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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, 09:40

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NOTES:
Two participants Leo and Marco
Same amount of time.
Leo eats 36 hot dogs
Marco easts 30 hot dogs

Ask:
What was Marcos average rate in hot dogs per hour?

SOLVE:

1) Marcos average rate was 6 hot dogs per hour less than leo.
36/T - 6 = 30/36
6 = 36/t-30/t 6=6/T T= 1hour
SUFFICENT

2) In the first 20minutes Leo ate 12 hot dogs.
We dont know if leo holds a solid rate. If he did then we could solve. But without that this is Not Sufficient.

Answer: A

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09 Jul 2025, 09:46

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Statement (1)

Taking this information you can arrive at

30/x = 36/x - 6

30 = 36 - 6x

6x = 6

x = 1

So in 1 hour Marco ate 6 less than Leo's tally of 36. Sufficient.

Statement (2)

If Leo ate 12 hot dogs in 20, he would have eaten all 36 in an hour.

Marco, ate 30 in an hour ie. 6 less than Leo. Sufficient.

D is correct.

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The question asks for Marco's average time eating hot dogs.
Number of hot dogs Marco ate / Total time = Marco's average rate of eating hot dogs.
We know LEO ate 36 hot dogs and Marco ate 30 hot dogs.

Let's look at the conditions.

Condition 1:
Total time is t.
30/t = 36/t - 6
6 = 6/t, so t = 1.
30/1 gives us Marco's average rate.
This condition is sufficient.

Condition 2:
It only tells us LEO's rate for the first 20 minutes,
12/(20/60).
However, we don't know how long it took him to eat the last 24 hot dogs.
So we can't figure out the total time.

This condition is not sufficient.

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Leo's work done = 36 hot dogs, Marco's work done = 30 hot dogs. Let Leo's rate be L & Marco's rate be M. Since they competed for the same time, we have 36/L = 30/M. We want to find M.

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
M = L-6 or L = M +6
Hence we have 36/(M+6) = 30/M, Solving this gives us M = 30 hotdogs/hr
Sufficient

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

12 hot dogs = 20mins
36 hot dogs = 20/12 *36 = 60mins or 1hr
Hence L (Leo's rate) = 36 hotdogs/hr

Putting L in 36/L = 30/M will give us M = 30 hotdogs/hr
Sufficient

Ans D

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The correct answer is (A)

Marco had 30 hot dogs
Leo had 36 hot dogs

TIME IS CONSTANT

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

Let Leo's average rate be x.
Rate Leo/work Leo=Rate Marco/work Marco
x/36=(x-6)/30
x=30

Marco's rate=(x-6)=24

Bunuel

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09 Jul 2025, 10:21

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Basis the prompt, we know that,

If "t" is the time in which Leo and Marco ate 36 and 30 hotdogs respectively, then,

$R_L = \frac{36}{t}$
$R_M = \frac{30}{t}$

We need to find the value of $R_M$

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

This says that,
$R_M + 6 = R_L$

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

$t = 1 $ hours

Plugging that back in $R_M = 30$ hotdogs per hour
So, sufficient.

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

This doesn't talk about the hourly rate for Leo, it could be the case that in the first 20 minutes Leo ate 12 hotdogs and then increased his rate to eat a total of 100 hotdogs in 1 hour.
Insufficient.

Answer A.

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09 Jul 2025, 10:26

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1) since Marco ate 6 less this it means it ate 30 hot dogs in an hour and hence his average rate is 30 hot dogs per hour Suff

2) we don’t know whether Leo at constant rate
NS

Ans A

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Given Information:
No. of hot dogs eaten by Leo in the given time = 36
No. of hot dogs eaten by Marco in the given time = 30

Let the given time be t hours.

Leo's Average rate (L)= \frac{36}{t}
Marco's average rate (M)= \frac{30}{t}

(1) L-6 = M

\frac{36}{t} - 6 = \frac{30}{t}
Solving this, we get: t=1
Marco's average rate = 30 hot dogs per hour
Sufficient.

