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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.

A
Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
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B
Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
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C
Both statements together are sufficient, but neither statement alone is sufficient.
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D
Each statement alone is sufficient.
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E
Statements (1) and (2) together are not sufficient.
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Solution

## The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.Since x + y = 10x, the relation x > y is equivalent to x > 10 - x, or x > 5. The given information is consistent with x = 5.5 and y = 4.5, and the given information is also consistent with x = y = 5. Therefore, it is possible for x > y to be true and it is possible for x > y to be false; NOT sufficient. Given that 3x + 5y < 40, or 3x + 5(10 - x) < 40, then 3x - 5x < 40 - 50. It follows that -2x < -10, or x > 5; SUFFICIENT. The correct answer is B; statement 2 alone is sufficient.

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