Question

If ``$P + Q - R \div T$'', how is $T$ related to $P$?

• A. Aunt
• B. Father
• C. Grandmother
• D. None of these
• A. \(P \times R - Q - T\)
• B. \(P \div T + R - Q\)
• C. \(P \div R - Q + T\)
• D. \(P \times T - Q + R\)
• A. Daughter
• B. Husband
• C. Son-in-law
• D. None of these
• A. Grandmother
• B. Mother-in-law
• C. Sister
• D. Grandfather
• A. Aunt
• B. Sister
• C. Brother
• D. Grandson
• A. Son
• B. Nephew
• C. Niece
• D. Grandson

Answer 1

The Correct Option is D

Step 1: Decode each link in order. \(P + Q\) means \(P\) is \(Q\)'s daughter.

Step 2: \(Q - R\) means \(Q\) and \(R\) are brother and sister, so \(R\) is also part of the same sibling generation as \(Q\).

Step 3: \(R \div T\) means \(R\) is \(T\)'s mother, so \(T\) is \(R\)'s child, placing \(T\) in the same generation as \(P\), since \(P\) is \(Q\)'s child and \(Q, R\) are siblings.

Step 4: Two children of siblings are cousins, and cousin is not one of the first three named options.
\[ \boxed{\text{None of these}} \]

Answer 2

Sketching this out as a small family tree makes the generations easy to see. Put the parents' generation on top and the children's generation below it.

1. Aunt: On the tree, \(P\) sits as a child of \(Q\), and \(T\) sits as a child of \(R\), both in the bottom row, with \(Q\) and \(R\) as siblings in the top row. An aunt would have to sit in the top row relative to \(P\), but \(T\) is in the bottom row, so this label doesn't fit.
2. Father: A father sits directly above his child in the tree. \(T\) is drawn in the same row as \(P\), not above it, so \(T\) is not \(P\)'s father.
3. Grandmother: A grandmother sits two rows above her grandchild. \(T\) is one row below where a grandmother would need to be, not two rows above \(P\), so this doesn't fit.
4. None of these: With \(Q\) and \(R\) drawn as siblings on the top row, and \(P\) and \(T\) each drawn as their respective children on the bottom row, \(P\) and \(T\) land side by side in the same row, exactly the position of cousins, a label the tree can show but that isn't offered as a choice.

The tree places \(T\) beside \(P\), not above or two levels above, which rules out every named option.

So the correct answer is None of these.

Answer 3

Step 1: A wife-husband pair must share children, with the husband as father and the wife as mother of the same child or children.

Step 2: In \(P \times T - Q + R\), \(P \times T\) shows \(P\) as father of \(T\), so \(P\) is male.

Step 3: \(T - Q\) shows \(T\) and \(Q\) are siblings, so \(Q\) is also a child of \(P\).

Step 4: \(Q + R\) shows \(Q\) is \(R\)'s daughter, so \(R\) is \(Q\)'s other parent. Since \(P\) is already \(Q\)'s father, \(R\) must be \(Q\)'s mother, making \(R\) the wife of \(P\).
\[ \boxed{P \times T - Q + R} \]

Answer 4

Instead of decoding each option from scratch, first write down the general shape a "wife of" expression must have, then check which option fits that shape.

A code showing \(R\) as \(P\)'s wife needs: \(P\) linked to some child by a father-symbol, \(\times\), that same child linked to a sibling, and the sibling linked to \(R\) by a daughter-symbol, \(+\), so that \(R\) turns out to be the mother of the same children \(P\) fathered.

1. \(P \times R - Q - T\): Here the multiplication symbol connects \(P\) directly to \(R\), not to a child shared with \(R\), so it doesn't match the shape at all.
2. \(P \div T + R - Q\): The very first symbol is division, not multiplication, so \(P\) is never shown as a father here, this doesn't match the required shape.
3. \(P \div R - Q + T\): Same issue, the first symbol is division, so this fails to match the shape from the start.
4. \(P \times T - Q + R\): The first symbol is multiplication, \(P\) father of \(T\), followed by a sibling link between \(T\) and \(Q\), followed by a daughter link between \(Q\) and \(R\). This is exactly the required shape.

Only the last expression follows the exact pattern needed to show \(R\) as \(P\)'s wife.

So the correct answer is \(P \times T - Q + R\).

Answer 5

Step 1: \(P \times T\) means \(P\) is \(T\)'s father, so \(T\) is \(P\)'s daughter.

Step 2: \(T \div Q\) means \(T\) is \(Q\)'s mother.

Step 3: \(Q + R\) means \(Q\) is \(R\)'s daughter, so \(R\) is \(Q\)'s other parent alongside \(T\), which makes \(R\) \(T\)'s husband.

Step 4: The husband of \(P\)'s daughter is \(P\)'s son-in-law.
\[ \boxed{\text{Son-in-law}} \]

Answer 6

Instead of decoding left to right, start from \(R\) and build outward toward \(P\), checking which label the path produces.

