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. |
For at most how many languages, the number of representatives who speak it is greater than the number of representatives who speak Language 1? |

✖ A. |
1 |

✖ B. |
2 |

✔ C. |
3 |

✖ D. |
4 |

✖ E. |
5 |

**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,

$D + E + F + G$:

$= 54 - 26= 28$

Number of representatives speaking Language 1 is 9.

Out of the 28 representatives, 10 representatives each can possibly speak at most two languages.

Hence, for at most **3** languages, the number of representative speaking it can be greater than the number of representatives speaking Language 1.