Data Interpretation Discussion

**Common Information**

In a UN summit, one representative from each of the 15 countries are participating. The representatives at the summit speak seven different languages namely Hindi, English, Spanish, Portuguese, German, French and Arabic.

Three representatives speak two languages each; two representatives speak three languages each; five representatives speak five languages each; one representative speaks one language and four representatives speak four languages each.

The following bar graph provides information about the number of representatives that speak a particular language.

The graph provides information about only three languages but does not specify them.

Q. |
If at least 5 representatives speak each language, then at most how many representatives speak a particular language? |

✖ A. |
11 |

✖ B. |
12 |

✔ C. |
13 |

✖ D. |
14 |

✖ E. |
15 |

**Solution:**

Option(**C**) is correct

It is given that out of the 15 representatives, three representatives speak two languages each; two representatives speak three languages each; five representatives speak five languages each; one representative speaks one language and four representatives speak four languages each.

Let the number of representatives that speak Language 1, Language 2, Language 3, Language 4, Language 5, Language 6 and Language 7 be $A, B, C, D, E, F$ and $G$

$A + B + C + D + E + F + G$:

$= 3×2 +2×3+5×5+1×1+4×4$

$=6+ 6+25+1+16=54$

$A + B + C = 9 + 7 + 10$

$= 26$

Therefore,

$D + E + F + G$:

$= 54 – 26= 28$

Since we need to maximize the number of representatives that speak a particular language, we will assume that three languages (let it be language 4, language 5 and language 6) are spoken by 5 representatives each.

Therefore, at most $28 – (5 + 5 + 5) = 13$ representatives speak a particular language.

**Lakshman**

*()
*

It doesn't matter which languages you select. We only need to check the possibility and that would remain same for any language in the second group (D, E, F and G).

So pick any three languages from these 4 and you are good to go.

.....D+E+F+G+HD+E+F+G+H :

=54–26=28.

After this, why are you assuming 3 Languages (Language 4, 5 and 6)? please explain.