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 deviceStatement 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.