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On January 1, 2010, Dave invests 70% of his retirement savings in Anta
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10 Jun 2021, 22:02
10 Jun 2021, 22:02
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On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then x is between
A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60
A. 10 and 20
B. 20 and 30
C. 30 and 40
D. 40 and 50
E. 50 and 60
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Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta
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13 Jun 2021, 03:12
13 Jun 2021, 03:12
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On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps
Let his retirement savings be 100
=> Antarctic largecap stocks investment = 70% of 100 = 70
=> Antarctic midcap stocks investment = 20% of 100 = 20
=> Antarctic smallcap stocks investment = 10% of 100 = 10
In 2010
Largecaps rise by 5% => New value = 70 + 5% of 70 = 1.05 * 70 = 73.5
Midcaps rise by 10% => New value = 20 + 10% of 20 = 1.1 * 20 = 22
Smallcaps rise by 15% => New value = 10 + 15% of 10 = 1.15 * 10 = 11.5
In 2011
Largecaps fall by 10% => New value = 73.5 - 10% of 73.5 = 0.9 * 73.5 = 66.15
Midcaps fall by 20% => New value = 22 - 20% of 22 = 0.8 * 22 = 17.6
Smallcaps rise by x% => New value = 11.5 + x% of 11.5
Total value = 66.15 + 17.6 + 11.5 + x% of 11.5 = 95.25 + x% of 11.5
On January 1, 2012, Dave has the same total amount of retirement savings as he did two years before
=> 95.25 + x% of 11.5 = 100
=> x% of 11.5 = 100 - 95.25 = 4.75
=> \(\frac{x}{100}\) * 11.5 = 4.75
=> x = 41.3%
So, answer will be D
Hope it helps!
Let his retirement savings be 100
=> Antarctic largecap stocks investment = 70% of 100 = 70
=> Antarctic midcap stocks investment = 20% of 100 = 20
=> Antarctic smallcap stocks investment = 10% of 100 = 10
In 2010
Largecaps rise by 5% => New value = 70 + 5% of 70 = 1.05 * 70 = 73.5
Midcaps rise by 10% => New value = 20 + 10% of 20 = 1.1 * 20 = 22
Smallcaps rise by 15% => New value = 10 + 15% of 10 = 1.15 * 10 = 11.5
In 2011
Largecaps fall by 10% => New value = 73.5 - 10% of 73.5 = 0.9 * 73.5 = 66.15
Midcaps fall by 20% => New value = 22 - 20% of 22 = 0.8 * 22 = 17.6
Smallcaps rise by x% => New value = 11.5 + x% of 11.5
Total value = 66.15 + 17.6 + 11.5 + x% of 11.5 = 95.25 + x% of 11.5
On January 1, 2012, Dave has the same total amount of retirement savings as he did two years before
=> 95.25 + x% of 11.5 = 100
=> x% of 11.5 = 100 - 95.25 = 4.75
=> \(\frac{x}{100}\) * 11.5 = 4.75
=> x = 41.3%
So, answer will be D
Hope it helps!
gmatclubot
Re: On January 1, 2010, Dave invests 70% of his retirement savings in Anta [#permalink]
13 Jun 2021, 03:12
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