Logical Reasoning Discussion

**Common Information**

In a survey conducted at a University, it was found that 51% of the students wanted to learn French as a foreign language, 48% wanted to learn German and 52% wanted to learn Russian.

Of the surveyed students, 21% wanted to learn both French and German, 23% wanted German and Russian and 24% wanted French and Russian. Only 12% wanted to learn all three languages. A total of 500 students were surveyed.

Q. |
How many students were not interested in any of the languages? |

✔ A. |
25 |

✖ B. |
30 |

✖ C. |
35 |

✖ D. |
40 |

**Solution:**

Option(**A**) is correct

The percentage of students not interested in any of the languages = 100% - (the percentage of students interested in any one language only) - (the percentage of students interested in any two languages only) - (the percentage of students interested in all three languages)

Percentage of students interested in *F* only,

$= 51 - 9 - 12 - 12$

$= 18\%$

Similarly we can find that the percentage of students interested in only Russian and German is 17% and 16% respectively.

∴ The percentage of students not interested in any of the languages

$= 100\%$ $- (18 + 17 + 16) \%$ $- (9 + 12 + 11)\%$ $- 12\%$

$= 5\%$

Therefore, the number of students not interested in any language,

$= 0.05 × 500$

$= \textbf{25}$