What least number must be subtracted from 1936 so that the resulting number…
2023
What least number must be subtracted from 1936 so that the resulting number when divided by 9, 10 and 15 will leave in each case the same remainder 7?
- A.
13
- B.
36
- C.
39
- D.
30
Attempted by 31 students.
Show answer & explanation
Correct answer: C
Key idea: If a number leaves remainder 7 when divided by 9, 10 and 15, it also leaves remainder 7 when divided by their least common multiple, 90.
Compute the LCM of 9, 10 and 15: 90.
Divide 1936 by 90: quotient = 21, remainder = 46.
We need the remainder to be 7, so decrease the current remainder from 46 to 7 by subtracting 46 − 7 = 39 from 1936.
Verify: 1936 − 39 = 1897. Dividing 1897 by 90 gives remainder 7, so dividing by 9, 10 and 15 also gives remainder 7.