Data Sufficiency

1. A certain IT department of fewer than 15 people hires coders and system admins. coders are paid 55000 per yr on avg, while sys. admins are paid 45000 per yr on avg. what is the ratio of coders to system admins?
(1) if two coders wer made system admin instead the yearly payroll for IT dept would be 535,000.
(2) if system admins salaries were reduced by one third and coders salaries were increased to 58000. the dept would save 57000 in yearly payroll.

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2.the ratio of SUVs to passenger cars sold at a particular automobile dealer has been declining since 2003 to 2007, while the total sales have remained constant. the total number of vehicles sold in 2007 was divisible by 10. In 2007 were more cars sold that SUVs.
(1)if in 2007 as many SUVs had been sold as cars were sold in 2003, there would have been 36% increase in total vehicle sales.
(2)In 2003 twice as many SUvs were sold as cars.

Please explain how to approach both the problems.

#1

Statement 1 tells us that the payroll is currently 555k (adding 2*10k to 535k)
The only way to get 555k out of 55k and 45k is to have 6*55 + 5*45. Sufficient.

Statement 2:
Reduction by 1/3 is a loss of 15k for sys-admins, so:
St 2 tells us that -15S + 3C = -57
-5S + C = -19
S = 4, C = 1
S = 5, C = 6
Insufficient.

suv + PCAR = 100 assume

1) if in 2007 as many SUVs had been sold as cars were sold in 2003, there would have been 36% increase in total vehicle sales.
This means that the number of cars sold in 2003 is more than number of SUV sold at 2007.
But this does not mean that the number of SUV sold on 2007 is less tha the number of car sold at 2007.

So insufficient

2)In 2003 twice as many SUvs were sold as cars.

This statement alone is insufficient too. it does not talk anything about 2007.


now combining both option 1) + 2)

in 2003
no of SUV = 2 number of cars
so we know the number of cars sold was less than number of suv sold on 2003.


now look into option 1.
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Now if we re read the option 1 :

if in 2007 as many SUVs had been sold as cars were sold in 2003,
there would have been 36% increase in total vehicle sales.

This means if the suv sales in 2007 were equal to the number of cars sold at 2003 ( WHich was less than 1/3 of the total sale) the sale would have increased by 36%

this means in 2007 the number of suv sold is even lesser than 1/3 of the t otal car sales.

hence we can answer the question:

In 2007 were more cars sold that SUVs.

GmatBoost-

I kind of solved it in a similar way. But the Answer for this question is D. I did not understand the sufficiency of #2.

Navami-

the answer is A according to the book. I do like the way you approached the problem. Just a quick question, what is the purpose of the information " divisible by 10".

I am not sure what to say about Statement 2, I don't see how it can be sufficient, since I have provided 2 possible values of S and C that both work and create different answers for the ratio S:C.

The first st. can be set up as an equation such that x is no of coders and y is the no of sys admin.then, 55x + 45y= 535, which maybe solved for x and y and can be adjusted to find original nos. st 1 is sufficient to find ratio.

st 2 can also be set up as a system of equation with single possible solution with fewer than 15 people total - 6 coders and 5 sys admins.

Either st is sufficient by itself. Hence answer is D.

This is the exact explanation provided. I did not understand anything. which is why I put it up on the forum.

Well, unfortunately, Statement 2 only provides one equation:
-15S + 3C = -57

All we know besides that is that S + C < 15, which is NOT an equation, it is an inequality...
So, I maintain that there are two solutions:
S = 4, C = 1
S = 5, C = 6

This isn't the first time that a GMAT Prep book from a major company has had an incorrect answer/explanation, and unfortunately it won't be the last time.

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gmatboost wrote:#1

Statement 1 tells us that the payroll is currently 555k (adding 2*10k to 535k)
The only way to get 555k out of 55k and 45k is to have 6*55 + 5*45. Sufficient.

Statement 2:
Reduction by 1/3 is a loss of 15k for sys-admins, so:
St 2 tells us that -15S + 3C = -57
-5S + C = -19
S = 4, C = 1
S = 5, C = 6
Insufficient.

I agree with the answer as A but shouldn't 2nd condition be written as

30S-3C=57 since system admin salary is reduced by 1/3 or 2/3rd of 45=30?