Three roommates—Bela, Gyorgy, and Janos—together saved m

Hi All,

We're told that 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 and the amount that Gyorgy saved was exactly 1/3 of the TOTAL amount saved by all 3 roommates. We're asked for the total amount saved for the trip by all 3 roommates. We'll clearly need a lot of information to answer this question, but that work can be done in a number of different ways, including Algebraically and by TESTing VALUES.

(1) Bela had a monthly income of $2,000.

With the information in Fact 1, we can determine what Bela saved (re: 8% of $2,000 = $160), but we don't know how much either of the two people saved.
IF....
Janos saved $160 and Gyorgi saved $160, then the total saved would be $160 + $160 + $160 = $480
Janos saved $40 and Gyorgi saved $100, then the total saved would be $160 + $40 + $100 = $300
Fact 1 is INSUFFICIENT

(2) Janos saved 1.5 times as much for the trip as Bela.

With the information in Fact 2, we have no actual values to work with, so the amount of money that could be saved could clearly be lots of different totals.
Fact 2 is INSUFFICIENT

Combined, we know...
-Bela had a monthly income of $2,000.
-Janos saved 1.5 times as much for the trip as Bela.

From Fact 1, we know that Bela saved $160; with Fact 2, we now know that Janos saved (1.50($160) = $240. So far, that's a total of $400. We also know (from the initial information in the prompt), that Gyorgi saved 1/3 of the TOTAL. With the $400 we have already, the only number that fits would be if Gyorgi saved $200; we can see that with the following equation:

G = (1/3)($400 + G)
3G = 400 + G
2G = 400
G = 200

Thus, the total saved must be $600.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

AbeNeedsAnswers wrote: ↑

Thu May 02, 2019 10:41 am

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.

C

Source: Official Guide 2020

Solution:

Question Stem Analysis:

We need to determine the total amount saved for the trip by all 3 roommates.

Statement One Alone:

Since Bela saved 8% of his monthly income for the trip, he saved 2,000 x 0.08 = $160 for the trip. However, since we don’t know the amounts saved by Gyorgy and Janos, we can’t determine the total amount saved for the trip by all 3 roommates. Statement one alone is not sufficient.

Statement Two Alone:

Even though we know Janos saved 1.5 times as much for the trip as Bela, we don’t know the actual amount saved by any one of the 3 roommates. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we know Bela saved $160 and Janos saved 160 x 1.5 = $240 for the trip. From the question stem, we also know that Gyorgy saved 1/3 of the total saved by all 3 roommates. If we let T be the total amount saved by all 3 roommates, we can create the equation:

160 + 240 + T/3 = T

400 = 2T/3

T = 400 x 3/2 = 600

We see that the total amount saved by all 3 roommates was $600. Both statements together are sufficient.

Answer: C