great collection !!1 thanks bunuel !!

Problem with your solution is that the red part is not correct.

\frac{x}{y}>1 does not mean that x>y. If both x and y are positive, then x>y, BUT if both are negative, then x<y.

From (2) \frac{x}{y}>1, we can only deduce that x and y have the same sigh (either both positive or both negative).

When we consider two statement together:

From (1): 2x-2y=1 --> x=y+\frac{1}{2}

From (2): \frac{x}{y}>1 --> \frac{x}{y}-1>0 --> \frac{x-y}{y}>0 --> substitute x from (1) --> \frac{y+\frac{1}{2}-y}{y}>0--> \frac{1}{2y}>0 (we can drop 2 as it won't affect anything here and write as I wrote \frac{1}{y}>0, but basically it's the same) --> \frac{1}{2y}>0 means y is positive, and from (2) we know that if y is positive x must also be positive.

OR: as y is positive and as from (1) x=y+\frac{1}{2}, x=positive+\frac{1}{2}=positive, hence x is positive too.

Answer: C.

Hope it's clear.
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hear it is not give that X is also a integer,

S1: if X=1/2 or -1/2 then also Y is integer ,

in this case Ans: B

Is i am missing somthing?
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3. is X^2+Y^2 > 4a?

1) (X+Y)^2= 9a

x^2+2xy+Y^2=9a

Insufficient

2) (X-y)^2= a

x^2-2XY+Y^2 = a

Insufficient

Combining 1 & 2, 2(X^2+Y^2)=10a X^2+Y^2 = 5a, thus C

Whoa, inequalities and AV's did me in for my first GMAT! Great thread!

OA' s and solutions for all the problems are given in my posts on pages 2 and 3.

OA for this question is E.

When we consider statement together we'll have: x^2+y^2=5a. Now, if x, y and a are different from zero (for example: x=3, y=4 and a=5) then x^2+y^2=5a>4a and the answer to the question is YES, but if x=y=a=0, then x^2+y^2=5a=4a=0 and the answer to the question is NO. Two different answers, thus not sufficient.

Hope it's clear.
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Hi Bunuel,
I forgot to thank you for these great questions and solutions. You are the BEST!!!!

If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1

(2) y<1, as we concluded y is never negative, and we are given that y is an integer, hence . Sufficient.

In the above problem, it is very obvious that Y is not equal to 0 from the 2nd statement.
Do you think GMAT questions will have this much obvious statements?

Doubt :The question is is |N|<4 ,from statement 2 we can see that n can only be a fraction or its value lies between 0 and 1 like say 1/2 .1/3 etc.same for negative fractions
for example for n =1/2 , 1/(|1/2|)=2 which is greater than n=1/2

Also for n=-1/2,1/(|-1/2|)=2 which is greater than n=-1/2


for negative integers also its true ,say we take n=-3 ,
1/|n|=1/3 which is greater than n=-3



But point to note is that both negative nos and fractions are less than 4 ,so this statement is equally sufficient ,correct me if i am wrong !!!!

1. If 6*x*y = x^2*y + 9*y, what is the value of xy?
(1) y – x = 3
(2) x^3< 0
First, devide the whole equation by y, and
6*x=x^2+9 => x^2-6*x+9=0 => (x-3)^2=0, x=3, -3
(1) We know x could be 3 oro -3, let's put these two numbers in and see, if x=3, y =6, xy= 18,... and if x=-3, y =0, xy= 0. We can't know for sure what the value of that is. .... Insufficient
(2)Now we know X^3 is less than 0, then x must be less than 0 too. that means it has to be -3, then the answer comes out! .... Sufficient
B

2. If y is an integer and y = |x| + x, is y = 0?
(1) x < 0
(2) y < 1
(1)Sufficient
(2)Sufficient, y couldn't be negative, the least it could be is 0.
D
3. Is x^2 + y^2 > 4a?
(1) (x + y)^2 = 9a
(2) (x – y)^2 = a

(1) (x+y)^2= x^2+y^2+2x*y
9a=x^2+y^2+2x*y Still Insufficient

(2) (x-y)^2=x^2+y^2-2x*y
a=x^2+y^2-2x*y Insufficient

Sum up equations (1) and (2) , then we can get 10a=2(x^2+y^2) => 5a=x^2+y^2, and we know a is necessarily positive since (x – y)^2 = a
With both factors, we can know x^2 + y^2 >4a

the answer is C

4. Are x and y both positive?
(1) 2x-2y=1
(2) x/y>1

(1)Insufficient
(2)that only tells you x is greater than y Insufficient
(1) and (2) together: x-y=0.5, and x is great than y, Insufficient
E


5. What is the value of y?
(1) 3|x^2 -4| = y - 2
(2) |3 - y| = 11

(1) we only know y must be positive, insufficient
(2)y coule be -8 or 14 insufficient
BOth (1) and (2): from statement (1) weve learned that y must be a positive number, along with statement (2) we know y is 14
the answer is C

6. If x and y are integer, is y > 0?
(1) x +1 > 0
(2) xy > 0

(1)x>-1, we wouldnt know anything about y with that, insufficient
(2)xy>0, if x is less than 0, then y too has to be less than 0 Insufficient

both (1) and (2): xy>0, x>-1, x could be 0 or any positive integer, and even if x=0, y still has to be great than 0 coz xy>0 Sufficient

C

7. |x+2|=|y+2| what is the value of x+y?
(1) xy<0
(2) x>2 y<2

(1)xy<0, that means either x or y is positive and the other negative. seems like x+y= -4, coz x+2=-2-y => x+y=-4, sufficient
(2) Sufficient too, same reasons as above

D

8. a*b#0. Is |a|/|b|=a/b?
(1) |a*b|=a*b
(2) |a|/|b|=|a/b|

(1) a*b has to be positive, a/b has to positive too. Sufficient

(2) we already know that for sure, Insufficient

A

9. Is n<0?
(1) -n=|-n|
(2) n^2=16

(1)since the absolute value must be positive, so we know n has to be negative, or 0 Not Sufficient
(2)ok, n could be 4 or -4, so what? Insufficient
BOth (1) and (2) together: ok, n could be 4 or -4, and it's less than or equal to zero, so it must be -4 Sufficient

C

10. If n is not equal to 0, is |n| < 4 ?
(1) n^2 > 16
(2) 1/|n| > n

(1) n>4 or n<-4, |n| must be greater than 4 sufficient
(2)we only know n<1, |n| could be greater than 4 if n < -4 insufficient

A

11. Is |x+y|>|x-y|?
(1) |x| > |y|
(2) |x-y| < |x|

Just leave it for a while


12. Is r=s?
(1) -s<=r<=s
(2) |r|>=s

(1) Not sufficient
(2) Not sufficient
Together: Still Not sufficient

13. Is |x-1| < 1?
(1) (x-1)^2 <= 1
(2) x^2 - 1 > 0

ill solve it next time

Great stuff.

Learned a lot from this set.
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