Question: Material A costs $3 per kilogram, and Material B costs $5 per kilogram. If 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B, is x > y ?

(1) y > 4
(2) The cost of the 10 kilograms of Material K is less than $40.

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.

“Material A costs $3 per kilogram, and Material B costs $5 per kilogram” is a topic of the GMAT Quantitative reasoning section of GMAT. The GMAT Data Sufficiency question is represented by a problem statement and two factual statements. This definite GMAT data sufficiency question tests the candidates' numerical proficiency and calculative skills in mathematics. GMAT Quant section contains 31 multiple-choice questions and the time limit is 62 minutes. GMAT data sufficiency comprises 15 questions out of these 31 GMAT quant questions which are two-fifths of the entire sum of questions. The candidates can improve their understanding by answering more questions from the book named “501 GMAT Questions”.

Solution and Explanation:

Approach Solution 1:

The problem statement states that:

Given:

• Material A costs $3 per kilogram
• Material B costs $5 per kilogram
• 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B i.e x+y = 10

Find out:

• If the value of x is greater than the value of y.

1. The statement implies that y > 4.
   If the value of y is equal to 4.5, then x=5.5 (since x+y=10)
   Therefore the value of x is greater than the value of y. Thus the answer to this problem is Yes.
   If the value of y is equal to 6, then x=4 (since x+y=10)
   Therefore the value of x is less than the value of y. Thus the answer to this problem is No.
   Therefore, the statement alone is not sufficient to answer the problem.
2. The statement indicates that the expense of the 10 kilograms of Material K is less than $40
   Therefore from this statement, we can conclude that 3x+5y < 40
   Since x+y= 10 that is y= 10-x, then by putting the value of y in the equation we get,
   3x+ 5(10-x) < 40
   2x > 10
   x > 5
   Therefore, x > y

Hence the statement alone is sufficient to answer this question.

Correct Answer: (B)

Approach Solution 2:

The problem statement states that:

Given:

• Material A costs $3 per kilogram
• Material B costs $5 per kilogram
• 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B i.e x+y = 10

Find out:

• If the value of x is greater than the value of y.

According to the question,
x kilograms are priced at 3$ per Kilogram and y kilograms are priced at 5$ per Kilogram
Let both these x kilograms and y kilograms produces10 kilograms at z$ per Kilogram
Further, it is given that, x+y=10
Therefore the equation would be : 3(x)+5(y)=10(z)
Now let's analyse the statements:

1. Statement (1) states y>4.
   It is required to note the fact that x+y=10.
   Therefore the value of x could vary between 0 and 6.
   Hence the statement alone is insufficient
2. Statement (2) indicates that the cost of the 10 kilograms of Material K is less than $40.
   Therefore, we can write it as 3(x)+5(y)<40.
   As we know x+y=10, then x=10−y.
   Therefore, 3(10−y)+5(y) < 40
   => 30−2y+5y<40
   => 2y<10
   => y<5

If the value of y is less than 5 then the value of x is greater than 5.
Therefore, x>y
Hence the statement alone is sufficient.

Correct Answer: (B)

Approach Solution 3:

The problem statement informs that:

Given:

• Material A costs $3 per kilogram
• Material B costs $5 per kilogram
• 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B i.e x+y = 10

Find out:

• If the value of x is greater than the value of y.

1. The statement cites that y > 4
   If y =4.5 then x=5.5
   Therefore, x>y
   However, if y= 5.5, then x= 4.5
   Hence, the value of x is not greater than y.
2. The statement implies that the cost of the 10 kilograms of Material K is less than $40.
   Therefore, we can say, 3x + 5y <40
   We can rewrite the equation as 3x + 3y + 2y < 40
   => 3(x + y) + 2y < 40
   Since x + y = 10, we can infer that:
   =>3(10) + 2y < 40
   =>30 + 2y < 40
   =>2y < 10
   Therefore, y < 5

Since the value of y is less than 5, then the value of x must be greater than 5. It is because the sum of x and y is 10.
Therefore, x>y
Hence the statement alone is sufficient.

Correct Answer: (B)

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