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

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The ratio of suv's to passenger cars sold at a particular automobile..  [#permalink]

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New post 17 Oct 2017, 08:13
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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. The total number of vehicles sold in 2007 was divisible 10. In 2007, were more cars sold than SUV's?

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.

2. In 2003, twice as many SUV's were sold as cars.
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The ratio of suv's to passenger cars sold at a particular automobile..  [#permalink]

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New post 17 Oct 2017, 08:46
asfandabid wrote:
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. The total number of vehicles sold in 2007 was divisible 10. In 2007, were more cars sold than SUV's?

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.

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


Hi..
Since total sales remain constant, if the ratio S to P decrease, S decreases and P increases with same amount.


Statement I.
Let the sale in 2007 be \(S_7.....&....P_7\) similarly for 2003..
Now the statement means \(P_3-S_7=0.36(S_7+P_7)......P_3+0.36*P_7=1.36*S_7...\)

Now \(P_3<P_7\) so LHS will be \((<P_7)+0.36*P_7= (<1.36)P_7.......\)
So a LESSER Number multiplied by P_7 = a higher number multiplied by S_7
Clearly P_7>S_7
Sufficient

Statement II..
We don't know about 2007
Insufficient

A
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The ratio of suv's to passenger cars sold at a particular automobile..  [#permalink]

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New post 02 Nov 2017, 11:51
chetan2u wrote:
asfandabid wrote:
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. The total number of vehicles sold in 2007 was divisible 10. In 2007, were more cars sold than SUV's?

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.

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


Hi..
Since total sales remain constant, if the ratio S to P decrease, S decreases and P increases with same amount.


Statement I.
Let the sale in 2007 be \(S_7.....&....P_7\) similarly for 2003..
Now the statement means \(P_3-S_7=0.36(S_7+P_7)......P_3+0.36*P_7=1.36*S_7...\)

Now \(P_3<P_7\) so LHS will be \((<P_7)+0.36*P_7= (<1.36)P_7.......\)
So a LESSER Number multiplied by P_7 = a higher number multiplied by S_7
Clearly P_7>S_7
Sufficient

Statement II..
We don't know about 2007
Insufficient

A


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
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Re: The ratio of suv's to passenger cars sold at a particular automobile..  [#permalink]

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New post 20 Sep 2018, 18:37
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

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Re: The ratio of suv's to passenger cars sold at a particular automobile..  [#permalink]

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New post 21 Sep 2018, 09:29
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asfandabid wrote:
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. The total number of vehicles sold in 2007 was divisible 10. In 2007, were more cars sold than SUV's?

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.

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


Responding to a pm:

SUV/Cars is declining. Total sales is same - so every year, fewer SUVs are being sold while more cars are being sold (to keep the sales same).
Total in 2007 = 10a

In 2007, was the ratio SUV/ Cars < 1? (were more cars than SUVs sold?)

Stmnt 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.

The total vehicle sale has remained same.
If No of SUVs in 2007 is replaced by no of cars of 2003, the total vehicle sale would increase by 36%. This means the number of cars sold in 2003 were more than the no of SUV's sold in 2007
Cars in 2003 > SUVs in 2007
Since number of cars being sold is increasing year or year, Cars in 2007 > Cars in 2003
So Cars in 2007 > SUVs in 2007
Sufficient to answer "Yes"

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

Let's assume the ratio was 20/10 in 2013 and it kept reducing year on year

Case 1:
20/10 > 19/11 > 18/12 > 17/13 > 16/14 (2007 ratio is more than 1)

Case 2:
20/10 > 15/15 > 14/16 > 13/17 > 12/18 (2007 ratio is less than 1)

We see that in one case 2007 ratio is more than 1 and in the other it is less. Not sufficient.

Answer (A)
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Re: The ratio of suv's to passenger cars sold at a particular automobile.. &nbs [#permalink] 21 Sep 2018, 09:29
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