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

Multiplying above by 3.
In the first 60 minutes, Leo ate 36 hot dogs.
Therefore, t= 1 hour.
Hence, Marco's average rate = \frac{30}{t }= \frac{30}{1} = 30 hot dogs per hour
Sufficient.

Both statements are alone sufficient. Therefore, answer is D.

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09 Jul 2025, 10:36

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Bunuel

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We know that Leo ate 36 hot dogs, and Marco ate 30 hot dogs. We need to find Marco’s average rate, in hot dogs per hour.

Stmt 1 : Marco’s average rate was 6 hot dogs per hour less than Leo’s.
Let t be the time both of them spend, Hmm so 30/t = 36/t -6 => t = 1 hr.

Hence we know the Marco’s average rate

Stmt 1 is sufficient.

Stmt 2 : In the first 20 minutes, Leo ate 12 hot dogs.
Wah, This is a tricky one. We don't know whether thy are eating at a constnat phase, May be he can complete 12 in 20 min and othr 24 in 2 hrs. Then the avg of Marco's changes.

Hence this stmt 2 is not sufficient.

Hence IMO A

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09 Jul 2025, 10:56

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Statement (1):
Marco’s rate was 6 less than Leo’s.
Let time = t hours
Leo’s rate = 36 / t
Marco’s rate = 30 / t
Given:
30 / t = 36 / t - 6
-6 / t = -6 -> t = 1
Marco’s rate = 30 / 1 = 30 hot dogs per hour
Statement (1) is sufficient

Statement (2):
Leo ate 12 hot dogs in 20 minutes
20 minutes = 1/3 hour
Leo’s rate = 12 ÷ (1/3) = 36 hot dogs/hour
Leo ate 36 hot dogs → time = 36 / 36 = 1 hour
Marco ate 30 hot dogs in 1 hour --> rate = 30 hot dogs/hour
Statement (2) is sufficient

Final Answer D

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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.

L = 36, M = 30

Rate L = 36/T, M = 30/T
Rate M = ? Identify so we need the value of T
(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
36/T= 30/T+6
36 = 30 +6T, T=1 Ans
Sufficient

(2) In the first 20 minutes, Leo ate 12 hot dogs.
Leo's first 20 min, but what is his average rate, we can't assume first 20 min rate is constant for all hour, or during 36 hot dog eating. Not sufficent

Ans. - A

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Let T be the total time of the contest in hours.
Statement (1): Marco's average rate was 6 hot dogs per hour less than Leo's. Marco's rate is 30/T and Leo's rate is 36/T. So, 30/T = 36/T - 6. Solving this equation gives us T=1 hour. With T=1 hour, Marco's average rate is 30 hot dogs per hour. This statement is sufficient.

Statement (2): In the first 20 minutes, Leo ate 12 hot dogs. This doesn't tell us if Leo maintained that rate for the entire contest. His eating speed could have changed. Since we don't know Leo's average rate for the entire contest, we can't determine the total time T. Therefore, we can't figure out Marco's average rate.
This statement is not sufficient. Thus the Answer is A.

Regards,
Lucas

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09 Jul 2025, 11:23

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since time given is constant here ,let 't' hrs
so rate for Leo is 36/t hotdogs per hr. & for Marco is 30/t hotdogs per hr.
to deduce rate for Marco we have to find 't'
1: 30/t=(36/t)-6 giving t=0(not possible) or t=1 SUFF.
2:Leo eats 12 hotdogs in 1/5 hr. i.e. 36/t=60 or t=3/5 SUFF.
hence D

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09 Jul 2025, 11:28

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Let total time Leo and Marco competed = T
Leo average rate in hot dogs per hour = l
Marco's average rate in hot dogs per hour = m

From the given condition,
l ×T=36
m ×T=30

From the two equations above, we can conclude
l/m = 6/5 ---> equation 1

Statement (1): Marco’s average rate was 6 hot dogs per hour less than Leo’s.
m =l−6
substitute equation 1 in above equation
m = (6/5)m - 6
6 = (6/5)m - m
6 = m/5
m = 30 hot dogs per hour.
Statement (1) alone is sufficient.

