In a race, an overtake between two participants refers to the event

Question

In a race, “an overtake” between two participants refers to the event of one of them moving ahead of the other. P and Q were two of the runners in a marathon that P won. At Time T, both P and Q crossed Point X together—after which neither stopped running before reaching the finish line. After Time T, Q overtook P at least three times, and each time P was behind and caught up with Q, P overtook Q. How many overtakes between P and Q occurred after Time T?

(1) Q overtook P exactly three times between Point X and the finish line.
(2) P overtook Q exactly three times between Point X and the finish line.

(1) Q overtook P exactly three times between Point X and the finish line.
(2) P overtook Q exactly three times between Point X and the finish line.

MartyMurray · Accepted Answer

In a race, “an overtake” between two participants refers to the event of one of them moving ahead of the other. P and Q were two of the runners in a marathon that P won. At Time T, both P and Q crossed Point X together—after which neither stopped running before reaching the finish line. After Time T, Q overtook P at least three times, and each time P was behind and caught up with Q, P overtook Q. How many overtakes between P and Q occurred after Time T?

(1) Q overtook P exactly three times between Point X and the finish line.
(2) P overtook Q exactly three times between Point X and the finish line.

How many overtakes between P and Q occurred after Time T?

Key information given:

“An overtake” between two participants refers to the event of one of them  moving ahead of the other .

At Point X and Time T, P and Q were "together."

After Time T, Q overtook P at least three times, and each time P was behind and caught up with Q, P overtook Q.

P won.

(1) Q overtook P exactly three times between Point X and the finish line.

This statement tells us only that Q overtook P three times.

If we go with the definition that an overtake is "one of them moving ahead of the other," then we have the following two possibilities.

Together at X - P moves ahead - Q moves ahead - P moves ahead - Q moves ahead - P moves ahead - Q moves ahead - P moves ahead and wins. 7 overtakes

Together at X - Q moves ahead - P moves ahead - Q moves ahead - P moves ahead - Q moves ahead - P moves ahead and wins. 6 overtakes

Insufficient

(2) P overtook Q exactly three times between Point X and the finish line.

Given that the passage says, "Q overtook P at least three times, and each time P was behind and caught up with Q, P overtook Q," if we go with the definition that an overtake is "one of them moving ahead of the other," then we have the following single possibility.

Together at X - Q moves ahead - P moves ahead - Q moves ahead - P moves ahead - Q moves ahead - P moves ahead and wins. 6 overtakes

Sufficient.

So, it appears that the correct answer is (B), for BUSTED question.

Bunuel · Answer

Is this from an official GMAT Prep mock? If so, which one? Could you please share a screenshot? That would help. Thank you.

consistentprep · Answer

https://gmatclub.com/forum/download/file.php?id=87517 Bunuel GMAT-Club-Forum-25oigy4u.png

Bunuel · Answer

____________________
Thank you! That helps!

consistentprep · Answer

KarishmaB   MartyMurray   chetan2u  Kindly help.

KarishmaB · Answer

Every time Q overtakes P, P overtakes Q after some time. So the overtakes occur in pairs. Since Q overtakes at least 3 times after X, P overtakes at least 3 times after X too. But what happened at X, we do not know.

(1) Q overtook P exactly three times between Point X and the finish line.

There are 2 possibilities assuming Q overtakes exactly 3 times AFTER X:

Case 1: Q is faster than P and overtakes P at point X. So P overtakes Q after X and is ahead now. Thereafter, Q overtakes P 3 times after X and P overtakes him back 3 times. So total 7 overtakes could happen after X.

Case 2: P is faster and is ahead of Q after overtaking him at X. Then Q overtakes P 3 times after X and P overtakes him back 3 times. So total 6 overtakes take place.

(2) P overtook Q exactly three times between Point X and the finish line.

Now we know case 2 happened. Q must have overtaken 3 times too since P overtook 3 times only. Total 6 overtakes happened.

Answer (B)

Stella5200 · Answer

Folks.... here's my take. My answer is D.

