GATE CSE 2017 Set 1 | Question: GA-7

Question

Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is

• A. $2$
• B. $3$
• C. $4$
• D. Cannot be determined

Comments

2 CASES

3 right handed men+3 left handed women so there is always 1 right handed men right beside a women so it can't be the case

4  men(1 left,3 right handed)+2 women this will satisfy

5 men and 6 men cant be taken as 2 women must be there

Answer 1

• $3$ Right handed person.
• Every woman is left handed.
• Immediate right to woman is left handed person.
   
• As already given every woman is left handed. So, given $3$ Right handed Person actually man.
   

So at this moment we have $\large^{\nearrow ^{\huge\text{ 3 Right handed man}}}_{\searrow_{\huge\text{ 2 Left handed man}}}$

We need $1$ more person to make total $6$ person and
that person may be either

$\rightarrow \text{Woman with left handed.}\\ \text{(or)} \\ \rightarrow \text{Man with either left handed or right handed.}$
 

$\text{Case-1:}$ Let us suppose that a person is a woman. So,  $3$ Right handed Men        $3$ Left Handed Women	Now we have no more left-handed person to put here. So, this case is not possible.
$\text{Case-2:}$         $3$ Right handed Men.         $2$ Left handed Women.         $1$ Left-handed Man.
$\text{Case-3:}$             $3$ right-handed person (men)         $2$ left-handed women         $1$ right-handed man  This case is also not possible, as W__ W__ - for this place we don't have any left-handed person. So this arrangement is not valid.

Correct Answer: $A$

Comments

So at this moment we have ↗ 3 Right handed man

                                                   ↘ 2 Left handed man //  ** woman should be there

Answer 2

Given -

There are atleast Two Men and Two Women.

There are atleast 3 Right Handed People and No women are Right Handed means there are 3 Right Handed Men.

So this rules out option C) as there can be atmost 3 women.

Now, every woman has a left handed person to her right and there are atleast 2 women. Now if we have 3 women ,there will be atleast 1 woman who will have a right handed person sitting next to her ( as there are 3 right handed men given above)

So we can have 2 woman , 1 left handed man and 3 right handed men on the table.

Answer 3

here we have to check with options

if we take 2 and try to assign all the conditions given it is successfull

but for 3 and 4 we can not impose all conditions given

so 2 is the answer

A is correct answer here

Answer 4

Answer is 2.

Explanation:

Given there are total six people. 

m - man,  w - women

Arrangement: m m m w w m  (it satisfy all condition, first three-men are right handed and the last one are left-handed  and both women are left handed as mention in question)

Comments

thanks@