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Robin split a total of $24,000 between 2 investments, X and Y. If inve

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Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post Updated on: 20 Feb 2017, 01:39
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Robin split a total of $24,000 between 2 investments, X and Y. If investment Y earns 7% simple annual interest, how much of that total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of the interest annually.
(2) Investment X earns 5 percent simple annual interest.

Originally posted by RyanDe680 on 09 May 2008, 17:14.
Last edited by Bunuel on 20 Feb 2017, 01:39, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 09 May 2008, 17:59
1.
24000-x=y
y*1.07=x*interest rate
(24000-x)*.07=x*interest rate
two variables
insufficient

2.
I don't know the total amount earned in interest annually
insufficient

1&2)
(24000-x)*.07=x*.05
->
x is some numeric value

24000-x=y
->
y is some numeric value

C
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 11 May 2008, 14:41
OA is C.

My confusion is how do you know what the "investment" is? Any investment can earn a certain percentage, but it doesn't mean you can calculate based off of that how much you invested in it....

Am I thinking too far into this?
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 11 May 2008, 16:19
RyanDe680 wrote:
OA is C.

My confusion is how do you know what the "investment" is? Any investment can earn a certain percentage, but it doesn't mean you can calculate based off of that how much you invested in it....

Am I thinking too far into this?


wrong. notice the 24000-x it is key to solving the problem.
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 05 Jan 2016, 21:45
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Bunuel or some moderator, please change "If investment earns 7% simple annual interest" to "If investment Y earns 7% simple annual interest" or merge it with this topic: http://gmatclub.com/forum/robin-split-a-total-of-24-000-between-2-investments-x-37523.html. Thanks!
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 05 Jan 2016, 22:06
TooLong150 wrote:
Bunuel or some moderator, please change "If investment earns 7% simple annual interest" to "If investment Y earns 7% simple annual interest" or merge it with this topic: http://gmatclub.com/forum/robin-split-a-total-of-24-000-between-2-investments-x-37523.html. Thanks!



Hi,
you are right that the Q seems to replicate the one you have linked...
But this Q also can act as a valid Q the way it is and would have C as the answer
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 12 Jun 2016, 02:40
RyanDe680 wrote:
Robin split a total of $24,000 between 2 investments, X and Y. If investment earns 7% simple annual interest, how much of that total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of the interest annually.
(2) Investment X earns 5 percent simple annual interest.


considering both statements together.
total interest earned 7% of 24000=1680
as per statement(1) each investment earns 1680/2=840 as nterest
from (2) investment X earns 5 percent simple annual interest
if a part of investment is X then another invested amount=24000-X
so X*5/100*1=840
giving x=12800
and Y=24000-12800=11200
Ans C
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 10 Feb 2017, 23:31
1
1 is insufficient because we do not know any relationship between the interest rates or the sums of money.
2 is insufficient because you can't tell anything about investment y, since, again, you do not have a relationship between x and y.

Put together, the two stmts are more efficient in solving the mystery. Since we know that 0.07y = 0.05x or that 7y = 5x and we also know that x + y = 24000. This is a simple set of equations with two unknown numbers, x and y.
So 7y = 5x
x + y = 24 000
Solve this system and you'll get the answer.

So answer is C.
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 11 Feb 2017, 01:16
anairamitch1804 wrote:
1 is insufficient because we do not know any relationship between the interest rates or the sums of money.
2 is insufficient because you can't tell anything about investment y, since, again, you do not have a relationship between x and y.

Put together, the two stmts are more efficient in solving the mystery. Since we know that 0.07y = 0.05x or that 7y = 5x and we also know that x + y = 24000. This is a simple set of equations with two unknown numbers, x and y.
So 7y = 5x
x + y = 24 000
Solve this system and you'll get the answer.

So answer is C.


Hi,

Please refer the highlighted part. It is not correct. 7 % interest rate is on the total amount, i.e. on 24000, not on y.

Thanks.
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 20 Feb 2017, 01:14
1
RyanDe680 wrote:
Robin split a total of $24,000 between 2 investments, X and Y. If investment earns 7% simple annual interest, how much of that total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of the interest annually.
(2) Investment X earns 5 percent simple annual interest.


Question stem is not very much clear, because 7% rate for Y is not explicitly mentioned .
M i ryt?
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Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 20 Feb 2017, 01:40
1
gauraha wrote:
RyanDe680 wrote:
Robin split a total of $24,000 between 2 investments, X and Y. If investment earns 7% simple annual interest, how much of that total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of the interest annually.
(2) Investment X earns 5 percent simple annual interest.


Question stem is not very much clear, because 7% rate for Y is not explicitly mentioned .
M i ryt?


Edited.

