The ratio of suv's to passenger cars sold at a particular automobile..

Hi Chetan,

Thanks for explanation, there is one small error in rearranging

\(P_3-S_7=0.36(S_7+P_7)......P_3+0.36*P_7=1.36*S_7...\)
\(P_3-S_7=0.36(S_7+P_7)......P_3-0.36*P_7=1.36*S_7...\)


Thanks

Hi All,

We're told that the RATIO of SUV's to passenger cars sold at a particular automobile dealership have been DECLINING from 2003 to 2007, while total sales have remained CONSTANT and the total number of vehicles sold in 2007 was divisible 10. We're asked if, In 2007, more cars were sold than SUVs. This is a YES/NO question and can be solved by TESTing VALUES (although it will take a lot of little 'steps' to properly deal with this prompt).

To start, it's worth noting that we're given a LOT of information in the prompt, so we have to properly 'set up' what we have before we consider the additional information in the two Facts. For the sake of ease, I'm going to create some variables:

T = the number of SUVs sold
C = the number of cars sold

We're told:

1) The RATIO of T/C is DECLINING. For a ratio to decline, the numerator decreases and/or the denominator increases.
2) The total number of cars sold is a CONSTANT. When combined with the information on the ratio of vehicles sold, this means that while the TOTAL vehicles sold stays the SAME each year, T will DECREASE and C will INCREASE from year to year.
3) T+C is a multiple of 10.

At this point, we do NOT know if T or C is larger in 2003 or in 2007. We do know that for each "1 less" SUV sold, we will have "1 more" car sold.

1) If in 2007 as many SUV's had been sold as cars were sold in 2003, there would have been a 36% increase in total vehicle sales.

Fact 1 gives us a hypothetical about the number of SUVs sold in 2007 - and many Test Takers would probably assume that it is insufficient information. However, we have so many 'restrictions' given to us in the beginning, we have to do a bit of work to PROVE whether Fact 1 is sufficient or insufficient.

In 2003, there are only 3 possibilities, T = C or T > C or T < C. Let's start with the easiest option....

IF... T = C
2003: 50 SUVs and 50 cars --> 100 total vehicles, ratio of T/C = 50/50 = 1/1
Hypo. 2007: 50 SUVs and X cars --> 100 + 36%(100) = 136
50 + X = 136
X = 86
Actual 2007: Y SUVs and 86 cars --> 100 total vehicles
Y = 14
Actual 2007: 14 SUVs and 86 cars --> 100 total vehicles, ratio of T/C = 14/86
This first example fits everything that we were told (re: constant total, decreasing ratio) and the answer to the question is YES.

IF... T > C
In this example, I'm going to stick with a total of 100 vehicles; with this total, it's worth noting that neither T nor C can exceed 100, so the numbers that I'm going to TEST have to account for that AND the hypothetical total of 136 vehicles sold in 2007.

2003: 63 SUVs and 37 cars --> 100 total vehicles, ratio of T/C = 63/37
Hypo. 2007: 37 SUVs and X cars --> 100 + 36%(100) = 136
37 + X = 136
X = 99
Actual 2007: Y SUVs and 99 cars --> 100 total vehicles
Y = 1
Actual 2007: 1 SUVs and 99 cars --> 100 total vehicles, ratio of T/C = 1/99
This second example fits everything that we were told (re: constant total, decreasing ratio) and the answer to the question is YES.

IF... T < C
2003: 20 SUVs and 80 cars --> 100 total vehicles, ratio of T/C = 20/80 = 1/4
Hypo. 2007: 80 SUVs and X cars --> 100 + 36%(100) = 136
80 + X = 136
X = 56
Actual 2007: Y SUVs and 56 cars --> 100 total vehicles
Y = 44
Actual 2007: 44 SUVs and 56 cars --> 100 total vehicles, ratio of T/C = 44/56
In this third example, the starting ratio (1/4) is LESS than the ending ratio (44/56), so the ratio is NOT decreasing. This does NOT fit what we were told, so this example is NOT permissible.

We have two examples that fit everything that we are told AND lead to the SAME answer (a "YES" answer both times). I can find no proof of an inconsistency, meaning that there does not appear to be a "no" answer under these conditions.
Fact 1 is SUFFICIENT.

2. In 2003, twice as many SUV's were sold as cars.

Fact 2 tells us NOTHING about the number of vehicles sold in 2007.
Fact 2 is INSUFFICIENT

Final Answer:

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Rich

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