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Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?
(1) w = 30
(2) y = 75
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
  • d)
    EACH statement ALONE is sufficient to answer the question asked
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Brand W nut mix contains 24% cashews by weight, and Brand X nut mix co...
Understanding the Problem
To find the value of \( x \), we need to set up an equation based on the given information about the nut mixes.
- Brand W contains 24% cashews.
- Brand X contains 9% cashews.
- The mixture of \( w \) pounds of Brand W and \( x \) pounds of Brand X results in \( y \) pounds of a mixture that is 15% cashews.
The equation for the total amount of cashews in the mixture can be expressed as:
\[ 0.24w + 0.09x = 0.15y \]
Using Statement (1): w = 30
Substituting \( w = 30 \) into the equation:
\[ 0.24(30) + 0.09x = 0.15y \]
This simplifies to:
\[ 7.2 + 0.09x = 0.15y \]
With this single equation and the known value of \( w \), we can solve for \( x \) if we have \( y \).
Using Statement (2): y = 75
Substituting \( y = 75 \) into the equation:
\[ 0.24w + 0.09x = 0.15(75) \]
This simplifies to:
\[ 0.24w + 0.09x = 11.25 \]
With this single equation and the known value of \( y \), we can solve for \( x \) if we have \( w \).
Conclusion
- Statement (1) gives us a specific value for \( w \) but needs \( y \) to find \( x \).
- Statement (2) gives us a specific value for \( y \) but needs \( w \) to find \( x \).
Since each statement alone allows us to express \( x \) in terms of the other variable, both statements independently provide sufficient information to solve for \( x \).
Therefore, the correct answer is option D: Each statement alone is sufficient to answer the question.
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Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?(1) w = 30(2) y = 75a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?
Question Description
Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?(1) w = 30(2) y = 75a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?(1) w = 30(2) y = 75a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Brand W nut mix contains 24% cashews by weight, and Brand X nut mix contains 9% cashews by weight. If w pounds of Brand W nut mix are combined with x pounds of Brand X nut mix to produce y pounds of nut mix that is 15% cashews by weight, what is the value of x?(1) w = 30(2) y = 75a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'D'. Can you explain this answer?.
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