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Bunuel
­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.­


­
­
(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.

If we only knew the number of words with the letter Q we could answer the question. But we don't.

INSUFF.

(2) \(\frac{1}{3}\) of the words contained the letter U.­

Thus \(\frac{2}{3}\) of \(108 \) or \(72\) words did not contain U. But we know nothing of T.

INSUFF.­

1+2

Total words = words with Q \(+\) words without Q 

Words with Q = Words with U \(= 36\)...from statement (2)

Words without Q and U \(= 108-36 = 72 \) -> Contained T

SUFF.

Ans C

Hope it helped.
 ­
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Sukrit_08
imo E

1) Says if a letter has Q it has U, and if a letter does not have Q does, it has T

Insufficient as does not give any information about number of letters that have Q,U or T

2) 1/3 of the words have U but does not give any information about T

Insufficient alone

1) + 2)

We know that since 1/3 of the words have U that means there are exactly 1/3 of the words that have Q => 2/3 of the words don't contain Q => at least 2/3 words have T because it may be possible that the letters that do have Q also have T because the condition is that if it does not have Q it has T but not if it has Q it does not have T.

There fore, both together insufficient.
­Cant it be that it doesnt contain Q but contains U aka both U and T?
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Bunuel
­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.­


­
­
(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.

If we only knew the number of words with the letter Q we could answer the question. But we don't.

INSUFF.

(2) \(\frac{1}{3}\) of the words contained the letter U.­

Thus \(\frac{2}{3}\) of \(108 \) or \(72\) words did not contain U. But we know nothing of T.

INSUFF.­

1+2

Total words = words with Q \(+\) words without Q 

Words with Q = Words with U \(= 36\)...from statement (2)

Words without Q and U \(= 108-36 = 72 \) -> Contained T

SUFF.

Ans C

Hope it helped.
 ­


But statement 1 talks only about the words that conatin letter Q. It does not talk about every word with letter U. A word that contains letter Q must have a letter U but that doesn't mean that every word containing letter U will have letter Q.

I mean there can be words that contain letter U but not letter Q. Since the total words with letter U is not clear IMO E

Posted from my mobile device
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Madhvendrasinh
stne
Bunuel
­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.­


­
­
(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.

If we only knew the number of words with the letter Q we could answer the question. But we don't.

INSUFF.

(2) \(\frac{1}{3}\) of the words contained the letter U.­

Thus \(\frac{2}{3}\) of \(108 \) or \(72\) words did not contain U. But we know nothing of T.

INSUFF.­

1+2

Total words = words with Q \(+\) words without Q 

Words with Q = Words with U \(= 36\)...from statement (2)

Words without Q and U \(= 108-36 = 72 \) -> Contained T

SUFF.

Ans C

Hope it helped.
 ­


But statement 1 talks only about the words that conatin letter Q. It does not talk about every word with letter U. A word that contains letter Q must have a letter U but that doesn't mean that every word containing letter U will have letter Q.

I mean there can be words that contain letter U but not letter Q. Since the total words with letter U is not clear IMO E

Posted from my mobile device

Statement 1 talks of two things:

1) Words with Q
2) Words without Q

Total words: Words with Q + Words without Q

(a)Words with Q will contain the letter U
(b)Words without Q will contain the letter T.

You are taking of words that will NOT contain Q but will have to contain both T and U.

I think from point (a) and (b) above the question states the conditions for "U" and "T" to exist in a word.

Hence IMO "U " and "T" cannot exist together. Hope it helps.­
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