You can have two situations one where P is in the lead first and Q is in the lead first. We will come back to this. 
Look at how an overtake is defined. Q can make three over takes that is the minimum. P can make overtakes only as a response to when Q makes over takes.

"Q overtook P at least three times, and each time P was behind and caught up with Q, P overtook Q. "

Interpretation: Q overtook P atleast 3 times. OK.

AND each time P was behind (WHEN Q overtook), it caught with up and overtook Q.

Now back to our scenarios:

P is in the lead
So order goes Q1, P1, Q2, P2, Q3, P3 (P must win remember) Great ! total Overtakes is 6

Q is in the lead
So order goes starts with P1... (right?....nope!) This branch doesnt work because P only over takes in response to Q; and Q here is NOT overtaking.

Why? Because being in the "lead" doesn't mean you are overtaking you can only overtake when you are behind them.. Am I making sense..... Q went from equal position to Lead.. an Overtake only works when you are behind them then you pass them.

Anyway since only the first branch works P=Q. You either need P or Q. Hence D.

I think the semantics were dirty on this one.

Let me know what you think of my approach

Bunuel   MartyMurray

nishant8780 · Answer

As per given information, 'overtake' means one participant moving ahead of the other. And one can move ahead compared to another even when both are at equal position ( which is given in question at time T) In that case, won't 'lead = overtake' ?

roshaun25 · Answer

I think this is the way that they intended it to be solved on the official mock, but they only specify that an overtake is "one of them moving ahead of the other", which doesn't rule out moving ahead from a tied position. IMO they left too much ambiguity here to say statement 1 is sufficient.

Stella5200 · Answer

I think the other thing I would use as a guiding pt is GMAT errs on the side of convention (though I know this is not universal)... an overtake conventionally if you think about cars on the road is only when you come from behind then take that leading car's position. In my view you cannot over take when you are at equal pts.. you can simply lead. there is no position to take over..

Bit largely agree that given the mental fatigue + time pressure you hit at this pt the shoddy wording would short circuit just about anyone. My tip is to not overthink, take a reasonable definition to guide and move on. I dont even know if my approach is right but it does eliminate an entire branch... which is helpful.

ShineFact · Answer

An  overtake  requires someone to be  behind first  and then move ahead. Since P and Q are tied at Time T, the first runner who simply pulls ahead after T has  not overtaken  the other runner.

So seven-overtake sequence needed an unstated preliminary step. Here is the accurate version.

Case 1: P pulls ahead first

This initial movement is  not counted  as an overtake:

Tie→P ahead

Then the counted overtakes can be:

Q, P, Q, P, Q, P

Q overtakes P three times.  
 P overtakes Q three times.  
 P finishes ahead.  
Total counted overtakes: 6

Case 2: Q pulls ahead first

Again, Q’s initial movement from a tie to the lead is  not counted :

Tie→Q ahead

Then the counted overtakes can be:

P, Q, P, Q, P, Q, P

Q overtakes P three times.  
 P overtakes Q four times.  
 P finishes ahead.   
Total counted overtakes:7

Therefore, statement (1)—“Q overtook P exactly three times”—still allows either  6 or 7  total overtakes, depending on who first pulled ahead from the initial tie. It is insufficient.

For statement (2), P overtook exactly three times, and the stem says Q overtook P at least three times. Since P ultimately won, the only possible counts are:

P=3,Q=3

Thus:
total=6

So the logically supported answer remains:

Statement (2) alone is sufficient.

Legallyblond · Answer

SO WHATS THE CORRECT ANSWER? I MEAN THE OG IS D YOU ARE SAYING B? @BUNNEL  karishma

Legallyblond · Answer

I DONT THINK LEAD AND OVERTAKE IS DIFFERENT HERE, I MEAN THERES ONLY ONE THING DESCRIBED AND KEEPING THESE 2 DIFFERENT WOULD BE AN ASSUMPTION

In a race, an overtake between two participants refers to the event

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