the majority of salespeople

[sanju09]

Are the majority of salespeople employed by XYZ Company commissioned?

[1] The number of salespeople employed by XYZ Company exceeds the number of employees at XYZ Company who are not salespeople.

[2] The percentage of XYZ Company's salespeople who are commissioned exceeds the percentage of employees at XYZ Company who are salespeople.



ORIGINAL SOURCE OF THIS QUESTION:
https://www.west.net/~stewart/gmat/

[top_business_2011]

The answer is C.

Let S: The total number of salespeople; and C: The total number of commissioned.

1] S> S', includes no data about C; thus insufficient.

2] C n S divided by S is greater than S divided by S+S'
It is insufficient since it we are not given any specific info. about the amounts of S and S'. That is, if S'>S, then S/S+S' would be less than 1/2. [e.g. let S' = 2S, hence, S/S+S' equals S/ S+ 2S which in turn equals S/3S, which is 1/3, the sales people who are commissioned are not majority] . However, if we know that S>S', then S/S+S' would be greater than 1/2.[e.g. let S' =S/2, then S/S+S' would be 2S/3S, which amounts to 2/3; and it indicates a clear majority]. Therefore, Statement 2 is, in itself, insufficient.

Combining Statement 1 with Statement 2 asserts that S>S', thus avoiding one of the conditions stated above. Hence, Sufficient.

Sorry if I have not been that clear.[/i][/url][/u]

[sanju09]

The answer is C.

Let S: The total number of salespeople; and C: The total number of commissioned.

1] S> S', includes no data about C; thus insufficient.

2] C n S divided by S is greater than S divided by S+S'
It is insufficient since it we are not given any specific info. about the amounts of S and S'. That is, if S'>S, then S/S+S' would be less than 1/2. [e.g. let S' = 2S, hence, S/S+S' equals S/ S+ 2S which in turn equals S/3S, which is 1/3, the sales people who are commissioned are not majority] . However, if we know that S>S', then S/S+S' would be greater than 1/2.[e.g. let S' =S/2, then S/S+S' would be 2S/3S, which amounts to 2/3; and it indicates a clear majority]. Therefore, Statement 2 is, in itself, insufficient.

Combining Statement 1 with Statement 2 asserts that S>S', thus avoiding one of the conditions stated above. Hence, Sufficient.

Sorry if I have not been that clear.[/i][/url][/u]

[spoiler]C is correct[/spoiler]

This problem involves the concept of proportion. During the GMAT, expect to encounter at least two proportion questions (either Problem Solving or Data Sufficiency) altogether. Notice that no arithmetical calculations are required here. That's because Data Sufficiency problems are designed to test you primarily on concepts, not on your ability to solve a problem by working to a quantitative solution. (That's what Problem Solving questions are for.)

In order to answer the question posed here, you need information about the number of commissioned salespeople relative to the number of non-commissioned salespeople. Statement (1) alone provides no such information. [You can eliminate the first and fourth answer choices (A and D).]

Statement (2) alone provides a meaningless comparison between percentages of two different "wholes"; the statement provides no information about the number of commissioned salespeople relative to the number of non-commissioned salespeople (the "whole" being the total number of salespeople). Thus, statement (2) alone is insufficient to answer the question. [You can eliminate the second answer choice (B).]

Considered together, however, statements (1) and (2) do suffice to answer the question. The correct response is the third answer choice (C). Statement (1) provides that more than 50% of the employees are salespeople. Statement (2) adds that this percentage is less than the percentage of salespeople who are commissioned. Thus, the percentage of salespeople who are commissioned must exceed 50%, and the answer to the question itself must be "yes." (In other words, you can answer the question considering the two statements together.)


ORIGINAL SOURCE OF THIS QUESTION:
https://www.west.net/~stewart/gmat/