📌 Section 1 is Logical reasoning specially designed for CAT

Researching accounts. Building lists. Writing sequences.

There's a better use of your team's time.

Apollo is the AI revenue engine that handles the busywork, so you can stay focused on selling.

Plus, everything you need is in one place:

Stop doing busywork and start building pipeline, faster.

With Apollo — the AI revenue engine powering 4M+ users.

Sign up for free

A head-hunting firm analysed the resumes of 50 candidates and found that each candidate mentioned in her resume that she was fluent in at least one language among English, French and Spanish. The firm interviewed the 50 candidates and found that while all the candidates definitely mentioned in their resume all the languages that they were actually fluent in, some of them lied in their resume by including languages that they were not fluent in. Also, every candidate was actually fluent in at least one language.

The following information is known about the languages that each person mentioned in her resume and the language that each person is actually fluent in:

i. The number of people who mentioned that they were fluent in both Spanish and French in their resume is 18, and the number of people who mentioned that they were fluent in only English and Spanish in their resume is 15.

ii. None of the candidates mentioned in their resume that they were fluent in only one language.

iii. While 4 candidates are actually fluent in all the three languages, the number of candidates who mentioned in their resume that they were fluent in all the three languages was double this number.

iv. The number of candidates who are actually fluent in at least two languages is 14, and the number of candidates who are actually fluent in Spanish is 21.

v. The number of people who are actually fluent in French but not Spanish is 19, and the number of people who are actually fluent in only French is 14.

The difference between growing stores and stagnant ones isn't more effort. It's better insights. StoreClaw analyzes your Shopify and Amazon data, surfaces your biggest growth opportunities, and helps you increase GMV while protecting profit. Start free with bonus tokens. No credit card required.

Try it FREE today

Question 1

Let the actual language categories be:

Only E, Only F, Only S, EF only, ES only, FS only, EFS

Given:

Actually fluent in all 3 = 4

Actually fluent in at least 2 languages = 14

So, actually fluent in exactly 2 languages = 14 - 4 = 10

Also:

Actually fluent in French but not Spanish = 19

Only French = 14

Therefore:

EF only = 19 - 14 = 5

Now exactly two-language people:

EF only + ES only + FS only = 10

5 + ES only + FS only = 10

So,

ES only + FS only = 5

Also, actually fluent in Spanish = 21

Only S + ES only + FS only + EFS = 21

Only S + 5 + 4 = 21

Only S = 12

So, answer for Q1

Only Spanish = 12

Nobody mentioned only one language.

So every resume mentions either:

EF only, ES only, FS only, or EFS.

Given:

Mentioned both Spanish and French = 18

Mentioned all three = 8

So, mentioned FS only = 18 - 8 = 10

Mentioned ES only = 15

Total candidates = 50

Therefore:

Mentioned EF only = 50 - 10 - 15 - 8 = 17

Resume table:

Anyone actually fluent in only one language must have lied, because nobody mentioned only one language.

Actual single-language candidates:

Only F = 14
Only S = 12
Only E = ?

Total candidates = 50

Known actual candidates:

Only F = 14
Only S = 12
EF only = 5
ES only + FS only = 5
EFS = 4

Total known = 14 + 12 + 5 + 5 + 4 = 40

So,

Only E = 50 - 40 = 10

Total only-one-language candidates:

10 + 14 + 12 = 36

All these 36 definitely lied.

The remaining 14 candidates are actually fluent in at least two languages, and they can be matched exactly with their resumes.

So minimum liars = 36

Answer: 36

Question 3

Given:

Actually fluent in only Spanish and French = 3

So,

ES only + FS only = 5

ES only + 3 = 5

ES only = 2

Candidates actually fluent in English and Spanish includes:

ES only + EFS

= 2 + 4

= 6

Answer: 6

Question 4

The 4 people actually fluent in all three languages must mention all three languages.

So, at least 4 people did not lie.

Now, there are 10 people actually fluent in exactly two languages.

To make them lie, they must mention all three languages.

But resume EFS count = 8.

Out of these 8 EFS resumes, 4 are already used by actual EFS people.

So only 4 more two-language people can lie by mentioning all three.

Remaining two-language people:

10 - 4 = 6

These 6 must mention exactly their two actual languages, so they did not lie.

Minimum truthful candidates:

4 + 6 = 10

Answer: 10

⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.

Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.

See you in tomorrow’s challenge!