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GMAT Club Olympics 2025 (Day 8): In a hot dog eating contest, two part

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Bunuel

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GMAT Club Official Explanation:

In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time. During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs. What was Marco’s average rate, in hot dogs per hour, during that time?

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.

Assuming Marco’s average rate was x hot dogs per hour, Leo's rate would be x + 6 hot dogs per hour. Since they competed for the same amount of time, we can equate by time: 36/(x + 6) = 30/x. Solving this gives x = 30 hot dogs per hour. Sufficient.

(2) In the first 20 minutes, Leo ate 12 hot dogs.

This implies that Leo's average rate for the first 20 minutes was 36 hot dogs per hour. However, we cannot assume that Leo maintained the same rate while eating the remaining 36 - 12 = 24 hot dogs. He could have eaten those in 1 hour or in 10 hours, resulting in different total durations and, therefore, different rates for Marco. Not sufficient.

Answer: A.

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[quote="Bunuel"]In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time. During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs. What was Marco’s average rate, in hot dogs per hour, during that time?

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.

(2) In the first 20 minutes, Leo ate 12 hot dogs.

[oly-gmatc2025][/oly-gmatc2025][/quote] total time is 1 hour since Leo ate 6 hots dogs more than Marco per hour,Leo ate 12 hots dogs in mins meaning 36 hot dogs per hence proves that Marco rate is 30 hot dogs per hour

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09 Jul 2025, 08:37

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Let Leo (L) and Marco (M) take time t each since
"competed for the same amount of time"
So
Rate of L = R_L=36/t
Rate of M = R_M=30/t

What was Marco’s average rate, in hot dogs per hour, during that time?
To answer this , we just need to know t now.

Statement 1
R_M + 6/1= R_L
30/t + 6 = 36/t
We can solve for t.
Thus, SUFFICIENT

Statement 2
We don't know if Leo’s rate is constant throughout. So this would not help.
Thus, INSUFFICIENT

Answer is A.

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Let's denote the time of the contest as t hours.
We know that Leo ate 36 hot dogs and Marco ate 30 hot dogs in the same time perlod t
Leo's rate = 36/t hot dogs per hour
Marco's rate = 30/t hot dogs per hour
We need to find Marco's rate.
Statement (1): Marco's average rate was 6 hot dogs per hour less than Leo's.
This means:
Marco's rate = Leo's rate - 6
30/t =36/t-6
30/t = (36 - 6t)/t
30 = 36 - 6t
6t=6
t= 1 hour
Since t = 1 hour, Marco's rate = 30/1 = 30 hot dogs per hour.
Statement (1) alone is sufficient.
Statement (2): In the first 20 minutes, Leo ate 12 hot dogs.
This means Leo's rate is 12 hot dogs per 20 minutes, which equals 36 hot dogs per hour.
So, Leo's rate = 36 hot dogs per hour.
However, this statement alone doesn't tell us anything about Marco's rate directly. We know Marco ate 30 hot dogs in time t, but we don't know what t is from this statement alone.
Statement (2) alone is not sufficient.
The answer is A) Statement 1 alone is sufficient, but statement 2 alone is not.

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In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time. During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs. What was Marco’s average rate, in hot dogs per hour, during that time?
L=36
M=30
Time for L and M is same

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
30/t =36/t -6
30=36-6t
t=1
Marco’s average rate= 30 hotdogs per hour
Sufficient

(2) In the first 20 minutes, Leo ate 12 hot dogs.
No information about Marco
Insufficient

A

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duration of the contest was same
Leo ate 36 hot dogs
Marco ate 30 hot dogs

target find Marco's avg rate

#1
Marco’s average rate was 6 hot dogs per hour less than Leo’s.
let x be duration of contest

Rate of Leo= 36/x
Marcos rate = 30 /x = 36/x - 6
solve for x= 1 hour
we know duration of contest i.e. 1 hour so Marco rate was 30 hot dogs per hour
sufficient

#2

In the first 20 minutes, Leo ate 12 hot dogs.

rate of Leo ; 12/20 ; 0.6 hot dogs per mins
time it took to eat 36 hot dogs ; 36/ 0.6 = 60 mins or say 1 hour

duration we know is 1 hour
so rate of Marco will be 30 hot dogs per hour

sufficient

OPTION D is correct

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Let's set up the two rate equations
L: rL x t = 36
M: rM x t = 30

We are asked to find rM.

Using statement (1):
rM = rL - 6. Because the time for each participant is the same, I can let their rate equations equal eachother's time where 36/rL = 30/rM and plugging in rM + 6 for rL, I can find rM. Thus, statement (1) alone is sufficient.

