GATE Electrical 2019 | GA | Question: 10

Question

Consider five people- Mita, Ganga, Rekha, Lakshmi, and Sana. Ganga is taller than both Rekha and Lakshmi. Lakshmi is taller than Sana. Mita is taller than Ganga.

Which of the following conclusions are true?

1. Lakshmi is taller than Rekha
2. Rekha is shorter than Mita
3. Rekha is taller than Sana
4. Sana is shorter than Ganga

 

• A. $1$ and $3$
• B. $3$ only
• C. $2$ and $4$
• D. $1$ only

Comments

from the given information only these 4 possiblilities are there:

$1) \, \, M > G > R \geq L > S$

$2) \, \, M > G > L > R \geq S$

$3) \, \, M > G > L = R > S$

$4) \, \, M > G > L > S \geq R$

Answer 1

Answer C.

It is confirmed that Mita is the tallest girl and Ganga is the 2^nd tallest girl. No height relationship between Rekha and Lakshmi, so we won’t assume anything. Also, Lakshmi is taller than Sana.

1. False because no height relationship given between the two girls.
2. True because Rekha is shorter than Ganga, who in turn is shorter than Mita. Thus, Rekha is shorter than Mita (Transitive relation).
3. False. No height relationship given between the two girls
4. True because Ganga is taller than Lakshmi, who is again taller than Sana. Thus, Ganga is taller than Sana.

Answer 2

From the given statements (using first letter for respective names)

$R < G,  S < L < G <M$

So, Mita is the tallest followed by Ganga.

1. Lakshmi is taller than Rekha -- may or may not be true
2. Rekha is shorter than Mita -- TRUE
3. Rekha is taller than Sana -- may or may not be true
4. Sana is shorter than Ganga -- TRUE

Correct answer: C

Answer 3

Let m,g,r,l,s represent mita,ganga,rekha,lakshmi,sana respectively..

If x is taller than y , i will indicate that by x>y.

It is given that:

g>r,g>l,l>s,m>g.

From above equations,we can infer:

g>s,m>r,m>l,m>s

There fore, rekha is shorter than mita and sana is shorter than ganga.

The relationship between heights of lakshmi ,rekha and rekha,sana can be anything (i.e, can be equal to, less than or greater than)

Answer 4

There is no relationship between the height of Rekha and Lakshmi so Statement 1 is eliminated

and also there is no relationship between the height of Rekha and Sana so Statement 3 is eliminated

and

from the graph, it is clear that Mita>Gita>Lakshmi>sana

so statement 2 and 4 are correct

so option C.

Answer 5

Ganga is taller than both Rekha and Lakshmi -
R < G
L < G

Lakshmi is taller than Sana -
R < G
S < L < G

Mita is taller than Ganga -
R < G < M

S < L < G < M

Hence, option (C)

Answer 6

Ganga is taller than Rekha and Laxmi means it can be either:

• Ganga, Rekha,Laxmi

                       or

• Ganga,Laxmi,Rekha.

Mita is taller than Ganga means Mita is the tallest person among all. 

since laxmi is taller than Sana. so total 3 sequences are possible:

1. Mita,Ganga,Rekha,Laxmi,Sana
2. Mita,Ganga,Laxmi,Rekha,Sana
3. Mita,Ganga,Laxmi,Sana,Rekha

Based on above order only option B & D satisfied.