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If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2)

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Re: If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2) [#permalink]

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If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2) [#permalink]

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New post 30 Jun 2015, 03:42
Bunuel wrote:
Hussain15 wrote:
If (x/y)>2, is 3x+2y<18?

(1) x-y is less than 2
(2) y-x is less than 2

It will be great to see how do you guys approach this lethal one.


I would solve this question with graphic approach, by drawing the lines. With this approach you will "see" that the answer is A. But we can do it with algebra as well.

\(\frac{x}{y}>2\) tells us that \(x\) and \(y\) are either both positive or both negative, which means that all points \((x,y)\) satisfying given inequality are either in I or III quadrant. When they are both negative (in III quadrant) inequality \(3x+2y<18\) is always true, so we should check only for I quadrant, or when both \(x\) and \(y\) are positive.

In I quadrant, as \(x\) and \(y\) are both positive, we can rewrite \(\frac{x}{y}>2\) as \(x>2y>0\) (remember \(x>0\) and \(y>0\)).

So basically question becomes: If \(x>0\) and \(y>0\) and \(x>2y>0\), is \(3x+2y<18\)?

(1) \(x-y<2\).

Subtract inequalities \(x>2y\) and \(x-y<2\) (we can do this as signs are in opposite direction) --> \(x-(x-y)>2y-2\) --> \(y<2\).

Now add inequalities \(x-y<2\) and \(y<2\) (we can do this as signs are in the same direction) --> \(x-y+y<2+2\) --> \(x<4\).

We got \(y<2\) and \(x<4\). If we take maximum values \(x=4\) and \(y=2\) and substitute in \(3x+2y<18\), we'll get \(12+4=16<18\).

Sufficient.

(2) \(y-x<2\) and \(x>2y\):
\(x=3\) and \(y=1\) --> \(3x+2y=11<18\) true.
\(x=11\) and \(y=5\) --> \(3x+2y=43<18\) false.

Not sufficient.

Answer: A.


Hi Bunuel,

In statement 1, you got y<2 and x<4 but when x=2 & y=1 or even your point x=4 & y=2 so x/y>2 is not satisfied because 2/1 or 4/2 is not bigger 2. How come still statement 1 sufficient?

Thanks
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Re: If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2) [#permalink]

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New post 30 Jun 2015, 08:07
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Mo2men wrote:

Hi Bunuel,

In statement 1, you got y<2 and x<4 but when x=2 & y=1 or even your point x=4 & y=2 so x/y>2 is not satisfied because 2/1 or 4/2 is not bigger 2. How come still statement 1 sufficient?

Thanks


Hi, responding to your Pm...

Since you have asked here only the above doubt...
y<2 and x<4.... you cannot take them as y=2 and x=4 as it is given both are less than these quantities...
so if y=1.9 .. statement 1 says x-y<2 or x-1.9<2 or x<3.9, so it satisfies x<4..
however if we take the values of x and y slightly more than the max possible(x<4).. x=4and (x<2)..y=2, we find value of eq <18.. so suff
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Re: If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2) [#permalink]

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New post 30 Jun 2015, 08:11
chetan2u wrote:
Mo2men wrote:

Hi Bunuel,

In statement 1, you got y<2 and x<4 but when x=2 & y=1 or even your point x=4 & y=2 so x/y>2 is not satisfied because 2/1 or 4/2 is not bigger 2. How come still statement 1 sufficient?

Thanks


Hi, responding to your Pm...

Since you have asked here only the above doubt...
y<2 and x<4.... you cannot take them as y=2 and x=4 as it is given both are less than these quantities...
so if y=1.9 .. statement 1 says x-y<2 or x-1.9<2 or x<3.9, so it satisfies x<4..
however if we take the values of x and y slightly more than the max possible(x<4).. x=4and (x<2)..y=2, we find value of eq <18.. so suff



Thanks for your response
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Re: If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2) [#permalink]

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New post 31 Jul 2016, 16:40
Hi!
can someone solve the question without graphical approach, though its my personal weakness to unable to solve using that.
Chetan4u , empowergmat , mathrevloution , harley ...
thanks
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Re: If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2) [#permalink]

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New post 12 Oct 2016, 06:00
Is there any trick for solving inequalities and modulus problems using number plugging?
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Re: If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2) [#permalink]

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New post 04 Jan 2017, 12:27
Experts!
Please help me with solution other than the one explained.
thanks
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Re: If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2) [#permalink]

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New post 19 Mar 2017, 19:26
If (x/y)>2, is 3x+2y<18?

x/y>2 means that both x & y have same sign.

(1) x-y < 2

Let x=3 & y=5/4....... check x/y=12/5=2.4>2

Check statement x-y<2.....3 -1.25=1.75 <2 ......So (3*3) + (2*5/4)<18..........(Note that you can choose positive numbers with narrow range such 2 & 5/6 and will achieve same answer Yes )

Let x=-10 & y=-1......check x/y=-10/-1=10>2

Check statement x-y<2.....-10+1=-9 <2............So (-10*3)+ (-1*2)<18.............Yes (Note that any negative numbers that satisfy both x/y> and fact 1 will always answer question with Yes)

Sufficient


(2) y-x < 2

Let x=3 & y=5/4....... check x/y=12/5=2.4>2

Check statement y-x<2.....1.25 - 3=-1.75 <2 ......So (3*3) + (2*5/4)<18.....Answer is Yes

Let x=10 & y=1.......check x/y=10>2

Check statement y-x<2.......1-10=-9<2................So (3*10) + (2*1)<18.....Answer is NO

Insufficient

Answer: A

This question needs high skills to spot the strategic numbers an spot pattern also.
Re: If (x/y)>2, is 3x+2y<18? (1) x-y is less than 2 (2)   [#permalink] 19 Mar 2017, 19:26

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