Using statement (2):
If L eats a third of his hotdogs in 20 mins, then he eats all of his hotdogs in 60 mins. Knowing t, and given that t is the same for L and M, I can find rM and say that statement (2) alone is sufficient.

Answer: D) Each statement alone is sufficient

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09 Jul 2025, 08:49

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In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time. During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs.

What was Marco’s average rate, in hot dogs per hour, during that time?

Let the time of competition be t hours

Marco's average rate, in hot dogs per hour = 30/t hot dogs/hour
Leo's average ate , in hot dogs per hour = 36/t hot dogs/hour

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
36/t - 30/t = 6
6/t = 6
t = 1 hour
Marco's average rate, in hot dogs per hour = 30/t = 30 hot dogs/hour
SUFFICIENT

(2) In the first 20 minutes, Leo ate 12 hot dogs.
Since it is not mentioned that Leo ate at a uniform rate during the entire competition, Leo's average rate per hour, in hot dogs per hour can not be derived. There is no relation mentioned in Leo's rate per hour and Marco's rate per hour.
NOT SUFFICIENT

IMO A

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Given,
In time, lets say 'T' hour,
Leo ate 36 hot dogs, and Marco ate 30 hot dogs.

Target Question ---> What was Marco’s average rate, in hot dogs per hour, during that time?

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
Lets Leo's average rate be L, Then Marco's average rate = L-6
Also Given, 36 = LT and 30=(L-6)*T,

Substitute T=36/L from equation 1 in equation 2, we will get L=36 , so M=30.
Sufficient

(2) In the first 20 minutes, Leo ate 12 hot dogs.
The information does not tell us about the rate at which Leo consumed remaining 34 hot dogs, he could have took 40 mins, 4 hours or 40 hours. For each of these total time taken will change and so will rate for Marco. Insufficient.

Hence correct choice is Answer A

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(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s. =>
lets say Leo's rate = R
then Marco's rate will be. = R - 6
and we are given they did same time t so
30/(R-6) = 36/R
5R = 6R - 36
So R = 36 then R-6 = 30
So this is Sufficient

(2) In the first 20 minutes, Leo ate 12 hot dogs. => Now in this we only know rate of leo that too for first 20 minutes we don't know what was his rate for rest and the total time. so we can't find 30/t which is marco's rate. Hence
Not Sufficient

Hence Ans A

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The Goal: Find Marco's average rate in hot dogs per hour.

Let:
RL = Leo's average rate (hot dogs/hour)
RM = Marco's average rate (hot dogs/hour)
T = Time spent competing (in hours)

From the problem statement:
Leo ate 36 hot dogs. So, RL = 36/T

Marco ate 30 hot dogs. So, RM = 30/T

We need to find the numerical value of RM
This means we need to find the value of T.

Analyzing Statement (1): Marco’s average rate was 6 hot dogs per hour less than Leo’s.

This can be written as an equation:
RM = RL − 6

Substitute the rate expressions in terms of T:
30/T = 36/T −6

Now, we can solve for T:
6= 36/T − 30/T

6= 6/T
6T=6
T=1 hour

Since we found T = 1 hour, we can now find Marco's average rate:
RM = 30/T = 30/1 =30 hot dogs per hour.

Since we can determine Marco's average rate, Statement (1) is SUFFICIENT.

Analyzing Statement (2): In the first 20 minutes, Leo ate 12 hot dogs.

First, convert 20 minutes to hours: 20 minutes = 20/60 hours = 1/3 hour.

This statement tells us Leo's rate during the first 20 minutes.
Leo's rate in the first 20 minutes =
12 hot dogs / {1/3 hour} =12×3=36 hot dogs per hour.

However, the problem states Leo ate 36 hot dogs during the entire competition. It does not state that Leo maintained a constant rate throughout the entire competition. It only states his overall average rate for the total time T was 36 hot dogs. His average rate for the first 20 minutes might be different from his average rate for the total time T.

If Leo's overall average rate (RL ) for time T was 36 hot dogs/hour, then T would be 1 hour (36/1=36).

If T=1 hour, then RM =30/1=30 hot dogs/hour. But this is an assumption that Leo's rate in the first 20 minutes is his overall average rate.

The question explicitly defines Leo's average rate as (total hot dogs) / (total time). Statement (2) provides an average rate for a portion of the time. We cannot assume that the rate in the first 20 minutes is the same as the rate for the entire contest unless specified. The problem says "Leo ate 36 hot dogs" (total) and "Marco ate 30 hot dogs" (total), and "competed for the same amount of time" (T). It does not say Leo's rate was constant.

