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Three roommates—Bela, Gyorgy, and Janos—together saved money for a trip. The amount that… – OG 2020 Question #363 with Solution

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?

  1. Bela had a monthly income of $2,000.
  2. Janos saved 1.5 times as much for the trip as Bela.
SourceOG 2020
TypeData Sufficiency
TopicWord Problems
Sub-TopicPercents/Ratio
DifficultyMedium

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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