GMAT Data Analysis

questioner · **Joined:** Sun May 30, 2010 3:15 am **Posts:** 424

A computer retailer sells only TFT and LCD style monitors. According to the graph above, where the x-axis represents the day of the week and the y-axis represents the number of monitors sold, on which day was the ratio of the number of LCD monitors sold to total number of monitors sold the greatest?
A. Monday
B. Tuesday
C. Wednesday
D. Thursday
E. Friday

(C) The number of LCD sales is the difference between total sales and TFT sales. For each day of the week, we can determine the ratio of the number of LCD monitors sold to the total number of monitors sold:
Monday: (18 – 10)/18 = 4/9
Tuesday: (22 – 12)/22 = 5/11
Wednesday: (24 – 12)/24 = 1/2
Thursday: (26 – 16)/26 = 5/13
Friday: (26 – 14)/26 = 6/13.

The greatest fraction is 1/2, so the ratio on Wednesday is the largest.The correct answer is choice (C).
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* let L represent the number of LCD monitors sold
* let T represent the number of TFT monitors sold
Why is the ratio calculated as (L-T)/L? I would expect it to be L/(L+T).

Thanks

Gennadiy · **Joined:** Sun May 30, 2010 2:23 am **Posts:** 498

Quote:

Why is the ratio calculated as (L-T)/L? I would expect it to be L/(L+T).

Please, note, that the blue line is "TOTAL sales" line, not "LCD sales" one.

The ratio is calculated (using your denotation):
[(L + T) -T] / (L + T), where (L + T) is the total sales amount.
Let us simplify:
L / (L + T)

But the number of LCD monitors sold is not directly given in the chart. So we have Total and TFT values. Thus we use the formula
(Total – TFT) / Total

As you can see it is the same as L / (L + T), where L = Total – TFT and Total = L + T.

questioner · **Joined:** Sun May 30, 2010 3:15 am **Posts:** 424

How is half the largest share? Its equal for both LCD and TFT.

Gennadiy · **Joined:** Sun May 30, 2010 2:23 am **Posts:** 498

questioner wrote:

How is half the largest share? Its equal for both LCD and TFT.

We are NOT looking for the day, on which the LCD share was greater than the TFT share. We are looking for the day, on which the LCD daily share was the greatest among all LCD daily shares throughout the week.

Let's approximate fractions with percentages.
Monday: 4/9 ≈ 44.44%
Tuesday: 5/11 ≈ 45.45%
Wednesday: 1/2 = 50%
Thursday: 5/13 ≈ 38.46%
Friday: 6/13 ≈ 46.15%

As you can see the retailer never sold more LCDs than TFTs, but on Wednesday the LCD share was the greatest among the LCD shares throughout the week (On Thursday it was the lowest).

questioner · **Joined:** Sun May 30, 2010 3:15 am **Posts:** 424

Hi there.

When the question asks for the greatest ratio, I thought that it might have been one of the others, 1/2 is the largest number but the difference between the two values isn't the biggest. e.g. for every 1 of a there is 2 of b. But with other ans it was for every 4 of a there is 9 of b. Just so I fully understand, could you please explain ways to fully understand what's being asked in the gmat, because I got the maths right, just misinterpreted. Thanks.

Gennadiy · **Joined:** Sun May 30, 2010 2:23 am **Posts:** 498

Quote:

When the question asks for the greatest ratio, I thought that it might have been one of the others, 1/2 is the largest number but the difference between the two values isn't the biggest. e.g. for every 1 of a there is 2 of b. But with other ans it was for every 4 of a there is 9 of b.

It seems as "4 out of 9" operates with larger numbers and gives larger quantities. However, in order to compare this fractions, 1/2 and 4/9, you need to use a common denominator. The least common denominator is 18.

1/2 = 9/18
4/9 = 8/18

Now we can easily compare "9 of every 18 monitors" and "8 of every 18 monitors".

Another way is to imagine percentages.
1/2 = 0.50 or "1 of every 2 monitors" tells us about 50% of monitors.
4/9 = 0.44… or "4 of every 9 monitors" tells us approximately about 44% of monitors.

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