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

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09 Jul 2025, 23:53

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Bunuel

Average rate = total number of hot dogs / total time

Let the total time taken be t hours for both, then
Leo's average rate = 36/t hot dogs per hour , Marco's average rate = 30/t hot dogs per hour

1. Leo's average rate - 6 = Marco's average rate
36/t - 6 = 30/t
36-6t = 30
6t=6
t=1 hour

Marco's average rate = 30/t hot dogs per hour = 30 hot dogs per hour - Sufficient.

2. In first 20 minutes Leo ate 12 hot dogs = or to eat 12 hot dogs Leo took 20 minutes.
However, we are not given whether Leo ate the hot dogs with same rate for the entire contest. --Insufficient.
A is the answer

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Assume the time both took to each hotdogs be 't'(hrs).
Leo hotdog/hr=36/t
Marco hotdog/hr=30/t

Statement I:
30/t=36/t - 6
solving this would result in t=1 hr
Ques can be answered by this statement

Statement II:
It is given that leo ate 12 hotdogs in 20min. bt we it is not known that how much more time leo took for the rem. 24 hotdogs. so cant answer the ques.

Ques. can be answered by statement I alone.

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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?

rate of Leo = 36/t
rate of Marco = 30/t

(1) only: Marco’s average rate was 6 hot dogs per hour less than Leo’s.
30/t = 36/t - 6
We can find t, hence can answer.

(2) In the first 20 minutes, Leo ate 12 hot dogs.
This isn't sufficient to answer.

Answer: A

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10 Jul 2025, 02:59

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Bunuel

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10 Jul 2025, 03:39

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Option A is the correct answer.

Lets understand the question before trying to answer it.

So the question starts by telling us that "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". Now the question asks us at what average rate does Marco eat hot dog at the competition.

Lets read the statements and see whether we can find out answer from there or not.

Statement 1: "Marco’s average rate was 6 hot dogs per hour less than Leo’s". This statement tells us that the Marco's average eating rate is 6 hot dogs less than Leo's eating rate which would mean that if Lea eats 12 hot dogs in a specific time then Marco can eat 6 hot dogs within that time. Lets try to check what are the values that satisfy this statement:

Lets take Leo's rate to be 12 then Marco's rate will be 6 but if we check that according to this Leo will finish his 36 hot dogs within 3 hours where as Marco will need 5 hours to finish his 30 which is incorrect as per the question because the question tells us that they both competed for the same amount of time.

Let Leo's rate be 24 then Marco's rate will be 18 but if we check that according to this Leo will finish his 36 hot dogs within 1:30 hours where as Marco will need 1:40 hours to finish his 30 which is incorrect as per the question because the question tells us that they both competed for the same amount of time.

Will can check all the values like that and in the end we will find out that only 1 value i.e. Leo's rate = 36 and Marco's rate = 30 satisfies the condition.

So from here we can say that 'Statement-1' is Sufficient to answer the question.

Statement 2: "In the first 20 minutes, Leo ate 12 hot dogs". This statement tells us that at first 20 minutes of the competition Leo ate 12 dogs but we don't know how many more did he ate at rest of the 40 minutes of the first hour of the competition, moreover we are concerned about the eating rate of Marco not Leo. This statement cannot give us any exact answer so this statement is Not Sufficient to answer the question.

After reading and checking both the statement we can conclude that only 'Statement-1' can answer our question that's why "Option-A" is our answer.

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10 Jul 2025, 04:17

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average of Leo = 36/ContestTime
average of Marco = 30/ContestTime

Do we know ContestTime?

(1)
average of Leo = average of Marco + 6
36/ContestTime = 30/ContestTime + 6
36 = 30 + 6*ContestTime
ContestTime=1

Statement (1) alone is sufficient.

(2)
We know that "In the first 20 minutes, Leo ate 12 hot dogs" but we don't know if in the next 20 minutes Leo ate 12 hot dogs too or any other number of hot dogs.

Statement (2) alone is insufficient.

Answer is A

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10 Jul 2025, 04:23

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The only trick in this question is Usual GMAT trick
DO NO assume after reading Statement (2) that Leo ate with same rate if we assume that then we can mark (D) but it is no where mention they ate with same average rate throughout.

so Answer is (A).

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10 Jul 2025, 04:31

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Given:
Leo ate 36 hotdogs and Marco ate 30 hot dogs in same time.

Question: Marco's avg Rate/hour?

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

So we know together they ate 66 hotdogs in a certain time
Also Marco's Avg rate/hour=Leo's Rate/hour-6 hotdogs/hour

Their combined rate is (L+L-6)=2L-6

Total time taken=66/(2L-6)=66/2(L-3)=33/L-3

Now We know total time taken is 33/L-3
Also we know Leo's Rate i.e L and Hotdogs he ate i.e 36. So we can say

L=36/33/(L-3)
L=(L-3)*12/11
11L=12L-36
L=36
So, M=30

Yes we can say this st. is sufficient alone.

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

In 20 mins Leo ate 12 hotdogs
in 60 min he will eat 12*3=36 hotdogs so we know he ate his 36 hot dogs in 1 hour

We know he and Marco took same amount of time.
Marco ate his 30 hot dogs in one hour

therefore, his rate/hour=30

This is also sufficient

So, Answer D both are sufficient alone.

Bunuel

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t=contest time

AverageLeo=36/t
AverageMarco=30/t

AverageMarco?

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

AverageMarco=30/1=30

SUFFICIENT

(2)
We don't know whether Leo's rate is constant or not, so we cannot deduce any average rate from the information.

INSUFFICIENT

IMO A

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10 Jul 2025, 05:08

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L=36/T
M=30/T

To calculate M, T="total time of the contest" is needed.

(1)
L=M+6
36/T = 30/T + 6 = (30+6T)/T
36 = 30+6T
T=1

M=30/1=30

Statement is sufficient

(2)
It's impossible to deduce any useful data from this because the problem doesn't say that the rate is constant.

Statement is insufficient

The right answer is A

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10 Jul 2025, 05:14

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Each option alone is sufficient to get the solution.

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Option D correct

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Leo=36/time
Marco=30/time

answer: Is it possible to deduce how long did the contest last?

(1)
30/time = 36/time - 6
30 = 36 - 6*time
time=1

Sufficient

(2)
If the rate were uniform it would be possible to deduce that the contest lasted for 1 hour.
But the question does not say that the rate is uniform.

Insufficient

Correct answer is A

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10 Jul 2025, 05:33

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Given,
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.
To find
What was Marco’s average rate, in hot dogs per hour, during that time?
We have,
Leo’s eating rate = 36 /t hot dogs/hour
Marco’s eating rate = 30 /t hot dogs/hour

Statement 1:
Marco’s average rate was 6 hot dogs per hour less than Leo’s.
Now, we have,
30/t = 36/t – 6
t= 1
So Marco’s average eating rate = 30/ t = 30 hot dogs /hour
Sufficient

Statement 2:
In the first 20 minutes, Leo ate 12 hot dogs.
We have Leo’s eating rate foe first 20 minutes, no way of knowing about how much he ate after that or overall.
Not Sufficient
Ans: A

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10 Jul 2025, 05:40

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Given -> Let competition time $=$ $x$ hours
Leo's rate $= \frac{36}{x}$
Marco's rate $= \frac{30}{x}$
To determine -> Marco's average rate, in hotdogs per hour. If we can find $x$, it is enough to answer the question.

Statement 1 -> Marco’s average rate was $6$ hot dogs per hour less than Leo’s.
$\frac{30}{x} = \frac{36}{x-6}$
$x=1$ hour
Statement 1 is sufficient.

Statement 2 -> In the first $20$ minutes, Leo ate $12$ hot dogs.
If Leo ate at a constant rate, then according to this information, he will eat $12$ hotdogs in $20$ minutes and $36$ hotdogs in $60$ minutes.
But we don't know if his hotdog eating rate was the same after the first $20$ minutes.
It could be he ate the remaining $24$ hotdogs in the next $100$ minutes. That will mean $x = 120$ minutes $= 2$ hours.
It also could be he ate the remaining $24$ hotdogs in the next $10$ minutes. That makes $x = 30$ minutes $= 1/2$ hours.
Different values of $x$. Not sufficient

Answer - A

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10 Jul 2025, 06:03

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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.

Both Leo and Marco take the same time to eat the hot dogs. Leo eats 36 hot dogs while Marco eats 30 hot dogs. The question asks what Marco's Average rate is

Marco rate= 30/T
Leo= 36/T

Statement 1

30/T= 36/T-6
6=36/T- 30/T
6= 6/T
6T=6
T=1
Marco's average rate is thus 30hot dogs per hour.
Statement 1 is thus sufficient

Statement 2
We know Leo time for 12 hot dogs. Thus we can get the rate for 12 hot dogs and assume this rate is constant. Thus we get the total time for 36 hotdogs and so can get Marco's rate. Statement 2 is sufficient

Leo's rate = 12/20
= 3/5
The time taken for 36 hotdogs:
=36/3/5
=60 mins or 1 hr
Thus Marco's time is 60 mins or 1 hr
Rate = 30/1

30 hot dogs per hour.

Thus statement 2 is sufficient.

Both statements are independently sufficient.

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10 Jul 2025, 06:06

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To find rate we need to find time give w=rxt
marco rate = 30/t
leo rate = 36/t
From S1 36/t=30/t+6
so t= 1 Meaning marcos rate is 36/1 = 36 hot dogs per hour hence sufficient
S2 We do not know about Leos rate the rest of time hence insufficient
ANS A

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10 Jul 2025, 06:06

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Let's suppose both take h hours

leo rate = 36/h
marco rate = 30/h

Statement 1:

(36/h) - 6 = (30/h)

sufficient

Statement 2:

20 min leo ate 12 hot dogs

in 60 min he will eat 36 hot dogs

leo rate = 36 hot dogs /hour
marco rate = 30 hot dogs /hour

sufficient

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10 Jul 2025, 06:16

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(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

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Lets suppose total time of competition is T hours, Leo ate 36 hot dogs in T hours, Marco ate 30 hot dogs in T hours,

We need to find 30/T, for which we need the value of T.

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

$\\
\frac{30}{T} = \frac {36} {T} - 6 \\
\frac{30}{T} = \frac {36- 6T} {T}\\
30T = 36 - 6T\\
$
T = 1

We have found the value of T, so we have average rate of Marco = 30/1 = 30 hot dogs per hour
Statement 1 is sufficient,

(2) In the first 20 minutes, Leo ate 12 hot dogs.
We don't know if Leo ate at a constant rate. If the question had explicitly stated this, we could have gotten total hours by multiplying 36 * 20/12. BUT we cannot assume Leo was eating at constant rate. He could have finished the remaining 14 hotdogs in 1 hour or 5 minutes - we don't know.
So using this information, we cannot find value of T, and hence cannot find Marco's average rate.

Statement 2 is insufficient

Answer is A