How much money do Vivek and Suman have together? Statements: I. Suman has 20…
2025
How much money do Vivek and Suman have together?
Statements:
I. Suman has 20 rupees less than what Tarun has.
II. Vivek has 30 rupees more than what Tarun has.
- A.
The data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient.
- B.
The data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient.
- C.
If the data in either Statement I alone or Statement II alone is sufficient to answer the question.
- D.
If the data in both Statements I and II together is not sufficient to answer the question.
Show answer & explanation
Correct answer: D
Data Sufficiency problems require translating each statement into an equation relating the unknowns, then checking whether the resulting system pins down a UNIQUE numerical value for the quantity asked. If, after using all the statements, the target quantity still depends on an unknown that no statement fixes, the data is insufficient -- regardless of how many statements are combined.
Let V, S, T denote the amounts of money with Vivek, Suman, and Tarun respectively.
From Statement I: S = T minus 20.
From Statement II: V = T plus 30.
Combine both statements to find V + S: V + S = (T plus 30) + (T minus 20) = 2T + 10.
Neither statement, alone or combined, fixes a numeric value for T -- no statement states Tarun's actual amount. Since V + S = 2T + 10 still varies with T, no single numeric answer for how much money Vivek and Suman have together can be pinned down even using both statements together.
So the data in both Statements I and II together is not sufficient to answer the question.