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

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Intern
Joined: 11 Dec 2016
Posts: 33
The ratio of suv's to passenger cars sold at a particular automobile..  [#permalink]

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17 Oct 2017, 09:13
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Difficulty:

95% (hard)

Question Stats:

38% (03:02) correct 62% (01:47) wrong based on 42 sessions

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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.
Math Expert
Joined: 02 Aug 2009
Posts: 6547
The ratio of suv's to passenger cars sold at a particular automobile..  [#permalink]

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17 Oct 2017, 09:46
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..
Insufficient

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

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02 Nov 2017, 12:51
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..
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
The ratio of suv's to passenger cars sold at a particular automobile.. &nbs [#permalink] 02 Nov 2017, 12:51
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