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# m24 - 19

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m24 - 19 [#permalink]  24 May 2008, 17:59
any ideas guys?

Price increased by M% from 1991 to 1992 and by N% from 1992 to 1993. What was the percentage increase in price from 1991 to 1993 ?

1. MN = 300
2. 100M + 100N + MN = 4300

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient
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Joined: 17 Nov 2007
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Re: m24 - 19 [#permalink]  24 May 2008, 19:22
Expert's post
B

$$P_{1992}=P_{1991}*(1+\frac{M}{100})$$

$$P_{1993}=P_{1992}*(1+\frac{N}{100})=P_{1991}*(1+\frac{M}{100})*(1+\frac{N}{100})=P_{1991}*(1+\frac{x}{100})$$

$$10000+100*M+100*N+M*N=10000+100*x$$

$$x=M+N+\frac{M*N}{100}$$

So, B is sufficient
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Re: m24 - 19 [#permalink]  24 May 2008, 21:19
chengliu wrote:
any ideas guys?

Price increased by M% from 1991 to 1992 and by N% from 1992 to 1993. What was the percentage increase in price from 1991 to 1993 ?

1. MN = 300
2. 100M + 100N + MN = 4300

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

we assume that the price in 1991 is A, then the price in 1992 and 1993 correspondingly are A(1+M/100) and A(1+M/100)(1+N/100)
So the price increase from 1991 to 1993 is: A(10000 + 100M + 100N + MN)/10000
As we can see statements (1) alone cannot be sufficient to define the percentage of price increase. But (2) alone is sufficient.
Re: m24 - 19   [#permalink] 24 May 2008, 21:19
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