A Clothing Manufacturer Makes Jackets That Are Wool or Cotton or a Combination of Wool and Cotton GMAT Data Sufficiency

Question: A clothing manufacturer makes jackets that are wool or cotton or a combination of wool and cotton. The manufacturer has 3,000 pounds of wool and 2,000 pounds of cotton on hand. Is this enough wool and cotton to make at least 1,000 jackets?

1) Each wool jacket requires 4 pounds of wool, and no cotton
2) Each cotton jacket requires 6 pounds of cotton, and no wool

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

‘A clothing manufacturer makes jackets that are wool or cotton or a combination of wool and cotton’  – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

There is only one approach to solve this problem statement.
Given

• A clothing manufacturer makes jackets that are wool or cotton or a combination of wool and cotton
• The manufacturer has 3,000 pounds of wool
• 2,000 pounds of cotton on hand.

Find Out:

• We need to determine whether there is enough cotton and wool to produce 1,000 jackets.

Approach:

• Now, to solve this problem, we will have to check all the options separately. We will check the 1st statement and then the 2nd statement. After that we will also check the combination of 2 sentences.

Let us take statement One Alone:
As per the statement, each wool jacket requires 4 pounds of wool, and no cotton.
Since there are 3000 pounds of wool, jackets produced will be:
3000/4 = 750
This means the manufacturer can make 750 wool-only jackets.
From this, we do not know how much cotton is needed to produce a cotton jacket. Since, we do not have enough information to answer the question, we can eliminate answer choices A and D.
Let us take statement Two Alone:
Each cotton jacket requires 6 pounds of cotton, and no wool.
Since there are 2000 pounds of cotton, jackets produced will be:
2000/6 = 333⅓
The manufacturer can make 333 cotton-only jackets.
However, since we do not know how much wool is needed to produce a wool jacket, we do not have enough information to answer the question. We can eliminate answer choice B.
Now, we will take Statements One and Two Together:
From statements one and two, we know that each wool jacket requires 4 pounds of wool and no cotton, and that each cotton jacket requires 6 pounds of cotton and no wool.
From the analysis of each statement, we know that the manufacturer can make a maximum of 750 wool jackets and 333 cotton jackets. Since we have enough cotton and wool to produce 750 + 333 = 1,083 jackets, we have enough cotton and wool to produce at least 1,000 jackets.
Hence, the correct Answer is C.

Correct Answer: C

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