Ms. Morris invested in Fund A and Fund B. The total amount : GMAT Problem Solving (PS)
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# Ms. Morris invested in Fund A and Fund B. The total amount

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Magoosh GMAT Instructor
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Ms. Morris invested in Fund A and Fund B. The total amount [#permalink]

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26 Oct 2012, 13:02
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Ms. Morris invested in Fund A and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly$200 greater than the interest earned in Fund A. How much did Ms. Morris invest in Fund A?
(A) $32,000 (B)$36,000
(C) $40,000 (D)$42,000
(E) $45,000 For this question, one could do an algebraic solution, but would it be faster to backsolve from the answers? I would argue for the latter, though I imagine there will be a difference of opinions on this question. My argument, along with a discussion of backsolving in general and a complete solution to this problem, is here: http://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/ Perhaps other experts would also like to chime in on the issue of when to solve algebraically vs. when to backsolve. Mike [Reveal] Spoiler: OA _________________ Mike McGarry Magoosh Test Prep Last edited by mikemcgarry on 26 Oct 2012, 15:28, edited 1 time in total.  Magoosh Discount Codes EMPOWERgmat Discount Codes Economist GMAT Tutor Discount Codes Director Joined: 22 Mar 2011 Posts: 612 WE: Science (Education) Followers: 98 Kudos [?]: 867 [1] , given: 43 Re: backsolving [#permalink] ### Show Tags 26 Oct 2012, 14:42 1 This post received KUDOS mikemcgarry wrote: Ms. Morris invested in Fund A and Fund B. The total amount she invested, in both funds combined, was$100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Ms. Morris invest in Fund A? (A)$32,000
(B) $36,000 (C)$40,000
(D) $44,000 (E)$45,000

For this question, one could do an algebraic solution, but would it be faster to backsolve from the answers? I would argue for the latter, though I imagine there will be a difference of opinions on this question.

My argument, along with a discussion of backsolving in general and a complete solution to this problem, is here:
http://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/

Perhaps other experts would also like to chime in on the issue of when to solve algebraically vs. when to backsolve.

Mike

The correct answer should be 42,000, and it is not listed neither above, nor in the question you published on your blog.
It just appears in the solution you posted.
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Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink]

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16 Nov 2012, 13:07
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chibimoon wrote:
Could someone post the algebraic way please

A+B=100k
0.17B=0.23A+200=> -23A+17B=20000

from first equation 23A+23B=2300K
40B=2320K
B=58K

A=100k-58k=42k
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Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink]

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02 Feb 2013, 15:35
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chibimoon wrote:
Could someone post the algebraic way please

A+B=100,000

0.17B=0.23A+200

You now have two equations, so you can either substitute or eliminate. In the explanation above, elimination is used, here I use substitution (elimination is easier in this case)

Take away decimals first: 17B=23A+20,000

Isolate first equation to solve for A (your goal): B=100,000-A

Plug in for B:
17(100,000-A)=23A+20,000
1,700,000-17A=23A+20,000
1,680,000=40A
1,680,000/40=A
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Magoosh GMAT Instructor
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Kudos [?]: 5640 [0], given: 60

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26 Oct 2012, 15:30
EvaJager wrote:
The correct answer should be 42,000, and it is not listed neither above, nor in the question you published on your blog.
It just appears in the solution you posted.

Yes, you're right --- a mistake on my part --- the OA is $42,000, and I just corrected the question above & the blog. Thank you very much. Mike _________________ Mike McGarry Magoosh Test Prep Intern Joined: 18 May 2012 Posts: 15 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink] ### Show Tags 16 Nov 2012, 12:07 Could someone post the algebraic way please Magoosh GMAT Instructor Joined: 28 Dec 2011 Posts: 3632 Followers: 1246 Kudos [?]: 5640 [0], given: 60 Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink] ### Show Tags 02 May 2013, 10:29 Here's another problem from that same article, one that's even less amenable to algebraic treatment. If the sequence a(n) is defined as a(n) = $$n^2 + n + \sqrt{n+3}$$, then which of the following values of n represents the first terms such that a(n) > 500? (A) 13 (B) 22 (C) 33 (D) 46 (E) 78 [Reveal] Spoiler: OA = (B) A full solution is shown at that that article: http://magoosh.com/gmat/2012/gmat-plugg ... -choice-c/ Mike _________________ Mike McGarry Magoosh Test Prep GMAT Club Legend Joined: 09 Sep 2013 Posts: 12882 Followers: 561 Kudos [?]: 158 [0], given: 0 Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink] ### Show Tags 19 Nov 2014, 05:23 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 12882 Followers: 561 Kudos [?]: 158 [0], given: 0 Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink] ### Show Tags 25 May 2016, 23:15 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ SVP Joined: 17 Jul 2014 Posts: 2075 Location: United States (IL) Concentration: Finance, Economics Schools: Stanford '19 GMAT 1: 550 Q39 V27 GMAT 2: 560 Q42 V26 GMAT 3: 560 Q43 V24 GMAT 4: 650 Q49 V30 WE: General Management (Transportation) Followers: 18 Kudos [?]: 248 [0], given: 124 Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink] ### Show Tags 10 Sep 2016, 12:12 took some time as the numbers were high... 0.17B-0.23A = 200 | * 100 17B-23A=20,000 A+B=100,000 B=100,000 - A 17(100,000 - A) - 23A = 20,000 1,700,000 - 17A - 23A = 20,000 1,680,000 = 40A divide by 40 first two digits: 42...so answer is D. Manager Joined: 24 Aug 2016 Posts: 64 Location: India WE: Information Technology (Computer Software) Followers: 0 Kudos [?]: 9 [0], given: 10 Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink] ### Show Tags 26 Sep 2016, 03:06 $$A + B = 100,000$$ $$0.17B = 0.23A + 200 ==> -23A + 17B = 20,000$$ For making our calculation easy, we can divide constant by factor of 1000 and get the result. $$A + B = 100$$ ==> $$17A + 17B = 1700$$ --{i) ==> $$-23A + 17B = 20$$ --(ii) Subtract (ii) from (i) 17A - (-23A) = 1700-20 40A = 1680 A =$$\frac{168}{4}$$= 42. A = 42,000 _________________ "If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate." Re: Ms. Morris invested in Fund A and Fund B. The total amount [#permalink] 26 Sep 2016, 03:06 Similar topics Replies Last post Similar Topics: 2 Jaya invests in a new mutual fund. The fund averages 10% growth annual 4 28 Feb 2016, 08:49 3 Bob invested$2000 in fund A and $1000 in fund B. Over the next two ye 7 22 Dec 2015, 20:47 32 John invested$100 in each of the funds A and B. After one year, the v 8 30 Sep 2015, 11:15
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