The stem reads: Robin split a total of $24,000 between 2 investments, X and Y. If investment Y earns 7% simple annual interest, how much of that total did Robin put into investment Y?
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Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 14 Dec 2017, 01:29
Stem Gives us

X + Y = 24000

Statement 1 Alone is insufficient. As 7 % of small amount can equal to 5 % of bigger amount . Or vice versa.
Statement 2 in clearly insufficient.

Combining two.

[7/100] * y= [5/100] *x Equation 1

Stem gave us X + Y =24000 -> X=24000- Y Equation 2

Two variables & Two equations.
Hence C is the answer.
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 24 Sep 2018, 15:08
RyanDe680 wrote:
Robin split a total of $24,000 between 2 investments, X and Y. If investment Y earns 7% simple annual interest, how much of that total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of the interest annually.
(2) Investment X earns 5 percent simple annual interest.

\(\left. \matrix{
X:\,\,\,24 \cdot k\,\,\,\,\,\,\,;\,\,\,\,\,\,{i \over {100}}\left( {24k} \right)\,\,\,\,\,{\rm{annual}}\,\,{\rm{simple}}\,\,{\rm{interest}}\,\,\left( * \right) \hfill \cr
Y:\,\,\,24 \cdot \left( {1 - k} \right)\,\,\,\,\,;\,\,\,\,\,\,{7 \over {100}}\left[ {24\left( {1 - k} \right)} \right]\,\,\,\,{\rm{annual}}\,\,{\rm{simple}}\,\,{\rm{interest}}\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\,\,\left[ {{\rm{unit}}:\,\,\,\$ \,\,{{10}^3}} \right]\)

\(\left( * \right)\,\,{\rm{just}}\,\,{\rm{a}}\,\,{\rm{initial}}\,\,{\rm{assumption}}\,\)



\(? = 24\left( {1 - k} \right)\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,\,\boxed{? = k}\,\,\,\,\,\,\left( {0 < k < 1} \right)\,\)


\(\left( 1 \right)\,\,\,\frac{i}{{100}}\left( {24k} \right) = \frac{7}{{100}}\left[ {24\left( {1 - k} \right)} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,\,ik = 7\left( {1 - k} \right)\,\,\,\,\,\left( {**} \right)\)

\(\left\{ \matrix{
\,{\rm{Take}}\,\,i = 7\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,? = k = 0.5\,\,\,\, \hfill \cr
\,{\rm{Take}}\,\,i = 0.0001\,\,\,\left( { \cong 0} \right)\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,? = k \cong 1\,\,\,\, \hfill \cr} \right.\)


\(\left( 2 \right)\,\,i = 5\,\,\,\left( {{\rm{trivial}}\,\,{\rm{bifurcation}}} \right)\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,k = 0.5\,\,\,\, \hfill \cr
\,{\rm{Take}}\,\,k = 0.6\,\,\,\, \hfill \cr} \right.\,\,\)


\(\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,\,\left( {**} \right)\,\,\,ik = 7\left( {1 - k} \right)\,\,\,\, \hfill \cr
\,\,\,i = 5 \hfill \cr} \right.\,\,\, \Rightarrow \,\,\,\,k\,\,{\rm{unique}}\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\)



This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve  [#permalink]

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New post 25 Sep 2018, 03:18
RyanDe680 wrote:
Robin split a total of $24,000 between 2 investments, X and Y. If investment Y earns 7% simple annual interest, how much of that total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of the interest annually.
(2) Investment X earns 5 percent simple annual interest.


Statement 1:
Test one case that also satisfies Statement 2.
Case 1: X = 5% and Y = 7%
For 5% interest and 7% percent interest to yield the same dollar amount,
$7 must be invested at 5% interest for every $5 invested at 7% interest:
X --> $7(0.05) = $0.35.
Y --> $5(0.07) = $0.35.
Thus:
\(\frac{X}{Y} = \frac{$7}{$5}\), implying that \(\frac{5}{12}\) of the $24,000 must be invested in Y:
\(\frac{5}{12} * 24,000 = 10,000\)

Test one case that does NOT also satisfy Statement 2.
Case 2: X = 3% and Y = 7%
For 3% interest and 7% percent interest to yield the same dollar amount,
$7 must be invested at 3% interest for every $3 invested at 7% interest:
X --> $7(0.03) = $0.21.
Y --> $3(0.07) = $0.21.
Thus:
\(\frac{X}{Y} = \frac{$7}{$3}\), implying that \(\frac{3}{10}\) of the $24,000 must be invested in Y:
\(\frac{3}{10}* 24,000 = 7200\)

Since the amount invested in Y can be different values, INSUFFICIENT.

Statement 2:
Here, the amount invested in Y can be any monetary value between $0 and $24,000.
INSUFFICIENT.

Statements combined:
Only Case 1 satisfies both statements.
In Case 1, the amount invested in Y = 10,000.
SUFFICIENT.


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Re: Robin split a total of $24,000 between 2 investments, X and Y. If inve &nbs [#permalink] 25 Sep 2018, 03:18
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