S_1 = 4 + 6 + 8 = 18 \)
• \( S_2 = 5 + 7 + 9 = 21 \); \( 2 \times S_2 = 42 \)
• Total: \( 18 + 42 = 60 \). Last digit \( 0

eq 2 \) (check digit). Invalid.

Option 4: \( \boldsymbol{AC1357928} \)

Digits: \( 1, 3, 5, 7, 9, 2 \), check digit: \( 8 \).

• \( S_1 = 1 + 5 + 9 = 15 \)
• \( S_2 = 3 + 7 + 2 = 12 \); \( 2 \times S_2 = 24 \)
• Total: \( 15 + 24 = 39 \). Last digit \( 9

eq 8 \) (check digit). Invalid.

Only \( AB1234563 \) passes the checksum.

Answer:

AB1234563