# GATE2010-62

5.5k views

Hari(H), Gita(G), Irfan(I) and Saira(S) are siblings (i.e., brothers and sisters). All were born on 1st 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)?

1. $HSIG$
2. $SGHI$
3. $IGSH$
4. $IHSG$

edited
1

if option B is correct i.e SGHI

S                            G                              H                         I

1st jan 2010            1st jan 2011               1st jan 2012          1st jan 2013

Their Age as of 1st jan 2019

9 yrs                        8 yrs                          7 yrs                     6 yrs

Hari's age + Gita's age > Irfan's age + Saira's age

7             + 8              = 6              + 9

15 = 15

Here  their sum are equal and not greater as mentioned in question.

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.

selected
0

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

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.
1
can someone explain bit more??
4

@ thor,

Take options one by one.

A) HSIG --> As per condition 2 and 3, geeta and saira should come consecutive. (False)

B) SGHI --> Take age of Saira as x then G becomes x-1 (since their age diff is 1)

H becomes x-4 (since max age diff could be 3)

I  becomes x-7 (since max age diff could be 3)

Now to follow condition no one age(H) + age(G) > age(I) + age(S) => x-4+x-1 > x-7+x => 2x-5 > 2x-7 (True)

C) IGSH --> Take age of Irfan as x then   G becomes x-3 (since max age diff could be 3)

S becomes x-4 (since their age diff is 1)

H  becomes x-7 (since max age diff could be 3)

Now to follow condition no one age(H) + age(G) > age(I) + age(S) => x-7+x-3 > x+x-4 => 2x-10 > 2x-4 (False)

D) IHSG --> Take age of Irfan as x then   H becomes x-3 (since max age diff could be 3)

S becomes x-6 (since max age diff could be 3)

G  becomes x-7 (since their age diff is 1)

Now to follow condition no one age(H) + age(G) > age(I) + age(S) => x-3+x-7 > x+x-6 => 2x-10 > 2x-6 (False)

So option B is correct.

2
I have a question, how can you take S and G equal ? their diff. is 1 @ujjwal saini
0
This comment should've been best answer..

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