Statement (2): In the first 20 minutes, Leo ate 12 hot dogs.
=> 20 minutes to hours = 1/3 hours
Leo's average rate = Number of hot dogs/ Time = 12/(1/3) =12×3=36 hot dogs per hour.

subsitute l=36 in equation 1
=36/m = 6/5
=6×5 = 30 hot dogs per hour.

Statement (2) alone is sufficient.

Both statements individually are sufficient.

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Statement 1:
If we know that Marco’s average rate was 6 hot dogs per hour less than Leo’s average rate, it means that for each hour in the contest, Marco ate 6 more than Leo.
Since the difference between the number of hot dogs they ate in the contest is 6, it means the contest lasted for 1 hour. So it answers the question, which is that Marco's average rate during the contest equals 30.
So, statement 1 is sufficient.

Statement 2:
If Leo ate 12 hot dogs in 20 minutes, he would eat 36 hot dogs in one hour. There is a problem, though, we have no information about whether he keeps eating at this rate. Maybe that is all he can do in 1 hour, or maybe he ate the other 24 hot dogs in 5 minutes. How long did the rest take? We don't know, so this statement is not sufficient.
So, statement 2 is not sufficient.

The answer is A.

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Bunuel

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In a Hot dog eating competition, two Participants Leo and Marco competed for the same amount of time.

Leo ate 36 hot dogs.

Marco ate 30 hot dogs.

Marco’s average rate = ?

Statement 1:

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

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

Thus, t = 1.

We can find Marco’s average rate. Hence, Sufficient.

Statement 2:

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

The question doesn’t mention the rate is constant. And first 20 minutes cannot be extrapolated to 60 minutes.

Hence, Insufficient

Option A

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09 Jul 2025, 12:06

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Rate of Macro = ?
Leo ate 36 hot dogs
Macro ate 30 hot dogs

Let average rate of Macro = M
average rate of Leo = L
L*t = 36
M*t =30
L/M = 6/5

Statement 1:
M = L-6
=> 1 = L/M - 6/M
=> 1 = 6/5 - 6/M
=> M = 30

This is sufficient

Statement 2:
In the first 20 minutes, Leo ate 12 hot dogs.
So rate of Leo in first 20 mins = 36
But this does not say what happens after 20minutes, whether rate remains constant or changes

Hence this is insufficient

So answer is A

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We have to find Marco’s avg. rate, in hot dogs/hr.

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

We need to know the value of t to determine Marco's rate

(1) Marco’s average rate was 6 hot dogs per hour less than Leo’s.
-> (30/t) = (36/t) - 6
Solving this equation would give us a unique value of t, so statement 1 is sufficient.

(2) In the first 20 minutes, Leo ate 12 hot dogs.
Since we don't know if Leo was eating at a constant rate, he might have slowed down or sped up after initial 12 hot dogs. So we can't use this to calculate Marco’s rate. Insufficient.

Ans : A

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09 Jul 2025, 12:51

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Solution:

Leo ate 36 hot dogs and Marco ate 30 hot dogs.

The question asks for Marco’s average rate, in hot dogs per hour.

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

	Rate	Time	Work
Marco	6-R	30/6-R	30
Leo	R	36/R	36

We don't know the value of R. So, Insufficient.

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

If in 20 minutes, Leo can eat 12 hot dogs, it means in 1/3 hour, Leo can eat 12 hot dogs. Also, we can calculate from here that Leo can eat 36 hot dogs in an hour.

	Rate	Time	Work
Marco			30
Leo	R	1	36

By combining both statements, we get an answer to Marco’s average rate, in hot dogs per hour.

	Rate	Time	Work
Marco	5/36	25/6	30
Leo	1/36	1	36

Hence, Option C

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09 Jul 2025, 12:57

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Question analysis: Rate is calculated as Hot Dogs (H) / Hours (T). We know that Tm = TL = T, HL = 36 and Hm = 30. If we can find T, we can find RL and Rm (Rates)

I- Rm + 6 = RL -> 30/T + 6 = 36/T -> One equation, one variable. T can be found -> SUF

II- The first 20 minutes can tell us nothing about the rest of the competition. Leo could have eaten the other 24 hot dogs in 1 hour or 3 -> Not Suf

--------------------
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.