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

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The correct answer is (A) Statement 1 is sufficient

Statement 1 - The question stem tells us that Leo at 36 at the same time Marco ate 30, therefore for similar amounts of time, the ratio of their hotdogs would be similar. Since statement 1 says Marco ate 6 less than Leo, this reflects the 30 and 36 from the question stem and fulfills that particular situation and we know that Marco ate 30 hotdogs in an hour on average.

Statement 2 - Leo eating 12 hotdogs in the first 20 minutes does not necessarily tell us about how many he ate in the full hour. Therefore we do not know enough about the rate per hour and this is not sufficient on its own to answer the question.

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

t is the time taken

we have to find Marco's rate so we need value of t.

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

marco's rate= Leo's rate -6
30/t=(36/t) - 6
solving for t, t=1

Sufficient.

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

We can find Leo's rate, but what about Marco's? we can not.

Insufficient.

A. Statement (1) alone is sufficient.

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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.

This question was provided by GMAT Club
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We need time to calculate the rate.

1) The difference of rate can help us find the time. Hence, the statement alone is sufficient.

2) The information on Leo's rate don't help us find Marco's rate. For different value of Leo's rate , Marco can have different rates and hence, the average rate can vary.

Option A

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L= 36 hot dogs, M=30 hot dogs
They competed for the same amount of time.
let the time be t
M's rate=30/t
(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
30/t=(36/t)-6
30/t-36/t=-6
t=1
M's rate=30/1=30
(2) In the first 20 minutes, Leo ate 12 hot dogs.
with this we cannot conclude as we dont know if this could be the average rate or the rest of hotdogs were at which rate
IMO:A

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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 L = Leo, M = Marco

R * T = W
Then
R = W / T

=====R====T====W
L .......36/t.........t.........36
M ......30/t.........t.........30

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

30/t = 36/t - 6/1
30/t = ( 36 - 6t ) / t
30 = ( 36 - 6t )
6t = 6
t = 1

Is it sufficient? Yes, it is. Eliminate answer choices B, C, and E.

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

Ok... But what about the next hot-dogs? It does not tell us if this is the "constant pace". With the information provided, the last 2 hot-dogs could be ate in 5 minutes, 20 hours, and so on. Is it sufficient? No, it is not. Eliminate answer choice D.

Answer = A Statement (1) alone is sufficient but Statement (2) alone is not sufficient.

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In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time (t hours). During that time, Leo ate (L) 36 hot dogs, and Marco ate (M) 30 hot dogs. What was Marco’s average rate, in hot dogs per hour, during that time?

Marco's Average Rate = M/t;

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

M/t = L/t - 6;

30/t = 36/t - 6; t=1 hour;

Marco's Average Rate = M/t = 30 per hour, Sufficient.

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

The remaining he may eat in 1 sec or 1 year, insufficient information for calculation.

Ans. A

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D. Each is sufficient by itself

L * t = 36
M * t = 30

(1)
M+6=L
(M+6)*t = 36
Mt + 6t = 36
Mt+6t - Mt = 36 - 30
6t=6
t=1
L=36
M=30
SUFFICIENT

(2)
L*1/3=12
L=36
t=1
M=30
SUFFICIENT

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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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Correct Answer: Marco rate is 30 hot dog per hour. We can answer this using statement I alone.
Given we have
Hot dog Marco ate= 30
Hot dog Leo ate= 36
For both time is same.

Now let’s check each statement:

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

Assume time= t
Average rate of Marco= 30/t
Average rate of Leo= 36/t
Now calculate value of t= 36/t-30/t= 6
= 6/t= 6
= t= 1
Marco rate= 30/1= 30 hot dogs per hour
Hence this statement alone can answer the question.

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

We can't answer this question using this statement alone.
As because we don't know in what time Leo ate the remaining hot dogs.
If we assume same rate then this statement will also be sufficient to answer this question.
Hence we can't assume this and thus statement I is sufficient to answer this question.

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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?

Given that Leo rate= 36/X where X is the time in hours
Marco Rate= 30/X

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

30/x=36/x-6
solving x=1 hour

clearly Marco's average rate was 30 hot dogs per hour.
Statement 1 is sufficient.

(2) In the first 20 minutes, Leo ate 12 hot dogs.
Leo rate for 20 mins= 12/1/3= 36 hot dogs/ hr
But we don't know what happens after 20 mins
Also we don't get to know what is the total time

whether X=1,2 or 3
Because different x will led to different rates for remaining time

So statement is insufficient.

Answer is A.

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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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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See, it is already mentioned that they are competing for same time.

In equation 1, we come to conclusion if Leo eat at rate of L dogs per hour, then marco would eat in L-6 dogs. now, we know

Number of Dog Marco Eat / Rate of eating dogs by marco = Number of dogs eaten by Leo / Rate of eating by Marco

so from here we can find L and can find Marco average rate too. So (1) alone is suffecient

Now for equation 2,

it is written than Leo eat 12 dogs in 20 mins, which means the ratio of dog eaten by marco and leo is same as dogs eaten in 20 minutes by them.

So if leo eats 36 dogs in same time as Marco eat 30, it means if leo eats 12, marco would eat 10. and now we know how many dogs marco ate in 20 minutes and so we know the average rate too. So (2) is sufficient.

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In this we know some amount of time in which Marco and Leo ate hot dogs.
From 1st statement we can say that in an hour Marco will eat 6 more hhot dogs than Leo.
From given data it is clear that difference is 6 so the time period is one hour and avg rate is also same.
From 2nd statement in 1st 20 min Leo ate 12 hot dogs so in an hour he will eat 36 hot dogs.
The statement also gives that Leo had eaten 36 hot dogs so again we get same conclusion.
Both statements independently are sufficient.

