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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pm; Thanked: 165 times; Followed by:70 members

DS - determine ratios

by karthikpandian19 » Mon Jun 11, 2012 6:31 pm

The inflation index for the year 2007 relative to the year 1996 was 1.78. This figure indicates that, on average, each dollar spent on a commodity in 1996 is equivalent to $1.78 spent on the same commodity in 2007. If the price of a TV increased precisely according to the inflation index, what was the price of a TV in 1996?

The price of a TV was $156 more in 2007 than in 1996.
The price of a TV was $356 in 2007.

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Source: Beat The GMAT — Data Sufficiency | Mon Jun 11, 2012 6:31 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Tue Jun 12, 2012 3:14 am

karthikpandian19 wrote:The inflation index for the year 2007 relative to the year 1996 was 1.78. This figure indicates that, on average, each dollar spent on a commodity in 1996 is equivalent to $1.78 spent on the same commodity in 2007. If the price of a TV increased precisely according to the inflation index, what was the price of a TV in 1996?

The price of a TV was $156 more in 2007 than in 1996.
The price of a TV was $356 in 2007.

Each dollar spent on a commodity in 1996 is equivalent to $1.78 spent on the same commodity in 2007.
Thus, if the price of a commodity in 2006 was $100, then the price in 2007 is $178, an increase of 78%.

Let p = the price in 2006.

Statement 1: The price of a TV was $156 more in 2007 than in 1996.
Thus, an increase of 78% is equal to $156:
.78p = 156.
p = 156/.78 = 15600/78 = 200.
SUFFICIENT.

Statement 2: The price of a TV was $356 in 2007.
Same information as that given in statement 1, in which p=200 and the increase = 156.
If we do the math:
1.78p = 356.
p = 356/1.78 = 35600/178 = 200.
SUFFICIENT.

The correct answer is D.

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