In a group, everybody speaks English or French. What percentage of

Question

In a group, everybody speaks English or French. What percentage of members speak only English?
 
(1) 80% members speak English.
(2) 60% members speak French.

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Dereno · Answer

In a group everybody speaks English or French. So the total population can be taken as 100%.

We need to find the number of people speaking English Only.

if a denote the group speaking English Only, b denotes the group speaking French only, and c denotes both English and French, d denotes neither.

d =0. As everyone speaks at least one of the two languages.

Statement 1:

80% members speak English.

a+c = 80, which means b =20

But, a and c can take any combination of numbers totalling 80.

Hence,  Insufficient.

Statement 2:

60% members speak French.

b+c = 60, which means a =40.

Hence,  Sufficient.

Option B

ExpertsGlobal5 · Answer

Explanation:

https://www.youtube.com/watch?v=D-NaAf4L6Xc

roshaun25 · Answer

In my opinion, this question is improperly worded for the supposedly "correct" answer. Based on the information given, everybody speaks English OR French, there is neither a mention of people who speak neither language nor a mention of people who speak both languages. Since you cannot make assumptions, the answer should be D, as either statement gives you an answer.

Can someone explain why it is appropriate to make the assumption that there is a set of people in the group that speaks both English and French?

Can someone explain why it is appropriate to make the assumption that there is a set of people in the group that speaks both English and French?

Bunuel · Answer

You are wrong. In a group, “everybody speaks English or French” means there is no one who speaks neither language. Also, the “or” here is inclusive, meaning everybody speaks English or French or both, so some people in the group could speak both.

Moving to the statements:

(1) is not sufficient because we do not know what percent speaks both, so we cannot determine the percent who speak only English. However, (2) is sufficient, because if 60% speak French, then the remaining 40% do not speak French and therefore must speak English only.

Advait01 · Answer

In a group everybody speaks English or French. So the total population can be taken as 100%.

We need to find the number of people speaking English Only.

if a denote the group speaking English Only, b denotes the group speaking French only, and c denotes both English and French, d denotes neither.

d =0. As everyone speaks at least one of the two languages.

Statement 1:

80% members speak English.

a+c = 80, which means b =20

But, a and c can take any combination of numbers totalling 80.

Hence, Insufficient.

Statement 2:

60% members speak French.

b+c = 60, which means a =40.

Hence, Sufficient.

Option B

In a group, everybody speaks English or French. What percentage of

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GMAT Data Sufficiency (DS) Questions

In a group, everybody speaks English or French. What percentage of

Prep Toolkit

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

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