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

After reading first conditon, it is clear that Saira and Irfan are younger than Gita and Hari and that's why their age sum is less than that of other 2

 

now, after reading second condition, it is clear that, Gita and Saira has age difference of 1 year and we know that Saira would have born first before Gita, so it is like SG,

now , the only option which is matching is option B and other options are already eliminated.

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Option B

 

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In case you want to use Option elimination: 

 

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

if there is a option HISG,
then is this correct 

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here it means siblings born on same date

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first of all calm down

only one thing you all can see is the difference between G and S is 1 year so either G-S=1 or S-G =1  so we can write like either S born before G as(SG) or G born before S as (GS) find in options --------we can eliminate option (a)   okay half of the work is done. now put values of either G or S according to (i) statement you will find out 2 cases in which both will conclude that the H is greater than G so after seeing the options again we only see option (B) satisfying the conditions.

 

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

eliminating the options is best method to solve this question right

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@Shaik Masthan In condition it is clearly mentioned that age difference between S and G is 1 so how in this answer S and G value is same?

Thanks

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1. Why do you need someone verification for that ? That is contradicting with the given in the condition in the question straightly.

2. Understand the best answer then identify the mistake in this answer.

3. Refer all the discussion availble on this question before asking that. Most of the time, your doubt will be solved with the existing discussions.

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.

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I'll not leave the answer, I'll rather give you all a hint so that you can think and come to a solution, USAGE OF MOD IS THERE, |H-G|=1.

Answer 5

Suppose: Hari's age : H, Gita's age : G,
Saira's age : S, Irfan's age : I

H+G>I+S

UsingStatement(2)both G-S= 1 orS-G=
1; G can't be oldest and S can't be
youngest.
There are no twins thus using statement (2) either GS or SG possible.

(a) HSIG: not possible as there is I between S
and G which is not possible using
statement (3)
 

(b) SGHI: SG order is possible, S > G> H> I
andG+H>S+I (possible)
Because if { S = G + 1: and G = H+1 and H =
I +2 then G + (I+2) > (G+1) +I)
 

(c) IGSH: according to this I > G and S > H
thus adding these both inequalities we get
I + S > G + H which is opposite of statement
(2) thus not possible.
 

(d) IHSG: accordingto this I > H and S > Gthus
addingbothinequalitiesl + S>H + Gwhich
is opposite of statement (2) thus not possible.