In 2009, the price of each Econolux car increased by 10 percent from t

Question

In 2009, the price of each Econolux car increased by 10 percent from the 2008 price. In 2010, they decreased by 5 percent and now cost between $18,000 and $19,800. Which of the following could be the price of a 2008 Econolux car?

I. $17,230
II. $18,180
III. $18,935

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

I. $17,230
II. $18,180
III. $18,935

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

nick1816 · Answer

Lowest price possible of the car in 2008= 18000/(0.95*1.1)=17224.xyz
Maximum price possible of the car in 2008=19800/(0.95*1.1)=18947.abc

IMO E

DarleneTran · Answer

Can you explain why the answer is E???
------
Here's my logic:

Let x is the price of a 2008 Econolux car
+The price of a 2009 Econolux car is 1.1x since it increases 10%
+The price of a 2010 Econolux car is 1.045x since it decreases 5%
-->From 2008-2010: the price of Econolux car increases 4.5%

I assume each given price is the price in 2008
+If x=$17,230, 1.1x= 17,402, 1.045x = approx. $17,316-->So, my calculation for the price in 2010 doesn't belong to $18,000-$19,800
+If x=$18,180, then 1.045x = approx. $18,270-->Belong to the price from $18,000-$19,800
+If x=$18,935, then 1.045x = approx. $19,030-->Belong to the price from $18,000-$19,800
Because of that, my conclusion is II & III, but then there's no such options for II & III

ManjariMishra · Answer

Can someone please explain this

Posted from my mobile device

Lampard42 · Answer

You have made an error in your calculation cause 17230*1.045 = 18,005
The approach is better than  nick1816  as it will help you save time through multiplication. Multiply 1.045 to option 1 and 3 to check if they are within the limits

ScottTargetTestPrep · Answer

Letting n = the price in 2008, we can create the following inequality:

18,000 < (1.1n)(0.95) < 19,800

18,000 < 1.045n < 19,800

17,224.88 < n < 18,947.37

Thus, we see the price could be I, II, or III.

Answer: E

CrackverbalGMAT · Answer

Since this is a ‘could be’ type of question, the ideal strategy would be try and make every statement true once. However, since we see a range given in the question, we can try to find out a range as well and then try to see which statements fit into the range.

We see that there are two successive percentage changes from 2008 to 2010. So, we can use the successive percentage formula to calculate the effective percentage change from 2008 to 2010.

If there are two successive percentage changes of a% and b% respectively, then the effective percentage change is given by:
 (a + b +  \frac{ab}{100} )
Depending on whether the change is an increase or a decrease, a and b will be positive or negative. 
In this question, we have a 10% increase followed by a 5% decrease. Therefore, a = 10 and b = -5. Substituting the values of a and b in the equation above, effective percentage change = 4.5%.

This means, both 18000 and 19800 represent 104.5% (or 1.045) of the prices in 2008. For simplicity, let us take the effective percentage change as 5%.

Therefore, 18000 = 1.05 (Price in 2008) which gives us the ‘Price in 2008’ as 17,142. 0.5% of this number is approximately 80. Therefore, the price in 2008 should be around 17220. This is the lower bound. Clearly, statement I could be the price. Therefore, answer options B and C can be eliminated.

Taking the upper value of the price in 2010, 19800, we see that dividing 19800 by 1.05 gives us a number close to 18850. Now, 0.5% of this number will be approximately 90. Therefore, the price in 2008 should be 18940. This is the upper bound. Statement II and statement III could also be the price.

The correct answer option is E.

Notice that, we have tried dividing both 18000 and 19800 by 1.05. But since the actual percentage change is 4.5% only, we then corrected by finding out 0.5% of the resultant number and adding it. Remember that when you divide a number by 1.05, you will get a smaller number compared to, when you divide the same number by 1.045. This is why, the 80 or the 90 needs to be added, as in the calculations above.

Hope this helps!

Ters · Answer

how do you do the math quickly?

In 2009, the price of each Econolux car increased by 10 percent from t

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In 2009, the price of each Econolux car increased by 10 percent from t

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