OG 2020: Question No. 363
Three roommates—Bela, Gyorgy, and Janos—together saved money for a trip. The amount that Bela saved was equal to 8% of his monthly income. The amount that Gyorgy saved was exactly 1/3 of the total amount saved by all 3 roommates. What was the total amount saved for the trip by all 3 roommates?
- Bela had a monthly income of $2,000.
- Janos saved 1.5 times as much for the trip as Bela.
| Source | OG 2020 |
| Type | Data Sufficiency |
| Topic | Word Problems |
| Sub-Topic | Percents/Ratio |
| Difficulty | Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- Three roommates—Bela(B), Gyorgy(G), and Janos(J)—together saved money for a trip.
- The amount that Bela saved was equal to 8% of his monthly income.
- The amount that Gyorgy saved was exactly 1/3 of the total amount saved by all 3 roommates.
We need to determine
- The total amount saved for the trip by all 3 roommates.
To find the total savings, we need to know their individual savings.
With this understanding, let us now analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, B had a monthly income of $2000.
From this question, we know that B saved 8% of his monthly income.
- 8% of B’s income = 2000
Therefore, from this statement, we can determine the monthly income of B.
However, we cannot determine the savings of all of them.
Hence, statement 1 is not sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, J saved 1.5 times as much for the trip as B.
- This gives us a relation between the savings of J and B.
- However, we cannot determine the savings of all them.
Hence, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Combining information from both statements, we know
- The monthly income and corresponding savings of B.
- And therefore, the savings of J.
Now, savings of G = 1/3 (savings of B + savings of J + savings of G)
- As we already know the savings of J and B, we can calculate the savings of G using the above equation.
- Therefore, we can answer the question using the information available in both statements.
Hence, the correct answer is option C.
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