NIMCET 2007 — Reasoning PYQ

Step 1: Analyze the Given Information

Let's break down the phrasing carefully:

• Number of boys = $13$ (Note: The text states "there are $13$ boys and $7$ girls with brown hair." This can be logically parsed as either $13$ boys in total, or $13$ boys with brown hair along with $7$ girls with brown hair. Let's establish the maximum scenario based on standard logical interpretation).

• If the statement means "($13$ boys with brown hair) + ($7$ girls with brown hair)", then:

  $$\text{Total persons with brown hair}=13+7=20$$

• Number of persons who do not have brown hair = $15$

Step 2: Calculate the Total Number of Persons

To find the maximum possible strength of the group, we combine the two mutually exclusive categories (those who have brown hair and those who do not have brown hair):

$$\text{Total persons}=(\text{Persons with brown hair})+(\text{Persons without brown hair})$$

$$\text{Total persons}=20+15=35$$

Step 3: Alternative Grammatical Interpretation (For Verification)

Let's look at the other possible reading: There are $13$ boys in total, and $7$ girls who have brown hair.

• To maximize the group size under this interpretation, the $13$ boys should have completely different hair (none of them have brown hair).

• This means the $13$ boys are included inside the $15$ people who do not have brown hair.

• Then, the remaining people without brown hair would be $15-13=2$ girls.

• Total people = ($7$ brown-haired girls) + ($15$ non-brown-haired persons) = $22$ persons.

Comparing both logical possibilities, the maximum value we can structurally reach from the given numbers is $35$ ($20$ with brown hair + $15$ without brown hair).

Step 4: Matching with Options

Since the maximum possible value computed is $35$, we check the given options:

• (a) $26$

• (b) $25$

• (c) $39$

Since $35$ is not listed in options (a), (b), or (c), it falls under option (d).

Final Answer

The correct option is (d) None.