Question

If the ratio of stocks to bonds in a certain portfolio is 5:3, then which of the following CANNOT be the total number of stocks and bonds?

• A. 8
• B. 50
• C. 120
• D. 160
• E. 200

Hint:

Whenever you see a ratio problem asking for a possible or impossible total, immediately add the parts of the ratio. The total must be a multiple of this sum. For a ratio of \(a:b\), the total must be a multiple of \((a+b)\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A ratio of 5:3 means that for every 5 stocks, there are 3 bonds. This implies that the total number of items can be thought of as being in groups, where each group contains \(5+3=8\) items (5 stocks and 3 bonds). Therefore, the total number of stocks and bonds must be a multiple of 8.
Step 2: Key Formula or Approach:
Let the number of stocks be \(5k\) and the number of bonds be \(3k\), where \(k\) is a positive integer representing the number of groups.
The total number of stocks and bonds is \(T = 5k + 3k = 8k\).
This shows that the total \(T\) must be divisible by 8. We need to check which of the given options is not a multiple of 8.
Step 3: Detailed Explanation:
We will test each option to see if it is divisible by 8.
(A) \(8 \div 8 = 1\). This is a multiple of 8. So, 8 is a possible total.
(B) \(50 \div 8 = 6.25\). This is not an integer. So, 50 is not a multiple of 8 and CANNOT be the total number.
(C) \(120 \div 8 = 15\). This is a multiple of 8. So, 120 is a possible total.
(D) \(160 \div 8 = 20\). This is a multiple of 8. So, 160 is a possible total.
(E) \(200 \div 8 = 25\). This is a multiple of 8. So, 200 is a possible total.
Step 4: Final Answer:
The only number in the options that is not a multiple of 8 is 50. Therefore, 50 cannot be the total number of stocks and bonds in the portfolio.