Therefore, we cannot determine T from this statement alone. Statement (2) is NOT SUFFICIENT.

Conclusion:

Statement (1) alone is sufficient to answer the question.

The final answer is A

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Bunuel

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Given : total hot dogs taken by Leo = 36 and by Marco = 30
asked: Marco's rate ?

Let L and M be rate per hour of Leo and Marco respectively.

Statement 1: M = L - 6 , Not sufficient as the value of L is not mentioned.

Statement 2: L = 12/20 minutes * 60(#to convert to jour) = 36 hot dogs/hour. Since Leo only ate 36 hot dogs then the specific time should have been 1 hour.
Since the total time is known the value of M can be known. hence sufficent.

Therefore the answer is Option B.

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From statement 1,

We can write the equation as 36/t-30/t=6[subtracting rates]
solve
30=36−6t
t=1
So Marco's rate is 30/1.So this is sufficient

from Statement 2

They gave in the first 20 minutes, Leo ate 12 hot dogs. But this is a trap.This is not sufficient because we don't know if he sped or decreased his rate after 20 minutes.
So this is inefficient.However, if the question had said they ate at a constant rate.Then this statement would have been sufficient

Hence, A is the answer

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Let R_m and R_l be the average rates for Marco and Leo in hot dogs per hour, and let T be the contest duration in hours. From the problem data, the rates can be expressed as R_m = 30/T and R_l = 36/T. To find a unique value for Marco's rate, R_m, a unique value for the total time, T, must be determined.

Statement (1) provides the equation R_m = R_l - 6. Substituting the expressions for the rates gives 30/T = 36/T - 6. This is a single equation with one variable, T, which solves to a unique value of T=1 hour. Therefore, Marco's rate can be determined, and this statement is sufficient. Statement (2) establishes Leo's rate only for the first 20 minutes of the contest as 12 dogs per 1/3 hour, or 36 dogs per hour. This does not determine his average rate for the entire contest, as his pace could have changed. The total time T could be one hour, or it could be longer if he slowed down. Since T cannot be uniquely determined, this statement is insufficient.

The correct answer is (A).

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Rate Leo rL= 36/t
Rate Marco rM= 30/t=??
or t=??

1. 36/t -30/t =6..t=1....YES SUFFICIENT
2. in first 20 min 12..what if he slowed down & took 2 hrs for the rest 24? NOT SUFFICIENT

Ans A

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To find Marco’s hourly rate we note that Marco ate thirty hot dogs while Leo ate thirty six. Statement one tells us that Marco’s rate fell six dogs below Leo’s rate. Since Leo’s rate matches thirty six in the same time we infer that the contest ran one hour. That means Marco ate thirty hot dogs in one hour which gives his rate. Statement two only says that Leo ate twelve in twenty minutes and that pace may not hold for the full contest. We cannot find Marco’s rate from that alone. Only statement one suffices.

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Let the amount of time be T
M ate=30
L ate=36
Mavg = 30/T = ?
T=?

S1
Marco’s average rate was 6 hot dogs per hour less than Leo’s.
36/T-30/T=6
6/T=6
T=1
sufficient

(2) In the first 20 minutes, Leo ate 12 hot dogs.
We know Leo's rate for the first 20 minutes but we don't know if the rate was constant
So we don't have enough info to get his avg rate or time he ate
Insufficinet

Answer A

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Bunuel

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Let's assume that both competed for 't' hours.

Leo's rate = 36/t
Marco's rate = 30/t

Question is 30/t = ?

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.

36/t - 30/t = 6

t = 1

Hence, we can find the rate.

The statement is sufficient.

(2) In the first 20 minutes, Leo ate 12 hot dogs.

We don't know the total time it took for Marco. Not sufficient.

Option A

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09 Jul 2025, 09:39

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Leo and Marco ate hot dogs for the same unknown amount of time. Statement (1) tells us Marco’s rate was 6 hot dogs per hour less than Leo’s. Using the total hot dogs eaten by each, we can set up equations to find the contest time and then Marco’s rate, so this statement alone is sufficient. Statement (2) says Leo ate 12 hot dogs in the first 20 minutes, which means his rate was 36 hot dogs per hour, and since he ate 36 total, the contest lasted exactly one hour. Knowing this, Marco’s rate is simply 30 hot dogs per hour. Thus, statement (2) alone is also sufficient. Therefore, either statement alone lets us find Marco’s average rate.