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Manager
Joined: 27 Jun 2007
Posts: 187
Robin split a total of $24,000 between 2 investments, X and Y. If inve [#permalink] ### Show Tags Updated on: 20 Feb 2017, 01:39 2 9 00:00 Difficulty: 25% (medium) Question Stats: 71% (01:19) correct 29% (01:04) wrong based on 360 sessions ### HideShow timer Statistics 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.
Manager
Joined: 16 Sep 2007
Posts: 208

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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?
Manager
Joined: 16 Sep 2007
Posts: 208

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05 Jan 2016, 21:45
1
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!
Math Expert
Joined: 02 Aug 2009
Posts: 7030

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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 Director Joined: 26 Oct 2016 Posts: 641 Location: United States Concentration: Marketing, International Business Schools: HBS '19 GMAT 1: 770 Q51 V44 GPA: 4 WE: Education (Education) Re: Robin split a total of$24,000 between 2 investments, X and Y. If inve  [#permalink]

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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.

_________________

Thanks & Regards,
Anaira Mitch

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Joined: 17 May 2015
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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? Math Expert Joined: 02 Sep 2009 Posts: 50585 Robin split a total of$24,000 between 2 investments, X and Y. If inve  [#permalink]

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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?
_________________
Manager
Joined: 02 Jan 2017
Posts: 76
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41

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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. _________________ Fabio Skilnik :: https://www.GMATH.net (Math for the GMAT) Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! Senior Manager Joined: 04 Aug 2010 Posts: 305 Schools: Dartmouth College Re: Robin split a total of$24,000 between 2 investments, X and Y. If inve  [#permalink]

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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. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. 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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