When to simplify problem?

Question

okay this might be a dumb question but, on a DS problem that asks:

"Is x^2 greater than x?"

why cant I simply it by dividing both sides by x and then getting "is x greater than 1?"

btw this is problem 81 of Quant (green book)

CMcAboy · Answer

Well, that would normally be fine, but there is 1 exception. If x were to be zero, you would not be able to divide x by both sides. (0 / 0 is undefined)

But that would be true for all integers not equal to 0.

humkate · Answer

so does that mean whenever i see a x^2 in the problem i shouldn't simplify like the way i did?

beyondgmatscore · Answer

Yes - In general, you should not cancel out x from such expressions if you have no other information about x. Of course, if the question stem explicitly mentions that x is not equal to 0 and you know about the sign that x is supposed to have in case of an inequality, then you can cancel x and manipulate the inequality according to the sign of x. But, as a rule, curb your instinct to cancel x right away.

gladvijay · Answer

If x2 > x then x > 1 or x < -1 
so unless you know the sign you cannot divide by x; coz when you divide the inequality with a -ve number you have to flip the sign as well..

hope it helps

Bunuel · Answer

Never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero. You would have two cases when dividing x^2>x by x: if x<0 you should flip the sign and write x<1 but if x>0 you should remain the sign and write x>1. From above, x^2>x holds true if x<0 or x>1. Solving inequalities: x2-4x-94661.html#p731476 inequalities-trick-91482.html data-suff-inequalities-109078.html range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535 everything-is-less-than-zero-108884.html?hilit=extreme#p868863 DS questions to practice: search.php?search_id=tag&tag_id=184 PS questions to practice: search.php?search_id=tag&tag_id=189 Hope it helps.

humkate · Answer

thank you!

how about this DS problem on gmat prep:

is (x+1)/(x-3) < 0 ?

1. -1 < x < 1
2. x^2 -4 <0

Can I cross multiply the beginning inequality and get x+1 < 0 ?
So does the problem become "is x < -1 "?

Bunuel · Answer

Again: never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero. So you can not multiply both sides of the equation by x-3 as you don't know whether x-3 is positive or negative. The question above is discussed here: data-suff-inequalities-109078.html P.S. Please post specific questions in PS or DS subforum.

PTK · Answer

Kate you have to brush-up your math concepts first.

mikeadwin · Answer

thank you all who contributed, it helped me I was seraching for this too

When to simplify problem?

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