Official Guide Explanation:
Data Sufficiency #101




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Solution and Metadata

Question: 101
Page: 281
Difficulty: 5 (Moderate)
Category 1: Word Problems > Mixture Problems >

Explanation: It takes a bit of analysis to recognize this, but it's essentially a weighted average question. The 10 kilograms of Material K consists of some A (x kg) and some B (y kg). If it were all A, the cost would be $30--10 kg at $3 each. It it were all B, the cost would be $50. If it were half and half, the cost would be $40, right in the middle.

Statement (1) is insufficient. If y > 4, then x < 6, since their sum must be 10. However, we don't know that the amounts are integer values. The mix could consist of 4.1 kg of B, in which case the answer is "yes." If the mix consisted of 6 kg of B, the answer is "no."

Statement (2) is sufficient. As described a moment ago, the price of a half - and - half mix of the two materials would be $40. If the price is less than $40, that means that more than half of the mix is of the cheaper variety--that is, Material A, which is $3 per kg. Since there is more A than B, x > y. Choice (B) is correct.

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