Three roommates—Bela, Gyorgy, and Janos—together saved money for a tri

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:

GMAT assassins aren't born, they're made,
Rich
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The Logical approach to this question would look for two pieces of information: either the amount saved by Gyorgy (as it is a third of the total amount) or the amounts saved by the other two (which is two thirds of the whole and thus will allow us to calculate it).
Since statement (1) gives us just the amount saved by Bela (i.e. the required number to calculate it) and statement (2) provides just the amount saved by Janos, we must have both in order to solve the question.
The correct answer is (C).

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hree 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.
So, Bela saved 8% of 2000 or 160.
Nothing about others..
Insuff

(2) Janos saved 1.5 times as much for the trip as Bela.
G saved x out of 3x. So, if bela saves b, Janos saves 1.5b..
Thus, 2.5b=2x.
No values known.. Insuff

Combined..
b=160, so 1.5b=1.5*160=240...
Thus, 2x=240 or x=120. Since total is 3x, answer is 3*120=360.

C
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g=1/3*(160+g+j)
2g=160+j
g=8% of monthly income
find g+b+j
#1
2000*.08 = 160
not sufficient as other details not given

#2
j=1.5*b
not sufficient
from 1&2
we can say
j= 1.5*160 ; 240
so 2g= 160+240
g= 200
j = 160
total 400+160 ; 560
IMO C

We want to have count info from the question term, so each of statement should provide count info:
+St1: we know only 1 count info, still missing J & G -->NS
+St2: no count info-->NS
St1 + St2: we now have count info, let's plug all to the equation: B+G+J and Gyorgy saved was exactly 1/3 of the total amount saved by all 3 roommates.
-->We can finally answer the question.
My choice is C

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.

Statement 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
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Answer: Option C

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Let's write the amount saved by the three as B + G + J = Total saved.

We know that the amount that Bela saved was equal to 8% of his monthly income but we can't quantify that so it doesn't help.
We also know that the amount that Gyorgy saved was exactly 1/3 of the total amount saved by all 3 roommates, so this gives us the following equation:

G = (1/3)*(B + G + J)

We have 3 unknowns.

(1) Bela had a monthly income of $2,000.
With this, we can quantify B, but it's still insufficient to calculate the rest because we still don't know G or J.

(2) Janos saved 1.5 times as much for the trip as Bela.
With this, we could express J in terms of B (J = 1.5 * B) and replace that in the equation, but it's still insufficient to calculate the rest because we still don't know G or B.

With both statements, because we can quantify B with statement 1 and express J in terms of B with statement 2, we can also quantify J. Then we can find G in the equation. We have found the amount that each saved for the trip.

Answer C
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