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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

1. $2$
2. $3$
3. $4$
4. Cannot be determined

retagged | 3.3k views

• $3$ Right handed person.
• Every Person 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

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

 $Case-1$ 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. $Case-2$         $3$ Right handed Men.         $2$ Left handed Women.         $1$ Left-handed Man. $Case-3$             $3$ 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: $A$

by Loyal (6.8k points)
edited
+1

So at this moment we have ↗ 3 Right handed man

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

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.
by Active (4.5k points)
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

by Boss (18k points)

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)

by Active (1.1k points)
0