A student was asked to divide a number by 6 and add 12 to the quotient. He,…
2026
A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been?
- A.
122
- B.
124
- C.
114
- D.
118
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept: When a problem describes an unintended (wrong) order of operations applied to an unknown number, and states the result of that wrong order, first solve for the unknown using that wrong-order equation. Then apply the originally intended, correct order of operations to that same unknown to obtain the required answer.
Let the original number be x.
The student actually added 12 to x first and then divided by 6, obtaining 112: (x + 12) / 6 = 112.
Solve for x: x + 12 = 6 × 112 = 672, so x = 672 − 12 = 660.
Apply the intended order instead — divide x by 6 first, then add 12: 660 / 6 + 12.
660 / 6 = 110, so the correct answer is 110 + 12 = 122.
Cross-check: Substituting x = 660 into the student's actual (wrong-order) working gives (660 + 12) / 6 = 672 / 6 = 112, matching the value stated in the question — confirming x = 660 and hence the correct result above.