1. Daughter: Starting at \(R\), the only link touching \(R\) is \(Q + R\), which makes \(R\) the parent of \(Q\), not anyone's daughter, so this label is wrong immediately.
2. Husband: \(R\) is \(Q\)'s parent, and \(T\) is also shown as \(Q\)'s parent through \(T \div Q\), so \(R\) and \(T\) parent the same child \(Q\) together, making \(R\) the husband of \(T\), not of \(P\). Since the question asks about \(P\) specifically, this label describes the wrong pair.
3. Son-in-law: Moving one more link out, \(T\) is linked to \(P\) by \(P \times T\), which makes \(T\) the daughter of \(P\). Since \(R\) is \(T\)'s husband, and \(T\) is \(P\)'s daughter, \(R\) is married into \(P\)'s family as the husband of \(P\)'s daughter, exactly a son-in-law.
4. None of these: The path from \(R\) outward to \(P\) does land on a clear, nameable relationship, so this fallback isn't needed.

Tracing outward from \(R\) through \(T\) to \(P\) lands exactly on the son-in-law relationship.

So the correct answer is Son-in-law.

Answer 7

Step 1: \(P \div R\) means \(P\) is the mother of \(R\), so \(P\) is female.

Step 2: \(R - Q\) means \(R\) and \(Q\) are siblings, so \(Q\) is also \(P\)'s child.

Step 3: \(Q \times T\) means \(Q\) is \(T\)'s father.

Step 4: Since \(P\) is \(Q\)'s mother and \(Q\) is \(T\)'s father, \(P\) sits two generations above \(T\) on the same family line, and being female, that makes her \(T\)'s grandmother.
\[ \boxed{\text{Grandmother}} \]

Answer 8

Pick real names to make the structure concrete. Say \(P\) is a woman named Radha. From \(P \div R\), Radha is the mother of \(R\), so let \(R\) be her son, Rohan. From \(R - Q\), Rohan has a sibling \(Q\), also Radha's child. From \(Q \times T\), \(Q\) is shown as a father, so this sibling of Rohan is a son, Qamar, Radha's other child, who is \(T\)'s father, say a boy named Tarun.

1. Grandmother: Radha is Qamar's mother, and Qamar is Tarun's father, so Radha is Tarun's father's mother, which is exactly a grandmother.
2. Mother-in-law: A mother-in-law would need to be the mother of Tarun's spouse, but Radha is the mother of Tarun's father, a completely different relationship.
3. Sister: Radha is two generations above Tarun in this worked family, not his generation-mate, so sister doesn't apply.
4. Grandfather: Radha was established as female from the start, a mother, so the male label grandfather cannot apply to her.

Working through named people the same way the code decodes, Radha lands exactly as Tarun's grandmother.

So the correct answer is Grandmother.

Answer 9

Step 1: \(R \div Q\) shows \(Q\) is \(R\)'s child.

Step 2: \(R \times T\) shows \(T\) is also \(R\)'s child, using the same style of operator elsewhere reserved for a male child, so \(T\) is read as male.

Step 3: Since \(Q\) and \(T\) are both \(R\)'s children, they are siblings.

Step 4: A male sibling is a brother, not a sister, aunt, or grandson.
\[ \boxed{\text{Brother}} \]

Answer 10

Assign names to check this concretely. Let \(R\) be a woman, Rani. From \(R \div Q\), Rani is \(Q\)'s mother, so let \(Q\) be her daughter, Queenie. From \(R \times T\), Rani is also shown as parenting \(T\) through the father-style operator, so despite Rani being female, this operator in the code family is the one used to mark a child as male, so let \(T\) be her son, Tarak.

1. Aunt: Tarak and Queenie are both Rani's children, sitting in the same generation as each other, not one generation apart, so "aunt", which needs a generation gap, doesn't fit.
2. Sister: Tarak was assigned male through the operator convention, so calling him Queenie's sister would be wrong on gender alone.
3. Brother: Tarak and Queenie share the same mother, Rani, making them siblings, and Tarak being male makes him Queenie's brother specifically.
4. Grandson: A grandson would be Queenie's own child's child, but Tarak is Queenie's sibling, one generation off from where a grandson would sit, so this doesn't fit.

With names assigned this way, Tarak comes out as Queenie's brother.

So the correct answer is Brother.

Answer 11

Step 1: \(R - P\) shows \(R\) and \(P\) are siblings.

Step 2: \(P \div J\) shows \(J\) is \(P\)'s child.

Step 3: \(J \times Q\) shows \(J\) is \(Q\)'s father, so \(J\) is male.

Step 4: A male child of one's sibling is a nephew, so \(J\) is \(R\)'s nephew, not son, which would need \(R\) to be \(J\)'s own parent, or grandson, two generations down.
\[ \boxed{\text{Nephew}} \]

Answer 12

Assign real names to see this clearly. Let \(R\) be a man, Ravi, and from \(R - P\), let his sibling be Priya. From \(P \div J\), Priya is the mother of a child, Jai. From \(J \times Q\), Jai is shown as a father, so Jai is male.

1. Son: For Jai to be Ravi's son, Ravi himself would need to be Jai's parent, but Jai's parent is Priya, Ravi's sibling, not Ravi, so "son" doesn't fit.
2. Nephew: Jai is Priya's son, and Priya is Ravi's sibling, so Jai is the son of Ravi's sibling, exactly the definition of a nephew.
3. Niece: Jai was established as male, so "niece," a female label, doesn't fit him.
4. Grandson: A grandson of Ravi would need to be the child of Ravi's own child, but Jai is one generation removed through Ravi's sibling, not through Ravi's own child, so this doesn't fit.

With names filled in, Jai lands exactly as Ravi's nephew, the son of his sibling.

So the correct answer is Nephew.