VIC problems – plugging in numbers vs. algebraic solution

[zliron]

Hi,

I tend to suffer from "choosing the wrong strategy at the wrong questions" when I need to choose between plugging in numbers and solving the questions using algebra.

I must admit that I prefer solving questions which is not very efficient at the GMAT... but sometimes (for example - please find below a question for which plugging in numbers in not an efficient strategy, as also mentioned in the solution)

Could you please advise where is it clever to use each strategy?

Thanks
Liron


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A publishing company produced a record high of 180 books today. In the 9 days prior to today, the same publishing company had produced an average (arithmetic mean) of x books per day. If today’s record high increased average daily production to y books per day, what is x in terms of y?

- (9y+180)/10
- (10y+180)/9
- (9y-180)/9
- (10y-180)/9
- 10y/9-180

Because this is a Variable In Answer Choices (VIC) problem, we can also use a Picking Numbers and Calculate a Target approach. However, for this problem, the Picking Numbers method turns out to be cumbersome and time-consuming; it is more efficient to tackle it using Direct Algebra.

[Rijul Negi]

9 days prior to today,
avg = x books per day
total no of books = 9x


now,
avg = y books per day
tot no of books = 10y
no of books produced today = 180


(9x+180)/10 = y
9x+180 = 10y
x = (10y-180)/9

Option D

[jnelson0612]

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A publishing company produced a record high of 180 books today. In the 9 days prior to today, the same publishing company had produced an average (arithmetic mean) of x books per day. If today’s record high increased average daily production to y books per day, what is x in terms of y?

- (9y+180)/10
- (10y+180)/9
- (9y-180)/9
- (10y-180)/9
- 10y/9-180

I actually disagree that picking a number is so difficult. It can require you to do some math calculations, but I think it's a good thing to be sharp at such calculations.

In this problem, I want to pick a number of books to be the average of the prior 9 days. I am going to say x=20, so there were 180 total books over the last 9 days. 180 added to the 180 on the tenth day gives me 360 books over 10 days, which averages to 36 books. Thus y=36.

Okay, so x=20 and y=36. Question is what is x (mentally ignore the "in terms of" on any VICs question). x=20, so that is our target number.

At this point it's just a matter of cranking through the answer choices using y=36 to find 20. I would quickly eliminate:

A--I can tell that I will not get an integer when I divide the top by 10.
E--will give me a negative number.

Those are the easy two; let's actually calculate the rest.
B--gives me 360 +180 = 540. Dividing that by 9 will give me 60, not 20.
C--I can look at that and know it will be too small.
D--bingo! There's the winner.

[jnelson0612]

Also, Ron has some really good tips on when to pick numbers in this thread: vics-chapter-7-t2411.html

Please let us know if you have further questions!

[rkafc81]

hi - i'm having trouble setting up problems like this one using the methodology outlined in the Thursday's with Ron session titled "Organisation for Word Problems".

Can someone please explain how you would go about identifying the quantities, mathematical relationships and then forming a chart for this problem?

thanks!

[jlucero]

Work = rate * time

First 9 Days: 9x = x * 9
Today: 180 = 180 * 1

All 10 Days: 9x + 180 = y * 10

Solve for x.

[rkafc81]

thanks Joe...

what's a good general technique/framework to translate these kinds of problems ? i.e. what method/thought process do you typically follow?

i.e.

step 1. read through the problem
step 2. read again, working out what quantities there are
step 3. work out what mathematical relationships are present
step 4. relate the quantities algebraically using the mathematical relationships from step 4#
step 5. solve

the way you did it, it made it look so easy :) I know these kinds of problems aren't mathematically tricky, they're just tricky to set up and organise...

thanks

[jlucero]

That's the GMAT for you- simple to solve, tricky to set up. Personally, I start these questions by immediately writing down the formula W = r * t. It's habit at this point after seeing so many questions of this type, but that instant recognition is exactly what's going to help you get faster on the real test. The rest of the way is just filling in the numbers that work in this particular scenario, but if I'm very comfortable with one way of doing these types of problems, I'm not thrown off by the differences between specific problems.