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Intern  Joined: 07 Mar 2019
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I recently started studying for the GMAT and my quant skills are lacking. I am struggling to understand why I cannot simply this answer further. This was the final solution to a problem:

$$\frac{zp+q}{x(zp+q)+yp}$$

Why does the zp+q in the numerator and denominator not cancel out? I see it as $$\frac{1}{x+yp}$$

I appreciate any feedback.
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If yp is multiply with x(zp+q) we can cancel. but in here x(zp+q) +yp is addition form .
that's why we can't cancel (zp+q)
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Not to sound rude, I would recommend that you revisit your math concepts. If you are stuck at such a basic concept, then chances are that you would need work on average to tough areas.

No to answer your query, please remember that ONLY common items cancel out in numerator and denominator.
Let's consider zp+q = A, now the expression becomes $$\frac{A}{xA+yp}$$. Do you notice that the term "yp" do not have the so-called common recent A. Hence, A is not actually the common element in the numerator and denominator. Therefore, we cannot cancel out A, i.e zp+q. I hope this explanation helps.

All the best.

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Hi Zixzix

your question is so basic and fundamental. You have a revise the basic rules of arithmetic.
This thread would help you learn every thing needed for GMAT. Start with the arithmatics, number properties and fractions.
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Senior Manager  G
Joined: 25 Feb 2019
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Hi ,

this is a fundamental question.

I would try to explain

we can only cancel in scenario where we have experssion in the form or multiplication

example

x*(x+y)*(y+z)

here these all are in multiply and each one in ()

is considered as a single unit

but if you put + or - then

we have ,

(x+x+y) *(y+z) then these two in () become two units

now x+x+y will be treated as a single unit for division operation

hope it helps

Posted from my mobile device
GMAT Tutor G
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1
A lot of people have questions like this, and when people start reviewing math again for the GMAT, it's in these kinds of situations where mistakes are most common. When you are canceling in a fraction, anything you cancel must be a factor of the entire numerator and of the entire denominator. So if you want to cancel something, you must be able to rewrite the numerator and denominator as products, where the thing you're canceling is part of each product. So in the basic case, with numbers:

8/36

We can rewrite the numerator and denominator as products, both containing the number '4':

(4)(2) / (4)(9)

and now we cancel the '4' to get 2/9.

The algebraic case is similar. I'll give one example where we can factor and cancel (using quadratic factoring) :

$$\frac{x^2 - 7x + 12}{x^2 - 5x + 6} = \frac{(x-3)(x-4)}{(x-3)(x-2)} = \frac{x-4}{x-2}$$

Notice we can cancel the "x-3" because it is part of a product in both the numerator and denominator. Or in this case you can cancel:

$$\frac{ab + ac}{ab - ac} = \frac{(a)(b+c)}{(a)(b-c)} = \frac{b+c}{b-c}$$

because "a" is a factor of both the numerator and denominator. But in cases like this, say:

$$\frac{xz + y}{xz - y}$$

no cancellation is possible, because there is no identical factor we can create in both the numerator and denominator (in fact there's no factorization we can even do here). So even though the numerator and denominator appear quite similar here, that is no guarantee that any cancellation will be possible - you need to see what factoring you can do.

Factoring is one of the most useful techniques in all of algebra, so if it's something you're not completely comfortable with yet, I'd suggest practicing it a lot, because it's a crucial skill for GMAT math.
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Intern  Joined: 25 Feb 2019
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IanStewart wrote:
A lot of people have questions like this, and when people start reviewing math again for the GMAT, it's in these kinds of situations where mistakes are most common. When you are canceling in a fraction, anything you cancel must be a factor of the entire numerator and of the entire denominator. So if you want to cancel something, you must be able to rewrite the numerator and denominator as products, where the thing you're canceling is part of each product. So in the basic case, with numbers:

8/36

We can rewrite the numerator and denominator as products, both containing the number '4':

(4)(2) / (4)(9)

and now we cancel the '4' to get 2/9.

The algebraic case is similar. I'll give one example where we can factor and cancel (using quadratic factoring) :

$$\frac{x^2 - 7x + 12}{x^2 - 5x + 6} = \frac{(x-3)(x-4)}{(x-3)(x-2)} = \frac{x-4}{x-2}$$

Notice we can cancel the "x-3" because it is part of a product in both the numerator and denominator. Or in this case you can cancel:

$$\frac{ab + ac}{ab - ac} = \frac{(a)(b+c)}{(a)(b-c)} = \frac{b+c}{b-c}$$

because "a" is a factor of both the numerator and denominator. But in cases like this, say:

$$\frac{xz + y}{xz - y}$$

no cancellation is possible, because there is no identical factor we can create in both the numerator and denominator (in fact there's no factorization we can even do here). So even though the numerator and denominator appear quite similar here, that is no guarantee that any cancellation will be possible - you need to see what factoring you can do.

Factoring is one of the most useful techniques in all of algebra, so if it's something you're not completely comfortable with yet, I'd suggest practicing it a lot, because it's a crucial skill for GMAT math.

Manhattan Prep Instructor G
Joined: 04 Dec 2015
Posts: 833
GMAT 1: 790 Q51 V49 GRE 1: Q170 V170 Show Tags

Zixzix wrote:
I recently started studying for the GMAT and my quant skills are lacking. I am struggling to understand why I cannot simply this answer further. This was the final solution to a problem:

$$\frac{zp+q}{x(zp+q)+yp}$$

Why does the zp+q in the numerator and denominator not cancel out? I see it as $$\frac{1}{x+yp}$$

I appreciate any feedback.

The reason is that to simplify a fraction, you have to divide the entire numerator and the entire denominator by the same thing.

In your example, you've divided the whole numerator by zp+q. That is, (zp+q)/(zp+q) = 1, so you've turned the numerator into 1.

However, you've only divided part of the denominator by zp + q. You divided the x(zp+q) part, but you would also have to divide the yp part.

Always divide the whole numerator and the whole denominator, even if there's addition or subtraction in one of them!
_________________ Chelsey Cooley | Manhattan Prep | Seattle and Online

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