manik11 wrote:a, b, and c are three distinct positive integers. What is the product abc?
1) a + b + c = 7
2) ab + bc + ca = 14
Statement 1:
Test the SMALLEST POSSIBLE CASE.
If the three distinct positive integers are 1, 2 and 3, then their sum is 6.
Too small.
Test the NEXT GREATEST CASE.
If the three distinct positive integers are 1, 2 and 4, then their sum is 7.
This works.
If we increase any of the three values, then their sum will EXCEED 7.
Thus, the three distinct positive integers must be 1, 2 and 4, implying that their product = 1*2*4 = 8.
SUFFICIENT.
Statement 2:
Since the two statements cannot contradict each other, the one case that satisfies statement 1 -- 1, 2 and 4 -- must also satisfy statement 2.
Implication:
If the three distinct positive integers are 1, 2 and 4, then ab + bc + ca = 14.
If we decrease 4 to 3, then the value of ab + bc + ca will decrease.
If we increase any of the three values, then the value of ab + bc + ca will increase.
Thus, the one case that satisfies statement 1 -- 1, 2 and 4 -- must also be the ONLY case that will satisfy statement 2.
Thus, the three distinct positive integers must be 1, 2 and 4, implying that their product = 1*2*4 = 8.
SUFFICIENT.
The correct answer is
D.
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