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. |
Which of the following cannot be TRUE? |

✖ A. |
German, French, Spanish and English are spoken by 9 representatives each. |

✖ B. |
English and Arabic are spoken by 15 and 11 representatives respectively. |

✖ C. |
One representative is speaks Portuguese. |

✔ D. |
Hindi, English and Portuguese are spoken by 8 representatives each and 5 representatives speak Spanish. |

✖ E. |
None of the above. |

**Solution:**

Option(**D**) 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,

$D + E + F + G$:

$= 54 – 26= 28$

**Option (A)** can be true. Let’s assume that Language 1 is German, therefore the aggregate number of representatives that speak French, Spanish and English is:

$9 + 9 + 9 = 27$

So, the remaining one language is spoken by:

$28 – 27 = 1$ representative.

**Option (B)** can be true.

Let the number of representatives that speak English and Arabic be $X$ and $Y$ respectively.

$X + Y = 15 + 11$

$= 26$

So there will be two languages spoken by one representative each.

**Option (C)** can be true.

There could be one representative speaking Portuguese. {Logic explained for options (A) and (B).

**Option (D)** cannot be true.

Since Hindi, English and Portuguese are spoken by 8 representatives each, therefore these languages cannot be either of language 1 or language 2 or language 3.

Let the number of representatives that speak Hindi, English and Portuguese be $M, N$ and P$ respectively.

$M + N + P = 8 + 8 + 8$

$= 24$

Hence, Spanish can only be spoken by:

$28 - 24 = 4$

representatives and not **5**