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01 Jan 2024, 02:30
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E
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Difficulty:
25%
(medium)
Question Stats:
79% (01:41) correct
21%
(01:11)
wrong
based on 98
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John invested $10,000 at m percent simple annual interest and also invested a different sum at n percent simple annual interest. What was the amount invested by John at n percent simple annual interest?
(1) The combined interest from both investments after one year amounted to $800.
(2) The investment of $10,000 was made at a 4 percent simple annual interest rate.
(1) The combined interest from both investments after one year amounted to $800.
(2) The investment of $10,000 was made at a 4 percent simple annual interest rate.
John invested $10,000 at 𝑚 percent simple annual interest and invested a different amount at 𝑛 percent simple annual interest. How much did John invest at 𝑛 percent simple annual interest?
(1) The total amount of interest earned from the investments in one year was $800.
(2) John invested $10,000 at 4 percent simple annual interest.
(1) The total amount of interest earned from the investments in one year was $800.
(2) John invested $10,000 at 4 percent simple annual interest.
01 Jan 2024, 04:11
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Let's denote the amount invested at n% as x. We know that the formula for simple interest is Interest = Principal*Rate*Time
Statement 1: The combined interest from both investments after one year amounted to $800
Using the simple interest formula:
- Interest from the first investment = 10,000*(m/100)*1 = 100m
- Interest from the second investment = x*(n/100)*1 = xn/100
According to the statement:
100m + xn/100 = 800
However, without knowing the values of m and n, we cannot determine x. So, Statement 1 alone is not sufficient.
Statement 2: The investment of $10,000 was made at a 4 percent simple annual interest rate
This means m = 4. However, this statement doesn't provide any information about the second investment. So, Statement 2 alone is also not sufficient.
Combining Statements 1 and 2:
Now that we know m = 4, we can rewrite the equation from Statement 1 as:
100*4 + xn/100 = 800
xn/100 = 400
xn = 40,000
Even with both statements, we do not have a value for n. Therefore, we cannot find the exact value of x, the amount invested at n percent interest.
Conclusion: Statements 1 and 2 together are NOT sufficient
Statement 1: The combined interest from both investments after one year amounted to $800
Using the simple interest formula:
- Interest from the first investment = 10,000*(m/100)*1 = 100m
- Interest from the second investment = x*(n/100)*1 = xn/100
According to the statement:
100m + xn/100 = 800
However, without knowing the values of m and n, we cannot determine x. So, Statement 1 alone is not sufficient.
Statement 2: The investment of $10,000 was made at a 4 percent simple annual interest rate
This means m = 4. However, this statement doesn't provide any information about the second investment. So, Statement 2 alone is also not sufficient.
Combining Statements 1 and 2:
Now that we know m = 4, we can rewrite the equation from Statement 1 as:
100*4 + xn/100 = 800
xn/100 = 400
xn = 40,000
Even with both statements, we do not have a value for n. Therefore, we cannot find the exact value of x, the amount invested at n percent interest.
Conclusion: Statements 1 and 2 together are NOT sufficient
01 Jan 2024, 06:42
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1) 800 = m% 10,000 + n% X
3 Variables In 1 linear equation cannot be solved INSUFFICIENT
2) m = 4% -- Investment 10,000
Question is value of the other investment. Cannot established Correlation INSUFFICIENT
1 & 2) Subs Eq 2 to 1 We still have 2 Variable with only 1 equation INSUFFICIENT
ANS: E
I hope I dont oversimplify it, Please guide us Bunuel
3 Variables In 1 linear equation cannot be solved INSUFFICIENT
2) m = 4% -- Investment 10,000
Question is value of the other investment. Cannot established Correlation INSUFFICIENT
1 & 2) Subs Eq 2 to 1 We still have 2 Variable with only 1 equation INSUFFICIENT
ANS: E
I hope I dont oversimplify it, Please guide us Bunuel
