In Lieberville, 6,000 people subscribe to the Herald or the Clarion.

Question

In Lieberville, 6,000 people subscribe to the Herald or the Clarion. How many people subscribe to both newspapers?

(1) Of the people in Lieberville, 2,100 subscribe to the Herald only.

(2) Of the people in Lieberville, 2,750 subscribe to the Clarion only.

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ankushsambare · Answer

Let
H = total Herald subscribers
C = total Clarion subscribers
Both = number who subscribe to both.

We know:
H + C – Both = 6,000.

(1) Herald only = 2,100.
But we still don’t know Clarion only or total Clarion.
Not enough.

(2) Clarion only = 2,750.
But we still don’t know Herald only or total Herald.
Not enough.

Using (1) and (2) together:
Total people = Herald only + Clarion only + Both.

6000 = 2100 + 2750 + Both
6000 = 4850 + Both
Both = 1150.

Answer: C  
 Both statements together are sufficient, but neither alone is sufficient.

Dereno · Answer

In Libreville, 6000 people subscribe to either Herald or Clarion.

How many people subscribe to Both newspapers ?

This can be solved using a two set Venn diagram, Herald Only + Clarion Only + Both ( Herald & Clarion) + None = 6000.

None = 0

Thus, Herald Only + Clarion Only + Both ( Herald & Clarion) = 6000.

Statement 1:

(1) Of the people in Lieberville, 2,100 subscribe to the Herald only.

Without knowing Clarion Only OR Both, we cannot find the solution.

Hence,  Insufficient.

Statement 2:

(2) Of the people in Lieberville, 2,750 subscribe to the Clarion only.

Without knowing Herald only and both Herald & Clarion. We cannot find the solution.

Hence,  Insufficient.

Combining both Statements 1 and 2, we get

2100 + 2750+ Both Herald and Clarion = 6000

Thus, Both (H&C) = 6000 - (2100+2750)

= 1150.

Hence,  Sufficient

Option C

megancdrake · Answer

How did you know to make neither 0? I've had questions where I assumed neither was 0 and was wrong so curious if there's a helpful tip for that. Because the question says "6,000 subscribe to Herald OR Clarion" that led me to think that "both" and "neither" are not included in the 6,000. Thank you!

Bunuel · Answer

Because the problem explicitly says the 6,000 people subscribe to the Herald or the Clarion, that group already excludes “neither.” So “neither = 0” is not an assumption, it’s built into the wording.

As for “both,” in “Herald or the Clarion” the word “or” is inclusive, so the 6,000 contains everyone who takes Herald only, Clarion only, and both.

Dereno · Answer

The set theory or Venn diagram has two important terms - AND , OR used in the question. AND - denotes the intersection part. For example , I would like to have dish A AND dish B. Focusing on the Overlapping part alone. https://gmatclub.com/forum/download/file.php?id=87105 While, OR - denotes the union regions. A only, B Only, and Both A and B. https://gmatclub.com/forum/download/file.php?id=87106 The question mentions, In Libreville , 6000 subscribe to either Herald OR Clarion. I am running my thought process, I believe you might get some insights from this. The first thing, it’s a two set Venn diagram. (Herald and clarion). It contains Herald only, Clarion Only, Intersection between Herald and Clarion, and the neither part. Secondly, Be sure, that we are not given the total population in this problem. Then, the question mentions 6000 subscribers belong to either Herald OR Clarion. Amongst, the population given, this 6000 fall into one of these two categories or might be in their intersection part. This is the first instance where u can say, NEITHER is excluded from the 6000. This boils down to a critical point- neither vs total population values ? We can definitely say, the 6000 is within the total population. However, Until unless, we have concrete information about neither or the total population. We cannot, for time being conclusively say neither is zero. Now, If it has been a quant question, with this data in hand, proceeding further might be impossible. As we have two unknowns - neither and total population. Being a data sufficiency question, we need to act within the constraints provided by the question stem. As the question directs us to find the intersection part. We have for the convenience of solving this question, assumed neither to be zero . So, that it brings the total population as 6000, providing a full picture to navigate the statements. If in case, they have mentioned the total population is 8000, then now u can concretely say, the extra 2000 falls into the neither category. As, Herald OR clarion denotes the UNION of the sets. Moreover, The sum of all elements in a set, should add to Total population . If in case, the question demands us to work with neither, then specific inputs will definitely be in place to address it. Hope this addresses your concerns. GMAT-Club-Forum-5mnjc5zn.png GMAT-Club-Forum-9aws2siq.jpeg

In Lieberville, 6,000 people subscribe to the Herald or the Clarion.

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In Lieberville, 6,000 people subscribe to the Herald or the Clarion.

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