GATE CS 2010 Q62 — General Aptitude

Let the ages of Hari, Gita, Irfan, and Saira be $H, G, I,$ and $S$ respectively. Since all siblings were born on $1^{\text{st}}$ January and there are no twins, their ages are distinct integers.

From Fact (ii), the age difference between Gita and Saira is exactly $1$ year. This means Gita and Saira must be adjacent in the birth order. This immediately eliminates Option A (where Irfan is between Saira and Gita).

Now, let us test the remaining options using Fact (i): $H + G > I + S$, which can be rewritten as:

• Option B (SGHI): The birth order from oldest to youngest is $S > G > H > I$. Since $S$ and $G$ are adjacent, $S - G = 1 \implies G - S = -1$. Substituting this into our inequality gives $-1 > I - H$, which means $H - I > 1$. Since $H > I$, this is easily satisfied if the age difference between $H$ and $I$ is $2$ years (e.g., ages $S=14, G=13, H=12, I=10$). This is perfectly valid.
• Option C (IGSH): The birth order is $I > G > S > H$. Here, $G - S = 1$. The inequality becomes $1 > I - H \implies I - H < 1$. But since $I$ is older than $H$ with two siblings in between, $I - H$ must be at least $3$, which is a contradiction.
• Option D (IHSG): The birth order is $I > H > S > G$. Here, $S - G = 1 \implies G - S = -1$. The inequality becomes $-1 > I - H \implies I - H < -1$. But since $I > H$, $I - H$ must be positive, which is a contradiction.

Thus, the correct birth order from oldest to youngest is SGHI.