percents question

[galit_d2d]

hi, learning now the plugging in principle. but I don't understand where should I plug in first in percent questions
like:
if 80% of a certain number x is 50% of y and y is 20% of z then what is x in terms of z?
1.5z
2.3z
3.z/4
4.z/5
5.z/8

the answer is 5. in the book they plug in 100 for x, I do understand why they took especially 100 but I can't understand why they chose x to plug in...
hope for a help...me galit

[Musiq]

hi, learning now the plugging in principle. but I don't understand where should I plug in first in percent questions
like:
if 80% of a certain number x is 50% of y and y is 20% of z then what is x in terms of z?
1.5z
2.3z
3.z/4
4.z/5
5.z/8

the answer is 5. in the book they plug in 100 for x, I do understand why they took especially 100 but I can't understand why they chose x to plug in...
hope for a help...me galit

Hi Galit,

This is a great picking numbers question.

X is needed to define Y.
Y is needed to define Z.

In theory, you could pick a number for Y and still get the answer, but its much more mathematically and mentally involved, rather than just picking a number for X.

There's also a further clue in how the question is phrased " What is X in terms of Z?". That tells us again that X is important.

[galit_d2d]

thanx for the explanation:)
but well...I don't seem to get this after all...
I tried plugging into z and well it did work that way, I think;)
well the answer was correct...

[mleviko]

Hi Galit,

I think you should plug-in as you wish, as long as it suits you. Try to think about a good plugged-in number that can handle the manipulations done to it in the question stem.

In a percentage question, the magical number is of course 100, and in my opinion you could plug-in 100 anywhere you wanted. Z is good enough to start with.

Z=100
and then: Y = 20 * Z / 100 = 20
and then: 80 * X / 100 = 50 * Y / 100 = 10
so: X = 10 * 100 / 80 = 100 / 8

We then have to recall that Z=100 , so look at the possible answers and see that one of them (5) is Z/8 = 100/8 in our case.


This was just to show that solving from Z backwars to X is possible as well, if you get quickly enough to the right solution.

Cheers

[Musiq]

thanx for the explanation:)
but well...I don't seem to get this after all...
I tried plugging into z and well it did work that way, I think;)
well the answer was correct...

Hi Galit,

Like mleviko correctly pointed out and like I have already said, this questiosn can be done with picking either of the 3 variables.

But, its best to start with X, since the equations are set up as such and also the question talks about X in terms of Z.

I only restate this because, as the problems keep getting harder and harder on the GMAT CAT, strategies like Picking Numbers and Backsolving best work when applied with a little more discretion AND focus.

One such place to look for direction, is the question itself.

[AleksandrM]

Forget about picking numbers. You are not being asked for a number. Just solve it using algebra:

.8x = .5y and y = .2z

then .8x =.5(.2z)

.8x = .1z

you are being asked to solve for x:

x = .1z/.8, then just multiply numerator and denominator by 100, and simplify into z/8.

[richardwang6430]

Great solution!