Worked examples: a checklist for certainty
A code is a small dictionary
A symbol has only the meaning supplied in that question. There is no universal blood-relations meaning of +, −, @ or #. These expressions are not arithmetic: do not use BODMAS.
For our example only: A + B means A is B’s father. A − B means A is B’s mother. Read X − Y + Z as two facts: X is Y’s mother; Y is Z’s father. Both facts must stay true together.
Write the facts before answering. Parent map: X → Y → Z. From Z, go to father Y, then his mother X. X is Z’s paternal grandmother. But Z’s gender is unknown, so “Z is X’s grandson” is not proved.
“Not determined” is a conclusion about the information, not a guess. Name the missing fact. If two different answers fit all the given clues, one exact answer has not been established.
A complete decoding example
Given: + means father of; − means mother of. Expression: X − Y + Z.
- Split into neighboring pairs: X − Y and Y + Z.
- Translate: X is Y’s mother; Y is Z’s father.
- Record X → Y → Z, with X female and Y male. Leave Z’s gender blank.
- For X to Z, start at Z: father’s mother → paternal grandmother.
- For Z to X, start at X: son’s child → grandchild. “Grandson” would require Z to be male.
Complete the reasoning
Change just one symbol: X − Y − Z. X is Y’s mother; Y is Z’s ____. X is now Z’s ____. Answers: mother; maternal grandmother.
Decision flow: prove or stop
Read the local symbol key → translate every adjacent pair → choose the requested viewpoint → trace only stated links → ask “Do I know every fact needed for this exact answer?”
- Yes: state the relation and the path that proves it.
- No: identify the missing fact and keep the answer general, or choose “cannot be determined” if the question requires an exact relation.
Do not select “cannot be determined” merely because a problem looks long. First try to prove the relation.
Here + means “is father of” and − means “is mother of”. In X − Y + Z, what does X − Y state?
Show answer
Correct answer: A
Read each pair using the local definition: left person X is mother of right person Y. These are not arithmetic operations.
Option A: Correct: the minus symbol says the left person X is the mother of the right person Y.
Option B: This reverses the left and right people. The key starts with X, not Y.
Option C: Neither symbol in the key means marriage.
Option D: Father is the plus symbol here; the question asks about the minus symbol.
Hint: Decode one pair at a time.
With those definitions, what is X to Z in X − Y + Z?
Show answer
Correct answer: B
X is Y’s mother; Y is Z’s father. From Z, go to father Y and then his mother X: paternal grandmother.
Option A: The middle person Y is Z’s father, not Z’s mother, so this is not the maternal branch.
Option B: Correct: X is the mother of Z’s father Y, so X is Z’s paternal grandmother.
Option C: This drops the intermediate person Y and one generation.
Option D: Both links are parent links; they do not put X and Z in a sibling relation.
Hint: Write two plain sentences before naming the relation.
In X − Y + Z, can we conclude that Z is X’s grandson?
Show answer
Correct answer: C
Z is X’s son’s child. The code fixes X and Y, not Z’s gender. Grandchild is established; grandson is not.
Option A: Grandchild is known, but grandson additionally requires Z to be male. That fact is missing.
Option B: The clues do not force Z to be female either. Unknown does not mean the opposite gender.
Option C: Correct: Z is X’s son’s child, but no clue says whether Z is a son or daughter.
Option D: X is definitely a grandparent: X is parent of Y, and Y is parent of Z.
Hint: A relation word can require one more fact than a generic term.
Now take the separate practice
Open this lesson’s Practice test: five new checks, about eight minutes, with explanations after answering. This is a low-stakes learning check, not an official SSC paper. Try without the notes, then return to the exact step that caused an error. The optional time estimate is not an exam speed target.
Comparison note: these prototype modules use parallel versions of the same skills. Repeated exposure can improve your score, so this is a format comparison, not a controlled experiment proving which method is best.
Feedback-design reference: Khan Academy’s Perseus exercise editor and renderer. These worked examples and questions are original, using PPDF’s existing quiz components rather than imported code.
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