Each candle in a particular box is either round or square and either

Question

Each candle in a particular box is either round or square and either scented or unscented. If 60% of the candles are round, what is the probability that a candle selected randomly from the box will be unscented?

(1) If a candle is scented, it has an 80% chance of being round.
(2) If a candle is square, it has a 25% chance of being scented.

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GMATinsight · Answer

Round 
 Sqaure 
 Total 
 
  scented 
 60

unscented

x 
 
  Total

100

Question: x/100 = ?

Statement 1 : If a candle is scented, it has an 80% chance of being round. 
=medium
    
  Round  
  Sqaure  
  Total  
 
   scented  
  60=0.8y  
  
  y  
 
   unscented

x  
 
   Total

100

i.e. 0.8y = 60
y = 75
i.e. x = 100-75 = 25
 SUFFICIENT

Statement 2 : If a candle is square, it has a 25% chance of being scented. 
=medium
    
  Round  
  Sqaure  
  Total  
 
   scented  
  60  
  0.25z

unscented

x  
 
   Total  
  
  z  
  100

NOT SUFFICIENT

Answer: Option A

Purnank · Answer

I think it's C.
lets assume total 100x 60% round (60x) rest are square that is (40x). moving to 2nd condition 25% of squares are scented so 10x are square scented and 30x unscented. now if we move to 1st condition we can deduce that the remaining 20% of scented are squares. So, if 10x is 20% of value that means 80% is 40x (scented round). and unscented round will become 20x (60x-40x) so both scented and unscented are in total 50x each. Thats how i approached to the question please let me know if anything is wrong here.

Akkiiii · Answer

According to me, the answer is C https://gmatclub.com/forum/download/file.php?id=82121 Statement 1: If a candle is scented, it has an 80% chance of being round. https://gmatclub.com/forum/download/file.php?id=82122 i.e. 80% of (100-x) 80-0.8x= round and scented insufficient since it doesn't say anything about unscented candles Statement 2: If a candle is square, it has a 25% chance of being scented. https://gmatclub.com/forum/download/file.php?id=82123 NOT SUFFICIENT 1 and 2 together 90-80=x-0.8x 10=0.2x x=50 Hence the answer C GMAT-Club-Forum-q9s6hayc.png GMAT-Club-Forum-m09yfbha.png GMAT-Club-Forum-3gixlrkr.png

Nidzo · Answer

Using a double matrix to plot and solve info:
60% of the candles are round, therefore 40% of the candles are square.
 
 \begin{tabular}{llll}
& S & nS & T \
R & & & 60\
Sq & & & 40 \
T & & & 100
\end{tabular}

(1) If a candle is scented, it has an 80% chance of being round.

Let the number of scented candles =  x 0.8x  candles that are scented and round, and therefore  0.2x  which are scented and square.

\begin{tabular}{llll}
& S & nS & T \
R & 0.8x & & 60\
Sq & 0.2x & & 40 \
T & x & & 100
\end{tabular}

However, without further information it is impossible to solve for the percentage of unscented candles.

INSUFFICIENT

(2) If a candle is square, it has a 25% chance of being scented.

As  25 % of the square candles are scented, then  0.25*40 = 10 % of all candles are square and scented. This means that  40-10 = 30 % of all square candles are unscented.

\begin{tabular}{llll}
& S & nS & T \
R & & & 60\
Sq &10 &30 & 40 \
T & & & 100
\end{tabular}

However, without further information it is impossible to solve for the percentage of unscented candles.

INSUFFICIENT

(1+2)

Looking at the two tables one notices that in the first table one has a value of  0.2x  for square cented candles, and that the value in the second table is  10 . Therefore  x = 50 . This means that  50 % of the candles are scented, and therefore  50 % of the candles are unscented. 
 
  SUFFICIENT

ANSWER C

Each candle in a particular box is either round or square and either

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GMAT Data Sufficiency (DS) Questions

Each candle in a particular box is either round or square and either

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