In a spelling competition, competitors were required to spell 108

Question

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.

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Problem Solving Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

Rucha.Shukla · Answer

IMO E

Because we don't know if every word that did not contain the letter Q but did contain the letter T, did not contain the letter U

Meaning, Option 1 only says words with Q have U but doesn't clarify that words without Q are also without U

Sukrit_08 · Answer

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.

stne · Answer

(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.

ribbons · Answer

Cant it be that it doesnt contain Q but contains U aka both U and T?

Madhvendrasinh · Answer

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

stne · Answer

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.

Vivek1707 · Answer

This question is involves more verbal skills (specifically conditional reasoning) than math skills

Some back ground

When we write  If x then y , think of  x  as a  smaller circle  which is inside the  larger circle which is y .

" Every  " ---> x part

For instance, if I say  every  guitarist is a musician ---> it would mean that  if  someone is a  guitarist  ---->  then  that person is a  musician

So here Statement 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 Q ----> U implying that Q is the smaller circle inside U (the larger circle). This also implies that  region outside Q must have T

So, this just tells us that the region  outside Q contains T  but we have  no way of finding out how many words  are there which contain T but not U  Not sufficient.

Statement 2 ---> This just tells us that 36 words contain U again 72 words don't contain U. But we don't know out of those 72 how many contain T  Not sufficient

When you combine ---> since we know that Q is inside U and the region outside Q contains T, we know that since 72 is the region outside U ---> it MUST contain T ---> hence 72 is the number words that contain T but not U  sufficient . i.e. Answer is C

In a spelling competition, competitors were required to spell 108

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

In a spelling competition, competitors were required to spell 108

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards