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Bunuel
A hotel purchased a number of hand towels and a number of bath towels. If the cost of each hand towel was $6.00 and the cost of each bath towel was $11.00, what was the total cost of the hand towels and bath towels purchased by the hotel?

(1) The total cost of the hand towels purchased by the hotel was $84.00.

(2) The total number of hand towels and bath towels purchased by the hotel was 32.


­
Deconstructing the Question
Let \(h\) be the number of hand towels ($6 each).
Let \(b\) be the number of bath towels ($11 each).

We need to find the total cost.
Target Question: What is the value of \(6h + 11b\)?

***

Analyze Statement (1)
"The total cost of the hand towels ... was $84.00."
This gives us the equation:
\(6h = 84\)
\(h = 14\)

We found \(h\), but we have zero information about \(b\) (the number of bath towels). The total cost \(6(14) + 11b\) cannot be determined because \(b\) is unknown.
INSUFFICIENT

***

Analyze Statement (2)
"The total number of hand towels and bath towels ... was 32."
This gives us the equation:
\(h + b = 32\)

We need to find \(6h + 11b\).
Since the price per item is different ($6 vs $11), knowing only the total count is not enough.
Example Case A: \(h=32, b=0 \implies Cost = 32 \times 6 = 192\)
Example Case B: \(h=0, b=32 \implies Cost = 32 \times 11 = 352\)
Different results are possible.
INSUFFICIENT

***

Combine Statements (1) and (2)
From Statement (1), we know \(h = 14\).
From Statement (2), we know \(h + b = 32\).

Substitute \(h = 14\) into the second equation:
\(14 + b = 32\)
\(b = 18\)

Now we have specific values for both variables (\(h=14, b=18\)). We can calculate the unique total cost:
\(Cost = 6(14) + 11(18)\)
(We do not need to perform the actual calculation; knowing that a unique value exists is enough).

SUFFICIENT

Answer: C
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Bunuel
A hotel purchased a number of hand towels and a number of bath towels. If the cost of each hand towel was $6.00 and the cost of each bath towel was $11.00, what was the total cost of the hand towels and bath towels purchased by the hotel?

(1) The total cost of the hand towels purchased by the hotel was $84.00.

(2) The total number of hand towels and bath towels purchased by the hotel was 32.


­
Let the number of Hand towels and Bath Towels purchased be a and b respectively.

The price of the Hand towels and Bath Towels purchased are : $6.00 and $11.00 respectively.

Total cost of purchase = (a*$6.00) + (b*$11.00)

Statement 1:

(1) The total cost of the hand towels purchased by the hotel was $84.00.

a * $6.00 = $84.00

a = 14

we don’t know the value of b. Hence, Insufficient.

Statement 2:

(2) The total number of hand towels and bath towels purchased by the hotel was 32.

a + b = 32

Both variables, a and b takes many different values.

Hence, Insufficient.

Combining both statements 1 and 2, we get

a+b = 32

Then, b = 32 - a = 32-14 =18

a= 14, b =18

Total cost = (a*$6.00) + (b*$11.00)

= (14*6)+(18*11)

= 282

Hence, Sufficient

Option C
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