M40-71

Question

On a joint company picnic, 160 employees of Alpha Ltd, Beta Ltd, and Gamma Ltd were engaged in several football matches. The average (arithmetic mean) number of goals scored by the employees of Alpha Ltd was 10, and the average (arithmetic mean) number of goals scored by the employees of Beta Ltd was 12.2. Was the average (arithmetic mean) number of goals scored by all 160 employees more than 11?

(1) The 75 employees comprising Gamma Ltd scored an average of 12 goals.

(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.

Show Answer

Official Answer

A

(1) The 75 employees comprising Gamma Ltd scored an average of 12 goals.
 
(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.

Bunuel · Answer

Official Solution:

On a joint company picnic, 160 employees of Alpha Ltd, Beta Ltd, and Gamma Ltd were engaged in several football matches. The average (arithmetic mean) number of goals scored by the employees of Alpha Ltd was 10, and the average (arithmetic mean) number of goals scored by the employees of Beta Ltd was 12.2. Was the average (arithmetic mean) number of goals scored by all 160 employees more than 11? 
 
The question  "Was the average (arithmetic mean) number of goals scored by all 160 employees more than 11?"  can be rephrased as  "Was the total number of goals scored by all 160 employees more than 160*11 = 1,760?" 
 
(1) The 75 employees comprising Gamma Ltd scored an average of 12 goals.
 
The statement implies that the total number of goals scored by all the employees of Gamma Ltd was 900. The least number of goals the remaining 160 - 75 = 85 employees could have scored is if we minimize the number of employees of Beta Ltd (since they scored on average more than the employees of Alpha Ltd). The minimum number of employees Beta Ltd could have is 5 because the total number of goals scored by them must be an integer, so (number of employees)*12.2 must be an integer, which means the least value of the number of employees is 5. Thus, the least number of goals the remaining 85 employees could have scored is thus 80*10 + 5*12.2 = 861. This would make the total number of goals equal to 900 + 861 = 1,761, which is more than 1,760. Sufficient.
 
(2) The ratio of the number of employees of Alpha Ltd to Beta Ltd to Gamma Ltd was 16:1:15.
 
The statement implies that in Alpha Ltd, Beta Ltd, and Gamma Ltd there are 80, 5, and 75 employees, respectively. The total number of goals scored by Alpha Ltd and Beta Ltd would thus be 80*10 + 5*12.2 = 861. If the 75 employees of Gamma Ltd scored a total of 1 goal, then the answer to the question would be NO. However, if they scored a total of 1,000 goals, the answer would be YES. Not sufficient.

Answer: A

mosesjchong · Answer

This question confuses me a bit because it states "The 75 employees comprising the Gamma LTD" seems like it is saying the 75 employees are from Gamma LTD. Rather, if it read  "The Gamma LTD comprising of 75 employees", would mean all employees in Gamma LTD are these 75 employees. Is my logic incorrect here?

Bunuel · Answer

When the problem says "The 75 employees comprising Gamma Ltd scored an average of 12 goals," it implies that these 75 employees are indeed all from Gamma Ltd. This means that Gamma Ltd, in the context of the problem, is composed entirely of these 75 employees.

The alternate phrasing you suggested, "The Gamma Ltd comprising of 75 employees," essentially conveys the same meaning: it states that Gamma Ltd is made up of 75 employees in total. Both phrasings indicate that Gamma Ltd consists of exactly 75 employees, and there are no other employees in Gamma Ltd outside of this group.

So, your logic isn't incorrect; it's just a matter of phrasing preferences, but both versions imply that Gamma Ltd has 75 employees in total.

ShravaniPen1234 · Answer

To be honest, I just started studying, so I'm not completely clear on the question structure. In this case, are we interpreting the 2 statements as substatements to the question, and the answers A is Yes and B is No. Or are we saying that 1 is A and 2 is B, in which A and B are scenarios where we would look for the statement, 'the average (arithmetic mean) number of goals scored by all 160 employees more than 11' to be satisfied?

Bunuel · Answer

Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post  ALL YOU NEED FOR QUANT .

Hope this helps.

Gemmie · Answer

Average goals scored by Alpha Ltd employees = x = 10
Average goals scored by Beta Ltd employees = y = 12.2
Average goals scored by Gamma Ltd employees = z

Number of Alpha employees: a
Number of Beta employees: b
Number of Gamma employees: c
a + b + c = 160

Question:  \frac{10a + 12.2b + cz}{160 > 11} ?

=> 10a + 12.2b + cz > 1760?

Statement 1: c = 75; z = 12

c = 75 => a + b = 85

10a + 12.2b min when b = 5 (in order for 12.2b to be an integer), a = 80
=> Min 10a + 12.2b = 800 + 61 = 861
=> Min 10a + 12.2b + cz = 861 + 900 = 1761 > 1760

=> Sufficient

Statement 2: a:b:c = 16:1:15

Given a + b + c = 160
=> a = 80; b = 5; c = 75

Total goals by 3 companies' employees: 800 + 61 + 75z = 861 + 75z

Since we do not know anything about z => Cannot conclude whether 861 + 75z > 1760 or not

=> Insufficient

==> Answer is A

mellowmev · Answer

This is a high-quality question and I agree with the explanation

M40-71

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards