Question

Evaluate the problem, and the two statements - labelled (1) and (2) - that contain certain data or information. Using the given statements, decide whether the information provided is sufficient to answer the question.
The graph shows the number of covid cases in a village in Madhya Pradesh in the years 2020 and 2021. What is the ratio of the difference between omicron and delta cases in the year 2020 to that in the year 2021? Variants A, B, and C are one of omicron, delta and beta variants, not necessarily in the same order.
(The graph is a stacked bar chart showing cases for Variants A, B, and C in 2020 and 2021).
(1) The number of cases of Beta and delta together in 2020 is 3000.
(2) The number of cases of Omicron and beta together in 2021 is 6000.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

In complex Data Sufficiency problems with multiple unknowns (like the identities of A, B, and C), treat it like a logic puzzle. Use each statement to narrow down the possibilities. If one statement isn't enough, see if the constraints from the second statement, when combined with the first, eliminate all ambiguity.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a Data Sufficiency problem that requires interpreting a stacked bar chart and using logical deduction to identify the variants. The goal is to find a specific ratio, which requires uniquely identifying the Omicron and Delta variants.
Step 2: Read the Data from the Graph:
By observing the stacked bars:

For 2020:

Variant A (blue) = 7000
Variant B (orange) = 9000 - 7000 = 2000
Variant C (grey) = 10000 - 9000 = 1000

For 2021:

Variant A (blue) = 4000
Variant B (orange) = 7000 - 4000 = 3000
Variant C (grey) = 9000 - 7000 = 2000

Let O, D, B be the number of cases for Omicron, Delta, and Beta respectively. We need to find the value of \( \frac{|O_{2020} - D_{2020}|}{|O_{2021} - D_{2021}|} \).
Step 3: Detailed Explanation:
Analyze Statement (1): The number of cases of Beta and Delta together in 2020 is 3000.
The 2020 values are {7000, 2000, 1000}. The two values that sum to 3000 are 2000 and 1000. This means \{Beta, Delta\} corresponds to \{Variant B, Variant C\}. The remaining variant, Variant A (7000 cases), must be Omicron. So, we know \(O_{2020} = 7000\). However, we don't know if Delta is Variant B (2000) or Variant C (1000).

If Delta = B, then \(|O_{2020} - D_{2020}| = |7000 - 2000| = 5000\).
If Delta = C, then \(|O_{2020} - D_{2020}| = |7000 - 1000| = 6000\).
Since we cannot find a unique value for the numerator of the ratio, Statement (1) is not sufficient.
Analyze Statement (2): The number of cases of Omicron and Beta together in 2021 is 6000.
The 2021 values are {4000, 3000, 2000}. The two values that sum to 6000 are 4000 and 2000. This means \{Omicron, Beta\} corresponds to \{Variant A, Variant C\}. The remaining variant, Variant B (3000 cases), must be Delta. So, we know \(D_{2021} = 3000\) and \(D_{2020} = 2000\). However, we don't know if Omicron is Variant A or Variant C.

If Omicron = A, then \(|O_{2020} - D_{2020}| = |7000 - 2000| = 5000\) and \(|O_{2021} - D_{2021}| = |4000 - 3000| = 1000\). The ratio is 5.
If Omicron = C, then \(|O_{2020} - D_{2020}| = |1000 - 2000| = 1000\) and \(|O_{2021} - D_{2021}| = |2000 - 3000| = 1000\). The ratio is 1.
Since we get two different possible ratios, Statement (2) is not sufficient.
Analyze Both Statements Together:
From (1), we know: Omicron = Variant A. From (2), we know: Delta = Variant B. This uniquely identifies two of the variants. The remaining variant must be Beta, so Beta = Variant C. Now we can calculate the ratio without ambiguity:

Difference in 2020: \(|O_{2020} - D_{2020}| = |\text{A}_{2020} - \text{B}_{2020}| = |7000 - 2000| = 5000\).
Difference in 2021: \(|O_{2021} - D_{2021}| = |\text{A}_{2021} - \text{B}_{2021}| = |4000 - 3000| = 1000\).
Ratio = \( \frac{5000}{1000} = 5 \).
Since we can find a unique value for the ratio, the statements together are sufficient.