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# If Aaron, Lee, and Tony have a total of \$36, how much money

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Math Expert
Joined: 02 Sep 2009
Posts: 58133
If Aaron, Lee, and Tony have a total of \$36, how much money  [#permalink]

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18 Feb 2014, 03:41
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Question Stats:

78% (01:29) correct 22% (01:28) wrong based on 335 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If Aaron, Lee, and Tony have a total of \$36, how much money does Tony have?

(1) Tony has twice as much money as Lee and 1/3 as much as Aaron.
(2) The sum of the amounts of money that Tony and Lee have is half the amount that Aaron has.

Data Sufficiency
Question: 97
Category: Algebra Applied problems; Equations
Page: 160
Difficulty: 650

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Re: If Aaron, Lee, and Tony have a total of \$36, how much money  [#permalink]

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18 Feb 2014, 05:45
1
From Statement 1, let the amount with Lee be 'x', so the amount

-> with Tony = 2x (twice as that with Lee)
-> with Aaron = 6x (3 times of Lee)

Now, 2x + x + 6x = 36 (since the total amount of money is \$36). This gives value of x.
Statement 1 alone is sufficient.

From Statement 2, you can find out money with Aaron, and the money with Tony + Lee, but you cannot find money with Tony alone.
Statement 2 is not sufficient.

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Re: If Aaron, Lee, and Tony have a total of \$36, how much money  [#permalink]

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18 Feb 2014, 21:49
1
Let Aaron, Lee and Tony be A, L and T.
We have, A + L + T = 36;
T = 36 - A - L;

Statement (1):
T = 2L & T = (1/3)A;

From this, we can find a unique value for T; FYI, T = 8. Sufficient

Statement (2):
T + L = A/2;

We can find the value of A, but not T; Not Sufficient;

Ans is (A).
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Re: If Aaron, Lee, and Tony have a total of \$36, how much money  [#permalink]

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18 May 2014, 10:32
1
from Q stem we get
A+L+T=36

FROM S1)
T=2L--------->L=T/2
T=1/3A------>A=3T

i.e
3T+T/2+T=36
9T/2=36
T=8

HENCE SUFF.

S2)
A=(L+T)/2------------>L+T=2A
NOT SUFF
Math Expert
Joined: 02 Sep 2009
Posts: 58133
Re: If Aaron, Lee, and Tony have a total of \$36, how much money  [#permalink]

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18 Feb 2014, 03:41
SOLUTION

If Aaron, Lee, and Tony have a total of \$36, how much money does Tony have?

(1) Tony has twice as much money as Lee and 1/3 as much as Aaron --> T = 2L and T = A/3 --> L = T/2 and A = 3T --> T/2 + 3T + T =36 --> we can find T. Sufficient.

(2) The sum of the amounts of money that Tony and Lee have is half the amount that Aaron has --> T + L = A/2 --> T + L + A = A/2 + A = 36. We can find A but the amounts Tony and Lee have cannot be found. Not sufficient.

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Re: If Aaron, Lee, and Tony have a total of \$36, how much money  [#permalink]

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18 Feb 2014, 04:12
Option A.
From S1:A+L+T=36 (1)
and T=2L=A/3
We can convert A and L to T and put it in (1) to find T.Suff

From S2: T+L=A/2 =>A=24 and T+L=12.Not suff to find T.
Math Expert
Joined: 02 Sep 2009
Posts: 58133
Re: If Aaron, Lee, and Tony have a total of \$36, how much money  [#permalink]

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22 Feb 2014, 06:50
SOLUTION

If Aaron, Lee, and Tony have a total of \$36, how much money does Tony have?

(1) Tony has twice as much money as Lee and 1/3 as much as Aaron --> T = 2L and T = A/3 --> L = T/2 and A = 3T --> T/2 + 3T + T =36 --> we can find T. Sufficient.

(2) The sum of the amounts of money that Tony and Lee have is half the amount that Aaron has --> T + L = A/2 --> T + L + A = A/2 + A = 36. We can find A but the amounts Tony and Lee have cannot be found. Not sufficient.

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Re: If Aaron, Lee, and Tony have a total of \$36, how much money  [#permalink]

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08 Aug 2019, 03:43
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Re: If Aaron, Lee, and Tony have a total of \$36, how much money   [#permalink] 08 Aug 2019, 03:43
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