Which of the following words cannot be formed using the letters of…
2021
Which of the following words cannot be formed using the letters of ‘PROFESSIONAL’?
Answer: C. NORMAL — ConceptA word can be formed from another word only when every required letter occurs no more times than it occurs in the source word. A reliable method is to…
- A.
PASSION
- B.
LESSON
- C.
NORMAL
- D.
FINAL
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
A word can be formed from another word only when every required letter occurs no more times than it occurs in the source word.
A reliable method is to build a letter-frequency inventory for the source and compare each candidate’s required frequency with that inventory.
Application
The source word PROFESSIONAL contains P1, R1, O2, F1, E1, S2, I1, N1, A1, and L1; it contains M0.
PASSION requires P1, A1, S2, I1, O1, and N1, all within the source inventory.
LESSON requires L1, E1, S2, O1, and N1, all within the source inventory.
NORMAL requires N1, O1, R1, M1, A1, and L1. Its requirement M1 exceeds the source inventory M0.
FINAL requires F1, I1, N1, A1, and L1, all within the source inventory.
Cross-check
Deleting the letters used by PASSION, LESSON, or FINAL from separate copies of PROFESSIONAL leaves no negative count. Trying the same with NORMAL fails immediately at M because the source contains no M.
Therefore, NORMAL cannot be formed from the letters of PROFESSIONAL.