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# A school must raise exactly \$2,500 over the next year by investing a

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Math Expert
Joined: 02 Sep 2009
Posts: 50007
A school must raise exactly \$2,500 over the next year by investing a  [#permalink]

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19 Mar 2017, 07:06
00:00

Difficulty:

55% (hard)

Question Stats:

79% (02:30) correct 21% (02:48) wrong based on 76 sessions

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A school must raise exactly \$2,500 over the next year by investing a total of \$30,000 in stocks, which yield 9% annual interest, and bonds, which yield 8% annual interest. If the school wants to invest as much as possible in stocks, then how much should the school invest in stocks?

A. \$1,000
B. \$10,000
C. \$20,000
D. \$29,000
E. \$30,000

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Joined: 19 Apr 2016
Posts: 274
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Re: A school must raise exactly \$2,500 over the next year by investing a  [#permalink]

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19 Mar 2017, 07:50
1
1
Bunuel wrote:
A school must raise exactly \$2,500 over the next year by investing a total of \$30,000 in stocks, which yield 9% annual interest, and bonds, which yield 8% annual interest. If the school wants to invest as much as possible in stocks, then how much should the school invest in stocks?

A. \$1,000
B. \$10,000
C. \$20,000
D. \$29,000
E. \$30,000

let x be the amount to be invested in stocks

9x/100 + (8/100)*(30000-x) = 2500

9x + 240000 - 8x = 250000

x = 10000

Hence option B is correct
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Joined: 28 Jun 2016
Posts: 15
Re: A school must raise exactly \$2,500 over the next year by investing a  [#permalink]

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19 Mar 2017, 07:55
0akshay0 wrote:
Bunuel wrote:
A school must raise exactly \$2,500 over the next year by investing a total of \$30,000 in stocks, which yield 9% annual interest, and bonds, which yield 8% annual interest. If the school wants to invest as much as possible in stocks, then how much should the school invest in stocks?

A. \$1,000
B. \$10,000
C. \$20,000
D. \$29,000
E. \$30,000

let x be the amount to be invested in stocks

9x/100 + (8/100)*(30000-x) = 2500

9x + 240000 - 8x = 250000

x = 10000

Hence option B is correct
Hit Kudos if you liked it

Sent from my ONE E1003 using GMAT Club Forum mobile app
Senior Manager
Joined: 19 Apr 2016
Posts: 274
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
A school must raise exactly \$2,500 over the next year by investing a  [#permalink]

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19 Mar 2017, 08:14
1
appu2693 wrote:
0akshay0 wrote:
Bunuel wrote:
A school must raise exactly \$2,500 over the next year by investing a total of \$30,000 in stocks, which yield 9% annual interest, and bonds, which yield 8% annual interest. If the school wants to invest as much as possible in stocks, then how much should the school invest in stocks?

A. \$1,000
B. \$10,000
C. \$20,000
D. \$29,000
E. \$30,000

let x be the amount to be invested in stocks

9x/100 + (8/100)*(30000-x) = 2500

9x + 240000 - 8x = 250000

x = 10000

Hence option B is correct
Hit Kudos if you liked it

Sent from my ONE E1003 using GMAT Club Forum mobile app

The school must raise exactly \$2,500 by investing as much as possible in stocks.
I have assumed that amount to be x.

Investment in stocks yields 9% therefore the returns from this investment = 9x/100

The remaining amount i.e. (30000-x) is invested in bonds, which yield 8% annual interest. i.e. (8/100)*(30000-x)

The sum of the returns from both investments = 2500. So,

9x/100 + (8/100)*(30000-x) = 2500
x = 10000

therefore the school must invest 10000 in stocks to raise exactly \$2,500 by investing as much as possible in stocks.

appu2693 : Hope its clear
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A school must raise exactly \$2,500 over the next year by investing a  [#permalink]

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14 Nov 2017, 00:51
One of the quickest way to solve this problem is using allegation.

If whole amount is invested in stock, the return: \$30000*9% = \$2700
If whole amount is invested in bond, the return: \$30000*8% = \$2400
But the return needed is exactly \$2500

See attachment.

Hence the total amount needs to be invested in stock and bond in the ratio 1:2.
Therefore amount invested in stock is \$30000*(1/3) = \$10000.
Attachments

Capture.JPG [ 12.7 KiB | Viewed 333 times ]

A school must raise exactly \$2,500 over the next year by investing a &nbs [#permalink] 14 Nov 2017, 00:51
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