12 Days of Christmas GMAT Competition - Day 1: After closing the

Question

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After closing the restaurant, a chef calculates the total weight of the steaks served that day by rounding each steak's weight to the nearest 100 grams. Was the number of steaks served that day fewer than 25? (1 kilogram = 1,000 grams)

(1) The difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms.

(2) The greatest difference between the rounded and actual weights of any steak was 25 grams.

Bunuel · Accepted Answer

GMAT Club's Official Explanation:

After closing the restaurant, a chef calculates the total weight of the steaks served that day by rounding each steak's weight to the nearest 100 grams. Was the number of steaks served that day fewer than 25? (1 kilogram = 1,000 grams)

Rounding each steak's weight to the nearest 100 grams means that if a steak weighed 480 grams, it would be rounded to 500 grams, and if it weighed 440 grams, it would be rounded to 400 grams. Note that the maximum difference between the rounded and actual weight of any steak is 50 grams. This occurs when the actual weight is exactly midway between two rounding points (e.g., 450 grams rounded to 500 grams, creating a difference of 50 grams).

(1) The difference between the total rounded weights and the total actual weights of the steaks was mote than 1.5 kilograms.

Since the maximum difference between the rounded and actual weights of any single steak is 50 grams, a total difference of 1.5 kilograms would require at least 1,500/50 = 30 steaks. This means that a difference of more than 1.5 kilograms would require more than 30 steaks, which is greater than 25. Sufficient.

(2) The greatest difference between the rounded and actual weights of any steak was 25 grams.

This statement is clearly insufficient to determine whether fewer than 25 steaks were served. Not sufficient.

Answer: A.

siddhantvarma · Answer

We want to know if the number of steaks served < 25

Statement (1): The difference between total rounded weights and total actual weights was more than 1.5 kilograms (1,500 grams)

When rounding to the nearest 100 grams, each steak can contribute a maximum rounding error of up to 50 grams (if a steak weighs, for example, 150 grams, it rounds to 200 grams, contributing a +50 gram error; similarly, if it weighs 250 grams, it rounds down to 200 grams, contributing a -50 gram error)

Hence we can say that if the total rounding difference is more than 1.5 kg, and each steak can be off by at most 50 grams

1,500 grams ÷ 50 grams = 30
This implies the number of steaks must be more than 25 (30>25) => Statement (1) is sufficient

Statement (2): The greatest difference between the rounded and actual weights of any steak was 25 grams
 
Knowing the maximum rounding difference for a single steak doesn't tell us the total number of steaks

Statement (1) ALONE is sufficient to answer the question. Therefore, the answer is A.

Kinshook · Answer

After closing the restaurant, a chef calculates the total weight of the steaks served that day by rounding each steak's weight to the nearest 100 grams. Was the number of steaks served that day fewer than 25? (1 kilogram = 1,000 grams)

(1) The difference between the total rounded weights and the total actual weights of the steaks was mote than 1.5 kilograms.
The maximum difference between actual weight and rounded weight = 50
The minimum number of steaks served that day = 1.5*1000/50 = 1500/50 = 30 > 25
SUFFICIENT

(2) The greatest difference between the rounded and actual weights of any steak was 25 grams.
The information is not sufficient to find number of steaks served that day.
NOT SUFFICIENT

IMO A

Krunaal · Answer

Statement 1.

Each steak’s weight is rounded to the nearest 100 grams, so the maximum rounding error for a single steak is ±50 grams.

For N steaks, the total rounding error (sum of the individual errors) satisfies:
 −50N ≤ Total Error ≤ 50N

If the absolute value of the total error exceeds 1.5 kilograms:

|Total Error|>1,500 => 50N>1,500 =>  N>30

Sufficient

Statement 2.

Here The total rounding error for N steaks is bounded by:
 −25N ≤ Total Error ≤ 25N

If N=20, the total error could be 20*25 = 500 grams

If N=40, the total error could be 40×25=1,000 grams

Both cases are possible under this condition.  Not Sufficient

Answer A.

Nutella024 · Answer

Statement (1): 
"The difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms."
 
 Each steak's weight is rounded to the nearest 100 grams. The maximum possible rounding error for a single steak is  50 grams  (0.05 kg). 
 If there are nnn steaks, the total rounding error will not exceed 50n50n50n grams (or 0.05n0.05n0.05n kilograms).  
Thus, for the total rounding error to exceed 1.51.51.5 kilograms:
0.05n>1.5 ⟹ n>30.0.05n > 1.5 \implies n > 30.0.05n>1.5⟹n>30.
This means there must be  more than 30 steaks  for the total rounding error to exceed 1.5 kilograms.
Therefore, the number of steaks served  cannot be fewer than 25 .
 Statement (1) alone is sufficient. 
 
 Statement (2): 
"The greatest difference between the rounded and actual weights of any steak was 25 grams."
 
 If the largest rounding error for a single steak is 252525 grams (0.025 kg), the total rounding error for nnn steaks will be at most:  
n×0.025 kilograms.n 	imes 0.025 	ext{ kilograms.}n×0.025 kilograms.
 
 For nnn steaks, the total rounding error cannot exceed 0.025n0.025n0.025n.  
If n=25n = 25n=25:
0.025×25=0.625 kilograms.0.025 	imes 25 = 0.625 	ext{ kilograms.}0.025×25=0.625 kilograms.
Since n×0.025n 	imes 0.025n×0.025 will always be less than 1.51.51.5 kilograms regardless of the number of steaks,  Statement (2) alone cannot determine whether there were fewer than 25 steaks. 
 Statement (2) alone is insufficient. 
 
 Combining Statements (1) and (2): 
From Statement (1), n>30n > 30n>30.
From Statement (2), the total rounding error cannot exceed 0.025n0.025n0.025n.
However, these two statements contradict each other. If n>30n > 30n>30, the maximum rounding error for nnn steaks exceeds 0.025n0.025n0.025n.
Since no consistent conclusion can be drawn when combining the statements, they are not helpful together.
 
 Answer: (A) 
 Statement (1) alone is sufficient.

Nikhil17bhatt · Answer

IMO A

To determine whether the number of steaks served that day was fewer than 25, we need to analyze the given statements and see if they provide sufficient information to answer the question.

Statement (1):
The difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms.

Analysis:

When rounding to the nearest 100 grams, the maximum difference between the rounded weight and the actual weight of a single steak can be up to 50 grams (since 50 grams is the midpoint, and anything above or below it rounds to the nearest 100 grams).
If the total difference is more than 1.5 kilograms (1,500 grams), we can estimate the number of steaks by dividing the total difference by the maximum possible difference per steak.
1
,
500
 grams
50
 grams per steak
=
30
 steaks
50 grams per steak
1,500 grams
​
 =30 steaks

This calculation shows that if the total difference is more than 1.5 kilograms, the number of steaks must be more than 30. Therefore, the number of steaks served must be more than 25.
Conclusion for Statement (1):

Statement (1) alone is sufficient to determine that the number of steaks served was more than 25.
Statement (2):
The greatest difference between the rounded and actual weights of any steak was 25 grams.

Analysis:

If the greatest difference between the rounded and actual weights of any steak is 25 grams, this means that each steak's weight was very close to the rounding point, with a maximum deviation of 25 grams.
The total difference for all steaks would be the sum of these small differences. To find the maximum number of steaks that could result in a total difference of more than 1.5 kilograms, we can use the maximum difference per steak:
1
,
500
 grams
25
 grams per steak
=
60
 steaks
25 grams per steak
1,500 grams
​
 =60 steaks

This calculation shows that if the total difference is more than 1.5 kilograms, and the maximum difference per steak is 25 grams, the number of steaks could be up to 60. However, this does not provide a clear indication of whether the number of steaks is fewer than 25.
Conclusion for Statement (2):

Statement (2) alone is not sufficient to determine whether the number of steaks served was fewer than 25.
Combined Analysis:
From Statement (1), we know that the total difference between the rounded and actual weights is more than 1.5 kilograms, which implies more than 30 steaks.
From Statement (2), we know that the maximum difference per steak is 25 grams, which supports the calculation from Statement (1).
Conclusion:

Statement (1) alone is sufficient to determine that the number of steaks served was more than 25.
Statement (2) alone is not sufficient.
Therefore, the correct answer is that Statement (1) alone is sufficient to answer the question.

Navya442001 · Answer

Given: 
 
Each steak's weight is rounded to the nearest 100 grams.
1kg=1000g.

