We need to determine the price of one bond, given that the total price of n equally priced bonds is 15000.
Let the price of one bond be P, and the number of bonds be n.
Thus, we have the equation:
n * P = 15000 (Equation 1)
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Evaluating Statement 1:
If the price of each bond had been 2 dollars more, the total price of the n bonds would have been 40000.
This gives the equation:
n * (P + 2) = 40000 (Equation 2)
Expanding:
nP + 2n = 40000
Using Equation 1:
15000 + 2n = 40000
2n = 25000
n = 12500
Plugging n into Equation 1:
12500 * P = 15000
P = 15000 / 12500 = 1.2
Since we have a unique value for P, Statement 1 alone is sufficient.
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Evaluating Statement 2:
If the price of each bond was doubled, the total price of n bonds would be 30000.
This gives the equation:
n * (2P) = 30000
Since we already know from Equation 1 that n * P = 15000, we substitute:
2 * 15000 = 30000
This equation always holds, but it does not help us determine a unique value for P.
Thus, Statement 2 alone is insufficient.
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Final Answer:
Statement 1 alone is sufficient, but Statement 2 alone is not.