Of five people-P, Q, R, S, and T-three form a set of triplets and two

Question

Of five people-P, Q, R, S, and T-three form a set of triplets and two are a pair of twins. Is P among the set of triplets or one of the pair of twins?

(1) P, Q, and R all have the same biological parents.

(2) P, S, and T do not all have the same biological parents.

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Official Answer

C

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sgoenka8 · Answer

IMO, statement 1 is sufficient to answer the question.
IF P,Q and R all have same biological parents, means that they are triplets.

Can someone please elaborate how is my reasoning incorrect?

Bunuel   KarishmaB   GMATCoachBen

Bunuel · Answer

(1) is not sufficient because it can be that P and Q are the twins (same parents), and R, S, and T are the triplets (also same parents).

WiziusCareers1 · Answer

The total population is 5 people (P,Q,R,S,T).
Set A: Triplets (3 people, same parents)
Set B: Twins (2 people, same parents)

Step 1: Evaluate Statement (1)
P, Q, and R all have the same biological parents.
This statement identifies a "parental cluster" of three people.

Possibility Alpha: P, Q, and R are the triplets.
Possibility Beta: All five people (P, Q, R, S, T) are siblings from the same parents. In this scenario, P could be one of the twins, and Q and R could be two of the triplets. They would still all share the same parents.
Conclusion: Because we don't know if the twins and triplets are siblings to each other, we can't be sure if P is a triplet or a twin.  Insufficient.

Step 2: Evaluate Statement (2)
P, S, and T do not all have the same biological parents.
This statement is a "negative" clue. It tells us that the five people are not all siblings.
It proves that the Triplets and the Twins come from two different sets of parents.
However, it doesn't tell us which group P belongs to. P could be a twin whose parents are different from the triplets S and T. Or P could be a triplet whose parents are different from the twins S and T.  Insufficient.

Step 3: Combining the Statements
We now have two vital pieces of information:
The Triplets and Twins have different parents (from Statement 2).
P, Q, and R share the same parents (from Statement 1).

If the Triplets and Twins have different parents, there is only one group of people in this set of five that can share parents: the Triplets. Since P, Q, and R share parents, they must be the Triplets. If P were a twin, he could only share parents with one other person (his twin), not two others (Q and R), because Statement 2 ruled out the possibility of the two groups being siblings.
Hence,
Triplets = {P, Q, R}
Twins = {S, T}

P is a triplet.

So, the answer is C (Both statements together are sufficient)

KarishmaB · Answer

The biological parents of triplets and twins can be the same. Say D and M had a pair of twins and then two years later, triplets! So statement 2 is needed.

Mayanknitt1 · Answer

nice question. in statement 2 ,i thought that all three had different parents initially. now i see that it just means all 3 dont have same parents, but 2 of them still can.

KarishmaB · Answer

Yes after all, there can be at most 2 different set of parents.

axeofflane · Answer

Great question - i messed up the first statement as my brain couldnt comprehend a single couple having 5 kids, where they have trips and deuce

Of five people-P, Q, R, S, and T-three form a set of triplets and two

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Of five people-P, Q, R, S, and T-three form a set of triplets and two

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