Question

How many people know only Spanish ?

• A. 10
• B. 20
• C. 40
• D. 60
• A. 100
• B. 160
• C. 140
• D. 120
• A. k
• B. g
• C. b
• D. i
• A. l
• B. j
• C. h
• D. e
• A. b
• B. j
• C. m
• D. k

Answer 1

The Correct Option is B

Step 1 — Map the labels: In the four-circle Venn diagram, the single-language regions are labeled as follows: Russian-only = a, English-only = c, Spanish-only = e, French-only = g. The overlapping parts are labeled with other letters (b, d, f, h, m, n), but they aren’t needed for this question because “only Spanish” refers strictly to region e.

Step 2 — Use the given values/relations:
We are told: a = 40, c = 2a, e = (1/2)·a, g = 2e.
These relations connect the single-language counts to one another using a as the reference.

Step 3 — Compute e (Spanish-only):
Since a = 40, then
    e = (1/2)·a = (1/2)·40 = 20.

Step 4 — Interpret the result: The value e is exactly the count of staff who belong to the Spanish circle and to no other circle, i.e., who know only Spanish.

Answer: 20 people know only Spanish.

Answer 2

Step 1 — Interpret the question:
We are asked to find the number of people who know only one language, but that language must not be French. This means we need to count:
- Russian-only (a)
- English-only (c)
- Spanish-only (e)
We do not include French-only (g) because the question says “except French.”

Step 2 — Recall the given relations:
We are told:
a = 40
c = 2a
e = (1/2)·a
g = 2e

Step 3 — Calculate each required value:
- Russian-only (a) = 40
- English-only (c) = 2a = 2 × 40 = 80
- Spanish-only (e) = (1/2) × 40 = 20

Step 4 — Add them together:
Total = a + c + e = 40 + 80 + 20 = 140

Step 5 — Final interpretation:
Therefore, the number of people who can read and write only one language, excluding French, is 140.

Answer: The correct option is (C) : 140.

Answer 3

Step 1 — Understand the question:
We need to identify the region in the Venn diagram that represents people who know all the languages except Spanish. This means such people know:
- Russian
- English
- French
but not Spanish.

Step 2 — Analyze the diagram:
In a four-circle Venn diagram labeled with a, b, c, d, e, f, g, h, m, n, i, etc., the specific region where Russian, English, and French overlap but Spanish is excluded is marked by the label i.

Step 3 — Interpret the representation:
Thus, the set of people who can read and write all the languages except Spanish is represented by i in the diagram.

Answer: The correct option is (D) : i.

Answer 4

Step 1 — Carefully understand the problem statement:
The question asks: "People who cannot read and write Russian, English and French, are represented by :".
This means we are looking for individuals who are not part of the Russian circle, not part of the English circle, and not part of the French circle. In other words, they must lie completely outside these three language sets.

Step 2 — Think about what this implies in terms of the Venn diagram:
In the four-circle Venn diagram, each circle represents knowledge of one language:
- Russian
- English
- French
- Spanish
If a person is outside Russian, English, and French, the only possible language they could still belong to is the Spanish circle. Therefore, the region we are trying to identify is the portion of the Spanish circle that does not overlap with any of the other three circles.

Step 3 — Locate the correct labeled region:
From the labels given in the diagram, the part of the Spanish circle that is unique to Spanish — i.e., Spanish-only — is represented by the region e.
This is because:
- Region e = Spanish-only (no Russian, no English, no French).
- All other Spanish-related regions (like overlaps with Russian, English, or French) would involve knowledge of at least one of those three languages, which the question specifically forbids.

Step 4 — Conclude with the reasoning:
Hence, the group of people who cannot read and write Russian, English, and French must belong exclusively to the Spanish-only region. This is exactly represented by e in the diagram.

Final Answer:
The people who cannot read and write Russian, English, and French are represented by region e.
Therefore, the correct option is (D) : e.

Answer 5

Step 1 — Interpret the question carefully:
The problem is asking us to find the group of people who:
- Cannot read and write Spanish
- Cannot read and write French
- But can read and write English and Russian

This means we are searching for the region in the four-circle Venn diagram where the English and Russian circles overlap, while at the same time excluding the Spanish and French circles.

Step 2 — Translate into Venn diagram logic:
- "Conversant with English and Russian" → We must look at the overlapping region between English and Russian circles.
- "Cannot read and write Spanish" → So we must exclude any overlap with the Spanish circle.
- "Cannot read and write French" → We must also exclude any overlap with the French circle.

Therefore, the required group is the part of the intersection of English ∩ Russian that does not intersect with Spanish or French.

Step 3 — Identify the correct labeled region:
In the given Venn diagram labeling, the region representing people who know both English and Russian, but do not know Spanish or French, is denoted by the letter b.

Step 4 — Explain why other regions are excluded:
- If we had chosen the English ∩ Russian ∩ Spanish overlap, then Spanish knowledge would be included, which is not allowed.
- If we had chosen the English ∩ Russian ∩ French overlap, then French knowledge would be included, which is not allowed.
- If we had chosen the English ∩ Russian ∩ Spanish ∩ French overlap, then both Spanish and French would be included, which again contradicts the condition.
Thus, the only correct region is b.

Step 5 — Final conclusion:
The region that represents people who cannot read and write Spanish and French but are conversant with English and Russian is b.

Answer: The correct option is (A) : b.