When the six-digit number PQRST7 is multiplied by 5, the six-digit number 7PQRST is obtained. P + Q + R + S + T = ______.16242028

The problem is asking for the sum of the digits P, Q, R, S, T in a six-digit number PQRST7 such that when it is multiplied by 5, the result is 7PQRST.

Step 1: We know that when a number ending in 7 is multiplied by 5, the result ends in 5. Therefore, the number 7PQRST must end in 5. This means that T = 5.

Step 2: Now we know that the number is PQRST5. When this is multiplied by 5, the result is 5PQRST. The last digit of the result (T in 5PQRST) is obtained by multiplying the last digit of the original number (5 in PQRST5) by 5. This means that S = 2.

Step 3: Now we know that the number is PQR25. When this is multiplied by 5, the result is 2PQR5. The second last digit of the result (R in 2PQR5) is obtained by multiplying the second last digit of the original number (2 in PQR25) by 5 and adding the carry from the previous multiplication. This means that R = 4.

Step 4: Now we know that the number is PQ425. When this is multiplied by 5, the result is 4PQ25. The third last digit of the result (Q in 4PQ25) is obtained by multiplying the third last digit of the original number (4 in PQ425) by 5 and adding the carry from the previous multiplication. This means that Q = 8.

Step 5: Now we know that the number is P8425. When this is multiplied by 5, the result is 8P425. The fourth last digit of the result (P in 8P425) is obtained by multiplying the fourth last digit of the original number (8 in P8425) by 5 and adding the carry from the previous multiplication. This means that P = 1.

Step 6: The sum of the digits P, Q, R, S, T is therefore 1 + 8 + 4 + 2 + 5 = 20.