algebra- DS

[BeatIsb17]

Given that x ≠ 0, y ≠ 0, and (x+y) ≠ 0, is y/x > y/(x+y)

Statement #1: x > -1

Statement #2: y > -1


I started by simplifying the expression in question

y/x > y/(x+Y)

y(y+x) >xy

y^2 > 0

so , anyways this statement would always be true ,

why do we need the two statements ,

however the answer is 'E'

[GMATGuruNY]

Given that x ≠ 0, y ≠ 0, and (x+y) ≠ 0, is y/x > y/(x+y)

Statement #1: x > -1

Statement #2: y > -1


I started by simplifying the expression in question

y/x > y/(x+Y)

y(y+x) >xy

The step in red assumes that x and x+y are positive.
If x<0 but x+y>0, then the inequality symbol must flip from > to <.
If x>0 but x+y<0, then the inequality symbol must flip from > to <.
Since the signs of x and y are unknown, I don't recommend this approach.

Alternate approach:
y/x > y/(x+y)

y/x - y/(x+y) > 0

(xy + y²)/[x(x+y)] - xy/[x(x+y)] > 0

y²/[x(x+y)] > 0.

Since y is nonzero, y²>0.
Thus, the inequality in blue will hold true only if x(x+y) > 0.
Question stem, rephrased:
Is x(x+y) > 0?

Statements combined:
If x=1 and y=1, then x(x+y) > 0.
If x=-1/2 and y=2, then x(x+y) < 0.
INSUFFICIENT.

The correct answer is E.

[BeatIsb17]

thanks

another one :

The system of equations has how many solutions?

3x - 6y = 9

2y - x - 3 = 0




My way : i wanna know the flaw in thought process

3x - 6y = 9

-> x - 2y = 3 -a

now, 2y - x - 3 =0
-> x - 2y = -3 -b

adding a and b

2x -4y = 0

-> x=2y

-> multiple solutions

but other way

subtracting b from a

we get

0=9 absurd

hence no solution ..

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Hi BeatIsb17,

GMAT questions can often be approached in more than one way, so taking an overly technical approach is usually NOT a good idea (it takes longer than other approaches and you'll be more likely to make a little mistake along the way).

Here, with just a little bit of organizational work, you should be able to find the 'key' to this question...

3X - 6Y = 9

Let's simply the first equation by dividing by 3...

X - 2Y = 3

Now, the second equation:

2Y - X - 3 = 0

If we rewrite the second equation we get...

-3 = X - 2Y

X - 2Y = -3

Looking at the two equations side-by-side, we see...

X - 2Y = 3
X - 2Y = -3

These are both linear equations - and a linear equation can't be equal to two different numbers. If you graph these equations, you'll end up with 2 PARALLEL lines, so there are 0 solutions to this pair of equations.

GMAT assassins aren't born, they're made,
Rich

[BeatIsb17]

thanks Rich ... Yeah I tried over simplification , number line clears the air and tells that both of the equations represent two parallel lines ..and no solution ... thanks for prompt answers

[Mo2men]

thanks Rich ... Yeah I tried over simplification , number line clears the air and tells that both of the equations represent two parallel lines ..and no solution ... thanks for prompt answers

If you have a linear equation in 2 variables, you need at least 2 equations to solve for both variables. The general form is :

ax + by =c

dx + ey =f

If (a/d)=(b/e)=(c/f) then there are infinite solutions. Any point satisfying one equation will always
satisfy the second.

If (a/d)=(b/e) and not equal to (c/f) then there is no such x and y which will satisfy both equations. No solution.

In case above, the second statement applies.