GATE ECE 2010 | Question: 65

Question

Hari (H), Gita (G), Irfan (I), and Saira (S) are siblings (i.e. brothers and sisters). All were born on $1^{st}$ January. The age difference between any two successive siblings (that is born one after another) is less than $3$ years. Given the following facts:

1. Hari's age $+$ Gita's age $>$ Irfan's age $+$ Saira's age.
2. The age difference between Gita and Saira is $1$ year. However, Gita is not the oldest and Saira is not the youngest.
3. There are no twins.

In what order were they born (oldest first)?

• A. HSIG
• B. SGHI
• C. lGSH
• D. IHSG

Answer 1

Given that all were born on $1^{st}$ January, every sibling must at least have 1 year age difference. 

Also, as it given the age difference between Gita and Saira is 1 year and Gita is not oldest and Saira is not youngest, we can conclude that both Gita and Saira needs to be born one after another

Hence the possible order needs to have SG or GS together, which straight way eliminates option Option A.

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Now solving it mathematically, by fact 1;

$\implies H+G>I+S$

$\implies G-S>I-H$

Now there are two possibilities as $|G-S|=1$;

Case 1: When G is elder than S;

$\implies 1>I-H$

which implies in this possibility H will be elder than I, Hence gives order HGSI

Case 2: When S is elder than G;

$\implies -1>I-H$

$\implies H-I>1$

which implies in this possibility H will be elder than I but only by 1 year which make them sibling, that gives order SGHI

Hence, Option B is correct.

Answer 2

C