Question: Removing x

Comment on Removing x

Shouldn't statement 2 simplify to 7M-3. A typo perhaps?
gmat-admin's picture

Good catch! At 3:18 in the video, the expression should simplify to 7M-3 (not 6M-3). I'll edit the video accordingly.
In the meantime, I should note that this does not change the fact that statement 2 is not sufficient.

Sum of N-1 Nos. = MN - x

Why we used same M here when we have told that mean is decreased by 3, immediately below that you have did so but first step looks like something wrong.
gmat-admin's picture

BEFORE we subtract x from the list, the sum = MN
So, AFTER we subtract x from the list, the NEW sum = MN - x

Note: At this point, we haven't yet addressed the fact that the mean has decreased by 3 (we use that information later in the solution)

Once we know that the sum of the REMAINING numbers = MN - x, the NEW mean = (MN - x)/(N - 1)

NOW, we'll use the fact that the NEW mean is 3 less than the old mean.
That is, the NEW mean = M - 3

So, we can write: M - 3 = (MN - x)/(N - 1)

Does that help?


Is there some kind of rule of thumb to determine whether (when there are 3 unknowns) an equation can be used to be plugged in into another one? In the first statement, it is very obvious that it can be plugged in. In the second then it seems obvious that it isn´t possible, and yet I am spending quite some time trying to think of a scenario where I might be able to plug it in. I kind of hestitate in those situations.


gmat-admin's picture

We can always plug an equivalent expression into an equation, but there's no rule that will guarantee that this will prove fruitful.

That said, if an equation resembles the target equation, then there's a higher likelihood that plugging in will help.

So generally, if the Statement equation doesn´t somehow resemble the target equation, it won´t help?

Like, if I look for x+y.

equation= 3x+3y= 15. YES

equation= 3x+2y = 15 NO, since there is no way to add/substract/multiply/divide in a manner that resembles x+y and thus seperates x+y to one side with numbers only on the other side?


gmat-admin's picture

If we're talking about replacing an algebraic expression with something that is equivalent, then "Yes, the expression we want to substitute must be such that we can replace it with its equivalent expression .

As such, the two expressions should look "similar"
Of course SIMILAR is a pretty subjective word.

For example, let's say I want to determine the value of 5x + 5y.
If I'm told that x + y = 11, then I may say "hey, the coefficients of 5x and 5y are the same (both coefficients are 5), AND the coefficients of x and y are the same (both coefficients are 1)"

Through this observation, I might take 5x + 5y and factor it to get 5(x + y)
At this point, I can replace (x + y) with 11 to get:
5x + 5y = 5(x + y) = 5(11) = 55

Perfect. In this case, it was useful to see that 5x + 5y looks similar to x + y.

However, let's say I want to determine the value of 5x - 5y.
If I'm told that x + y = 7, then I still might observe that 5x - 5y and x + y = 7 looks similar (similar structure of coefficients).
However, when I do some factoring, I get 5(x - y)
So, knowing that x + y = 7 doesn't help me determine the value of 5x = 5y

Here's another example:
Let's say I want to determine the value of 2x + 3y.
If I'm told that 5x = 25 - 7.5y, would this be enough to determine the value of 2x + 3y?
Well, the two expressions don't look similar.
However, with some rearranging, we get: 5x + 7.5y = 25
Factor to get: 2.5(2x + 3y) = 25
Divide both sides by 2.5 to get: 2x + 3y = 10
Aha! We can determine the value of 2x + 3y, even though 5x + 7.5y = 25 doesn't look similar to 2x + 3y

So, I wouldn't place too much emphasis on whether two expressions look similar.

Does that help?


Totally helps, thanks Brent!

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