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# In a class of 34 students, X know how to sing, Y know how to dance. If

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
In a class of 34 students, X know how to sing, Y know how to dance. If  [#permalink]

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02 Jul 2018, 10:28
00:00

Difficulty:

85% (hard)

Question Stats:

29% (02:17) correct 71% (02:11) wrong based on 15 sessions

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In a class of 34 students, X students know how to sing, Y students know how to dance. If each of these 34 students knows at least one skill out of singing and dancing, then how many know how to both sing and dance?

(1) Out of 34 students, Y-3 students do not know how to sing.

(2) Out of 34 students, X-3 students do not know how to dance.
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
Re: In a class of 34 students, X know how to sing, Y know how to dance. If  [#permalink]

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04 Jul 2018, 22:11
amanvermagmat wrote:
In a class of 34 students, X students know how to sing, Y students know how to dance. If each of these 34 students knows at least one skill out of singing and dancing, then how many know how to both sing and dance?

(1) Out of 34 students, Y-3 students do not know how to sing.

(2) Out of 34 students, X-3 students do not know how to dance.

Out of 34 students, X can sing, Y can dance and there could be some common students who could dance as well as sing. We have to identify how many are those common students. Lets assume those to be K. So now,
X students can sing, out of which K can also dance. This means X-K are those who can only sing, but not dance.
Y students can dance, out of which K can also sing. This means Y-K are those who can only dance, not sing.
We have to find K.

(1) Y-3 cannot sing, so they are those who can only dance (everyone can do at least one of singing or dancing). This means Y-K = Y-3 or K=3. Sufficient.

(2) X-3 cannot dance, so they are those who can only sing (everyone can do at least one of singing or dancing). This means X-K = X-3 or K=3. Sufficient.

Re: In a class of 34 students, X know how to sing, Y know how to dance. If &nbs [#permalink] 04 Jul 2018, 22:11
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