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In a spelling competition, competitors were required to spell 108 diffe

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nislam
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In a spelling competition, competitors were required to spell 108 diffe [#permalink] New post   19 Oct 2021, 10:11
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In a spelling competition, competitors were required to spell 108 different words. How many of these words contained the letter T but did not contain the letter U?

1. Every word that contained the letter Q also contained the letter U, and every word that did not contain the letter Q did contain the letter T.

2. \(\frac{1}{3}\) of the words contained the letter U.
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abhishekmayank
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In a spelling competition, competitors were required to spell 108 diffe [#permalink] New post   20 Oct 2021, 01:56
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Should not answer be A ?

We can divide the the words consisting of Q and not consisting of Q.

We need to discard the words not consisting of Q, as absence of Q marks the absence of T and we are looking for words consisting of T.

Now in the remaining set of words consisting of Q, as per the option A, U will also be part of these words. So we don't have any word with T and without U.

Number of words with T and without U = 0
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RahulHGGmat
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Re: In a spelling competition, competitors were required to spell 108 diffe [#permalink] New post   20 Oct 2021, 21:00
Requesting someone to provide with the detailed solution to this one.
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Re: In a spelling competition, competitors were required to spell 108 diffe [#permalink] New post   21 Oct 2021, 02:02
Statement 1: We can conclude that Q lies within U because every word that contained the letter Q also contained the letter U. Also from the statement "every word that did not contain the letter Q did contain the letter T", it can be inferred that the entire set (containing U & Q) is a subset of T.

However, its doesn't give any information on the number. Hence NOT sufficient. Option A & D ruled out.

Statement 2: Provides information about U, doesn't provide information on overlap or anything else to conclude. Hence NOT sufficient

Combining 1 & 2 - U + Q = 1/3

Therefore, T = 2/3

Thus C.

Can anyone confirm if the approach is correct ?
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In a spelling competition, competitors were required to spell 108 diffe [#permalink] New post   24 Oct 2021, 05:21
abhishekmayank wrote:
Should not answer be A ?

We can divide the the words consisting of Q and not consisting of Q.

We need to discard the words not consisting of Q, as absence of Q marks the absence of T and we are looking for words consisting of T.

Now in the remaining set of words consisting of Q, as per the option A, U will also be part of these words. So we don't have any word with T and without U.

Number of words with T and without U = 0


abhishekmayank,

It can't be option A because we can't get a specific number as the solution. Kindly note that we are not given the number of words that contain U or T so, we can't determine the number of words with T and without U to be 0.

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Re: In a spelling competition, competitors were required to spell 108 diffe [#permalink] New post   01 Nov 2021, 11:40
Could anyone provide better explanation from the math.
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gmatclubot
Re: In a spelling competition, competitors were required to spell 108 diffe [#permalink]
01 Nov 2021, 11:40
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