GATE CSE 2010 | Question: 62

Question

Hari(H), Gita(G), Irfan(I) and Saira(S) are siblings (i.e., brothers and sisters). All were born on $1^{\text{st}}$ January. The age difference between any two successive siblings (that is born one after another) is less than three 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 one year. However Gita is not the oldest and Saira is not the youngest.
3. There are no twins.

In what order they were born (oldest first)?

• A. $\text{HSIG}$
• B. $\text{SGHI}$
• C. $\text{IGSH}$
• D. $\text{IHSG}$

Comments

if we take 

H=3

S=2

I=1.5    /

G=1

THEN IT SATISFY THE OPTION A PLEASE SOMEONE EXPLAIN WHAT IS HERE WRONG IN MY EXAMPLE

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You have to take integer age by default – not float.

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@Arjun Ji Sir !

Answer 1

Given that, 

• $H+G > S+I$
• No twins, 
• And either $G=S+1$ or $S = G+1$
• $G$ is not the oldest and $S$ is not the youngest. 

Lets analyze each case, 

Case 1:

$G=S+1$, 

It implies, $H > I - 1$, Since twins are not possible $H>I$

Case 2:

$G = S - 1$, 

It implies $H > I + 1$

Therefore, both cases imply $H$ is older than $I,$ also $G$ and $S$ must be placed successively. 

Only option B satisfies these implications. 

Comments

I can't understand case (i). What does the twins exactly mean? 

 

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Twin means having same age (here).

No twins means no जुड़वाँ ( no body has same age).

Case i: G = S+1

=>H + G > S+ i

=>H + S + 1> S +i   (putting G value)

=>H + 1 >i (cancelling S of both side)

=> H> i-1

 

Case ii) G = S-1

H + G> S + i

H + S -1> S + i

H -1 > i

H > i +1

Answer 2

Correct answer is B. Though, its a hit-n-trial method.

option A: There is no such possibility, as it is given that there are no twins, so S and G must be consecutive.

option B.For some combination of ages of SGHI we can satisfy (1) condition like taking ages as, S=5 G=5 H=3 I=1, (2) and (3) are also satisfied. So, all the 3 conditions are satisfied.

option C: IGSH, so I > G and S > H (as there are no twins) and so I + S > G + H - violates condition 1.

option D: IHSG, so I > H and S > G and so I + S > H + G - violates condition 1.

Comments

This comment should've been best answer..

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@amolagrawal The max. difference can be 2 since in question, 

”The age difference between any two successive siblings (that is born one after another) is less than three years.”

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eliminating the options is best method to solve this question right

Answer 3

see ,if this approach helps

Answer 4

According to me, option “c” should be the answer. 

Reason-    Hari's age + Gita's age > Irfan's age + Saira's age   (given)  ---------1

  saira’s age – gita’s age=1   (given) ---------2

from (1)     hari – irfaan > saira – gita 

                  hari – irfaan >1     (from 2)

hence only option C satisfies this

 

@Lakshman Patel RJIT correct me if anything is wrong

Comments

but, you have taken only one case of the age difference between Gita and Saira i.e., S-G=1 and you got the result as H-I>1. You didn’t take G-S=1, then the answer would have been 1>I-H. So, in both the ways we can see that H is older than I, and (B) satisfies it.