Directions: Read the following information carefully and answer the question given below.

Seven individuals — K, L, M, N, O, P, and Q — were born in seven different years: 1954, 1962, 1970, 1980, 1991, 1998, and 2007, on the same month and day. (Consider 2024 as the base year for age calculations). The combined age of P and Q is equal to the age of O. P's age is an even number divisible by 13. K is immediately older than P. L's age is a multiple of 9. M is older than N.

How many individuals were born between M and P?

The correct answer is Three.

Step 1: Calculate the age of each individual based on the base year 2024.

Using the age calculation formula (Age = 2024 - Year of birth), we determine the age corresponding to each birth year:

• Born in 1954: 2024 - 1954 = 70 years old

• Born in 1962: 2024 - 1962 = 62 years old

• Born in 1970: 2024 - 1970 = 54 years old

• Born in 1980: 2024 - 1980 = 44 years old

• Born in 1991: 2024 - 1991 = 33 years old

• Born in 1998: 2024 - 1998 = 26 years old

• Born in 2007: 2024 - 2007 = 17 years old

The complete set of ages is {70, 62, 54, 44, 33, 26, 17}.

Step 2: Determine P's age and birth year.
P's age is given as an even number divisible by 13.
Among the set of ages, 26 is an even number and is divisible by 13 (since 26 = 13 × 2).
Therefore, P's age is 26, which means P was born in 1998.

Step 3: Determine K's age and birth year.
It is given that K is immediately older than P.
Since P was born in 1998 (age 26), the person immediately older than P is the one born in 1991 (age 33).
Therefore, K's age is 33, which means K was born in 1991.

Step 4: Determine Q's and O's ages and birth years.
It is given that the combined age of P and Q is equal to the age of O:
$\text{Age of P}+\text{Age of Q}=\text{Age of O}$
Substituting P's age (26):
$26+\text{Age of Q}=\text{Age of O}$
From the remaining available ages {70, 62, 54, 44, 17}, the only pair that satisfies this relation is:
$26+44=70$
Thus, Q's age is 44 (born in 1980) and O's age is 70 (born in 1954).

Step 5: Determine L's age and birth year.
It is given that L's age is a multiple of 9.
From the remaining ages {62, 54, 17}, 54 is divisible by 9 (since 54 = 9 × 6).
Therefore, L's age is 54, which means L was born in 1970.

Step 6: Determine M's and N's ages and birth years.
The remaining ages to assign are 62 (born in 1962) and 17 (born in 2007).
Since M is older than N, M's age must be 62 (born in 1962) and N's age must be 17 (born in 2007).

Final Arrangement (Oldest to Youngest):
• 1954 (Age 70): O
• 1962 (Age 62): M
• 1970 (Age 54): L
• 1980 (Age 44): Q
• 1991 (Age 33): K
• 1998 (Age 26): P
• 2007 (Age 17): N

Conclusion:
M was born in 1962 and P was born in 1998. The individuals born between M and P are L (1970), Q (1980), and K (1991).
Therefore, there are three individuals born between M and P.