Question

In which category was the percentage of spam emails increasing but at a decreasing rate?

• A. Financial
• B. Scams
• C. Products
• D. None of the above
• A. was larger
• B. was smaller
• C. was equal
• D. cannot be determined
• A. was larger
• B. was smaller
• C. was equal
• D. cannot be determined

Answer 1

The Correct Option is C

Step 1: Understand the question:
'Increasing at a decreasing rate' means two things together. First, the share goes up in every period. Second, each rise is smaller than the rise before it.
The four dates Sep-02, Dec-02, Mar-03 and Jun-03 are three months apart, so the gaps between readings are equal and we can compare the rises directly.

Step 2: Find the rise in each period for every category:
Adult: 38, 33, 19, 17. Changes: -5, -14, -2. It falls.
Financial: 25, 30, 37, 45. Changes: +5, +7, +8. It rises, and the rises grow bigger.
Health: 11, 19, 5, 18. Changes: +8, -14, +13. It goes up and down.
Internet: 5, 3, 10, 6. Changes: -2, +7, -4. It goes up and down.
Products: 3, 7, 10, 11. Changes: +4, +3, +1. It rises every time, and each rise is smaller.
Scams: 5, 6, 11, 2. Changes: +1, +5, -9. It rises first and then falls.
Others: 13, 2, 8, 1. Changes: -11, +6, -7. It goes up and down.

Step 3: Pick the category:
Only Products has all changes positive and shrinking: \( +4 \), then \( +3 \), then \( +1 \).

Step 4: Check the options:
Financial is rising, but at an increasing rate (5, 7, 8), so (1) is wrong.
Scams rises and then drops sharply to 2, so (2) is wrong.
Products fits both conditions, so (3) is right.
(4) None of the above is wrong because Products qualifies.

Final Answer:
Products is the only category whose share keeps rising while each rise gets smaller. This is option (3). \[ \boxed{\text{Option (3): Products}} \]

Answer 2

Step 1: Understand the question:
The table gives percentages, not numbers of emails. The number of health spam emails is the health percentage multiplied by the total spam of that month.
The passage also tells us the total in December 2002 was larger than the total in June 2003. So the question can be solved by comparing both factors.

Step 2: Write the two numbers:
Let the total spam in December 2002 be \( D \) and in June 2003 be \( J \). The passage says \( D > J \).
Health spam in December 2002 is 19% of \( D \), that is \( 0.19\,D \).
Health spam in June 2003 is 18% of \( J \), that is \( 0.18\,J \).

Step 3: Compare:
Since \( D > J \), we get \( 0.19\,D > 0.19\,J \).
Also \( 0.19\,J > 0.18\,J \), because \( J \) is a positive number.
Joining the two: \[ 0.19\,D > 0.19\,J > 0.18\,J \]
So health spam in December 2002 is larger than in June 2003.

Step 4: Check the options:
(2) was smaller: wrong, we proved it is larger.
(3) was equal: wrong, the inequality is strict.
(4) cannot be determined: wrong, because the passage gives \( D > J \), and both the share and the total are bigger in December, so the answer is fixed.
(1) was larger: correct.

Final Answer:
Both the percentage (19 against 18) and the total mail (December larger than June) favour December 2002, so health spam was larger then. This is option (1). \[ \boxed{\text{Option (1): was larger}} \]

Answer 3

Step 1: Understand the question:
Again the table has percentages. The count of financial spam in a month is the financial percentage times the total spam of that month.
The passage says the total in September 2002 was larger than the total in March 2003, but it does not say by how much.

Step 2: Write the two numbers:
Let the total in September 2002 be \( S \) and in March 2003 be \( M \), with \( S > M \).
Financial spam in September 2002 is 25% of \( S \), that is \( 0.25\,S \).
Financial spam in March 2003 is 37% of \( M \), that is \( 0.37\,M \).

Step 3: Find when each one is bigger:
The count in September is larger exactly when \( 0.25\,S > 0.37\,M \), that is when \( \frac{S}{M} > \frac{37}{25} = 1.48 \).
The passage only gives \( \frac{S}{M} > 1 \). A ratio above 1 may be 1.2, which is below 1.48, or it may be 2, which is above 1.48. Both are allowed.

Step 4: Try two possible cases:
Case 1: \( S = 120 \), \( M = 100 \). Then \( 0.25 \times 120 = 30 \) and \( 0.37 \times 100 = 37 \). September is smaller.
Case 2: \( S = 200 \), \( M = 100 \). Then \( 0.25 \times 200 = 50 \) and \( 0.37 \times 100 = 37 \). September is larger.

Step 5: Check the options:
Both cases obey every condition in the passage but give different answers. So neither 'was larger', 'was smaller' nor 'was equal' is always true.
Hence the comparison cannot be determined, which is option (4).

Final Answer:
The share is lower in September 2002 but the total is higher, and the data does not tell which effect wins. So it cannot be determined. This is option (4). \[ \boxed{\text{Option (4): cannot be determined}} \]