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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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In a hot dog eating contest, two participants, Leo and Marco, competed for the same amount of time.
Time = T hours

During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs
L = 36
M = 30

Rates
m = 30/T hotdogs/hour
l = 36/T hotdogs/hour

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

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
m = l - 6
30/T = 36/T - 6
=> 36 - 30 = 6T
=> 6 = 6T
=> T = 1 hour
Now m = 30/T = 30/1 = 30 hotdogs/hour

(2) In the first 20 minutes, Leo ate 12 hot dogs.
Cannot generalize the time of Leo basis only the first 20 minutes

Option A

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Where x is the time taken by each of them. Note (Marco's time=x and Leo's is also=x)

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

Average rate = Total work/Total time
Marco's total work= 36
Marco's time = x
Marco's average rate = 36/x
The statement says that this average is 6 hot dogs per hour less than Leo's
Therefore, Leo's average rate is (36/x)-6
Recall that total work = (average rate)*total time
Leo's total work is ((36/x)-6)*x=30
this simplifies to x=1

Statement 1 alone is sufficient

Statement (2) In the first 20 minutes, Leo ate 12 hot dogs.
Since we have no idea whether, Leo maintained that rate, how long the total contest lasted
and we don’t know Marco’s behavior at all. This statement alone is not sufficient

Answer choice A. Statement 1 alone is sufficient

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Let the total contest time be t hours.
Leo's rate=36/t
Marco's rate= 30/t

To find: 30/t- Marco's rate.

Statement 1: Sufficient.
30/t= 36/t-6
t = 1
Marco's rate = 30/1= 30.
Sufficient.

Statement 2: Not sufficient.
Leo ate 12 hot dogs in 20 minutes.
rate = 36 hot dogs/hour (only for first 1/3 hour)
This doesn't guarantee Leo maintained that rate throughout the contest.
Contest duration remains unknown.
Not Sufficient.

Answer: (A) Statement 1 alone is sufficient but statement 2 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?

(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.

participant	hotdogs	time	rate
Leo	36	t	36/t
Marco	30	t	30/t

Statement 1: 30/t + 6 =36/t
on solving we get t = 1,
so marco's rate = 30 hotdogs per hour

SUFFICIENT

Statement 2:
from the information of first 20 minutes we cannot find out the average for 1 hour

So insufficient

Answer: A

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Let's say they competed for $t$ hours

Leo's rate, $L=\frac{36}{t}$

Marco's rate, $M=\frac{30}{t}$

$M=?$

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

$M=L-6$

$\frac{30}{t}=\frac{36}{t}-6$

$t=1$

$M=\frac{30}{1}=30$

Sufficient

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

How many hot dogs Leo ate in the remaining $(t-\frac{20}{60})$ hours. Did he maintain the same rate or have different rate?

And how is this rate related to Marco's?

Not Sufficient

Answer: A

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Ans: A [statement 1 is sufficient]

Leo and Marco, competed for the same amount of time. Tl = Tm
During that time, Leo ate 36 hot dogs, and Marco ate 30 hot dogs. = Marco ate 6 fewer HotDogs than Leo (in that similar duration)
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.
We already know that Marco ate 6 fewer hot dogs in that given time, and this statement says that Marco's average rate was 6 less than Leo's. It means they competed for an hour and that makes Marcos' rate 30 hot dogs/hr [Sufficient]

(2) In the first 20 minutes, Leo ate 12 hot dogs.
If Leo has 12 hot dogs in the first 20, but we do not know after that.. Leo could have ate next 24 hot dogs in 2 hours or 4 hours or 40 minutes. this could give us any average hotdog/hr eating speed for Leo. From this we can not get Leo's speed in hot dogs/hr thus can not find Marco's speed. [Not Sufficient]

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Statement (1):
Marco's average rate was 6 hot dogs per hour less than Leo's.
Let t be the time (in hours) they both competed.
Then:

Leo’s rate = 36/t
Marco’s rate = 30/t

Given:
30/t = (36/t) − 6
This equation holds and lets us solve for t:
(36/t) − (30/t) = 6
=> 6*t = 6
=>t=1
So Marco's rate = (30 / 1) = 30 hot dogs/hour.
Statement (1) is sufficient.

Statement (2):
In the first 20 minutes, Leo ate 12 hot dogs.
This tells us something about Leo’s rate in the first 20 minutes, but:

We do not know if Leo maintained this pace the whole time.
We don’t know how long the contest lasted.
We are not told anything about Marco's rate or pace.

So this info is not enough to find Marco’s average rate.
Statement (2) is not sufficient.

(A)

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.

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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(2) is not sufficient since it is not necessarily the average rate. He might have eaten faster in the first 20 min and slow remaining time or vice-versa. Not sufficient.
(1) is sufficient, so Option A

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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?

(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.

Given:
Say, the time taken is t(same for both).
L -> 36 / t
M -> 30 / t

Question is to find Mrate (per hour.) That is basically to find time t.

Statement 1:

Mrate = Lrate - 6
=> 30/t = 36/t - 6
=> t = 1

This is sufficient as we got the required t to find the rate in per hour terms. Options A or D.

Statement 2:

Lrate = 12/(20/60) (convert minute to hours)
=> Lrate = 12 * 3 = 36 per hour
=> t = 1 => Mrate = 30 per hour. Sufficient. So option D.

Answer is D.

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