The mental age of a 6 (six) years old girl is 7.5 (seven years six months) years her I. Q. will be :

Question

Accepted Answer

The correct option is 1:

To determine the Intelligence Quotient (I.Q.) of the girl, we must use the classic formula proposed by William Stern: $	ext{I.Q.} = (	ext{Mental Age (MA)} / 	ext{Chronological Age (CA)}) 	imes 100$. In this scenario, the girl's Mental Age is $7.5$ years, and her Chronological Age is $6$ years. Substituting these values into the formula gives us: $	ext{I.Q.} = (7.5 / 6) 	imes 100$. First, dividing $7.5$ by $6$ yields $1.25$. Then, multiplying $1.25$ by $100$ results in an I.Q. of $125$. An I.Q. score of $125$ is significantly above the average score of $100$, indicating that the girl is performing intellectually above her age peers, a fact that is directly supported by her mental age being greater than her chronological age.

The incorrect option is 2: 90
An I.Q. of $90$ would suggest a slightly below-average intelligence for her age. This is calculated if the Mental Age were $5.4$ years, which is substantially lower than the given $7.5$ years. Therefore, $90$ is incorrect as it does not align with the provided data.

The incorrect option is 3: 75
An I.Q. of $75$ is significantly below average and often borders on the range for intellectual disability. This score would only be correct if the girl's mental age were $4.5$ years. Since her mental age is given as $7.5$ years, this option is clearly incorrect.

The incorrect option is 4: 140
An I.Q. of $140$ is classified in the gifted range and would require a Mental Age of $8.4$ years for a $6$-year-old. While the girl's I.Q. is high, the calculated value is $125$, making $140$ an overestimation and therefore an incorrect answer based on the mathematical calculation.