(1) The difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms. 
Analysis:
 
 When a steak's weight is rounded to the nearest 100 grams, the  maximum error  for each steak (the difference between actual and rounded weight) is  50 grams  (half of 100 grams). 
 If n is the number of steaks, the  total rounding error  for all steaks can be at most n×50 grams.  
Convert this into kilograms:
Total maximum rounding error=n×(50/1000) kg=0.05n kg.
We are told that the total error is  more than 1.5 kilograms :
0.05n>1.5
Solve for n:
n>1.50/0.05
n>30
Thus, n>30. This means  more than 30 steaks  were served.
 Statement (1) is sufficient. 
 
 (2) The greatest difference between the rounded and actual weights of any steak was 25 grams. 
Analysis:
 
 The maximum rounding error for any steak is given as  25 grams . 
 Since the total rounding error cannot exceed the  sum of the individual rounding errors , the total error for n steaks is at most n×25grams.  
Convert to kilograms:
Total maximum rounding error=n×(25/1000) kg=0.025n kg.
The  total rounding error  is limited to 0.025n kilograms. For n=25, the total error would be:
0.025×25=0.625 kg.
Thus:
 
 If n=25, the maximum total error is 0.625 kg. 
 If n>25, the total error increases proportionally.  
The question asks whether the number of steaks served was fewer than 25. However:
 
 From this statement, there is  no information about the total rounding error , so we cannot conclude whether n<25 or n>25  
 Statement (2) is insufficient.

missionmba2025 · Answer

The difference between the rounded weight and the actual weight is called the rounding error.

The maximum rounding error can be in the case can be 50. For example, a steak of weight 50.00000000000000001 grams is rounded to 100 grams.

The minimum rounding error can be zero, or a value very close to zero.

Statement 1 :

Round error = 1500 grams

Min Steaks sold = 1500 / 50 = 30

Sufficient to conclude that the value is greater than 25

Statement 2:

Rounded Weight - Actual Weight < = 25

This statement provided sufficient detail to conclude whether the number of steaks sold was greater than 25.

For example, if difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms, the number of steaks sold would be greater than 25. However, if difference between the total rounded weights and the total actual weights of the steaks was say 25 grams and the difference between the rounded and actual weights of any steak was 25 grams, the number of steaks sold = 1.

The statement alone is not sufficient.

Option A

Karanjotsingh · Answer

Understanding the Problem: 
 
 Each steak's weight is rounded to the nearest 100 grams. 
 The difference between the actual weight and the rounded weight of each steak can be at most ±50 grams. 
 The total difference between the rounded and actual weights is given or can be inferred from the statements.  
 Statement (1): 
 The difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms. 
 
  Interpretation: 
Total Difference >1500 grams. 
  Maximum Possible Difference Per Steak: 
±50 grams. 
  Total Difference Calculation: 
Total Difference ≤ 50 × N, where N is the number of steaks. 
  Given: 
50 × N >1500
N > 30 
  The conclusion from Statement (1): 
If N>30, then the number of steaks served is  not fewer than 25 . This statement alone is sufficient to answer the question.

Now we eliminate B C and E. Let's check the D

Statement (2): 
 The greatest difference between the rounded and actual weights of any steak was 25 grams. 
 
  Interpretation: 
The difference for each steak is at most 25 grams. 
  Total Difference Calculation: 
Total Difference ≤ 25 × N 
  Conclusion from Statement (2): 
Without knowing the actual total difference, we cannot determine the exact number of steaks. For example:
 
 If the total difference is 1000 grams, N ≥ 40. 
 If the total difference is 100 grams, N ≥ 4.  
Therefore, this statement alone is  not sufficient  to answer the question.

A) Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.

Lizaza · Answer

First, let's establish the range of possible difference between total actual and rounded weight. Ideally, all the steaks are multiples of 100 grams, so   the minimum diff. is 0  . However,   the maximum difference can only be roughly 50   grams per steak  (meaning that 149 would be rounded to 100, subtracting 49g, and 150 would be counted as 200, adding 50g).  
 Hence, the possible range is from zero to  50X , where  X  is the number of steaks sold.

The difference between the total rounded weights and the total actual weights of the steaks was more than 1.5 kilograms. 
 The maximum possible difference for 25 steaks would be  50X=50*25=1250  (grams), or 1,25kg. Therefore, if this difference is above 1.5kg, we must definitely have more than 25 steaks - and    this is sufficient to answer the question.

Without knowing the quantity of steaks, we have no way of using this fact to estimate the overall selling volume.    Insufficient by itself.

So,    the answer is A.

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