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Whether x>y>z?
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12 Apr 2010, 14:21
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50% (01:48) correct 50% (02:04) wrong based on 350 sessions
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Whether x>y>z? (1) xy = xz+zy (2) x > y
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Re: is x>y>z
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13 Apr 2010, 02:41
xyztroy wrote: Whether x>y>z? 1. xy = xz+zy 2. x > y Q: is \(x>y>z\)? (1) \(xy=xz+zy\) First of all as RHS is the sum of two nonnegative values LHS also must be nonnegative. So \(xy\geq{0}\). Now, we are told that the distance between two points \(x\) and \(y\), on the number line, equals to the sum of the distances between \(x\) and \(z\) AND \(z\) and \(y\). The question is: can the points placed on the number line as follows zyx. If you look at the number line you'll see that it's just not possible. Sufficient. OR algebraic approach: If \(x>y>z\) is true, then \(xy=xz+zy\), will become \(xy=xzz+y\) > \(z=y\), which contradicts our assumption \(x>y>z\). So \(x>y>z\) is not possible. Sufficient. (2) \(x>y\) > no info about \(z\). Not sufficient. Answer: A.
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Re: is x>y>z
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12 Apr 2010, 16:35
IMHO E
from the given equation.
1. xy = xz+zy
we can have four cases,
a) x > z > y . The given equations gives no result. b) x > z and z < y. We get y=z c) x < z and z > y. We get x=z d) y > z > x. We get x=y
Though we have 3 (b,c and d)results which implies that x > y > z cannot be true. But the result from a is not clear. So we cannot confidently state that x > y > z is true. INSUFFICIENT.
2. x > y. INSUFFICIENT.
From 1 and 2.
given x > y.(Statement 2).We can only consider cases a, b and c.(From statement 1).
Again from a, b and c. NOT SUFFICIENT.
OA plz.



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Re: is x>y>z
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13 Apr 2010, 04:35
Bunuel wrote: xyztroy wrote: Whether x>y>z? 1. xy = xz+zy 2. x > y Q: is \(x>y>z\)? (1) \(xy=xz+zy\) First of all as RHS is the sum of two nonnegative values LHS also must be nonnegative. So \(xy\geq{0}\). Now, we are told that the distance between two points \(x\) and \(y\), on the number line, equals to the sum of the distances between \(x\) and \(z\) AND \(z\) and \(y\). The question is: can the points placed on the number line as follows zyx. If you look at the number line you'll see that it's just not possible. Sufficient. OR algebraic approach: If \(x>y>z\) is true, then \(xy=xz+zy\), will become \(xy=xzz+y\) > \(z=y\), which contradicts our assumption \(x>y>z\). So \(x>y>z\) is not possible. Sufficient. (2) \(x>y\) > no info about \(z\). Not sufficient. Answer: A. hello Brunel.. Can u please help me with my approach..where i have gone wrong..!! IMHO E from the given equation. 1. xy = xz+zy we can have four cases, a) x > z > y . The given equations gives no result. b) x > z and z < y. We get y=z c) x < z and z > y. We get x=z d) y > z > x. We get x=y Though we have 3 (b,c and d)results which implies that x > y > z cannot be true. But the result from a is not clear. So we cannot confidently state that x > y > z is true. INSUFFICIENT. 2. x > y. INSUFFICIENT. From 1 and 2. given x > y.(Statement 2).We can only consider cases a, b and c.(From statement 1). Again from a, b and c. NOT SUFFICIENT.



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Re: is x>y>z
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13 Apr 2010, 05:27
nverma wrote: hello Brunel..
Can u please help me with my approach..where i have gone wrong..!!
IMHO E
from the given equation.
1. xy = xz+zy
we can have four cases,
a) x > z > y . The given equations gives no result. b) x > z and z < y. We get y=z c) x < z and z > y. We get x=z d) y > z > x. We get x=y
Though we have 3 (b,c and d)results which implies that x > y > z cannot be true. But the result from a is not clear. So we cannot confidently state that x > y > z is true. INSUFFICIENT.
2. x > y. INSUFFICIENT.
From 1 and 2.
given x > y.(Statement 2).We can only consider cases a, b and c.(From statement 1).
Again from a, b and c. NOT SUFFICIENT.
For (a) you are checking scenario x > z > y. But if we have this case then the answer to the question is x>y>z is still NO. Let's do this in the way you are solving: Question: is \(z<y<x\)?(1) We have \(xy = xz+zy\). This statement is true. Now let's check in which cases is this true: As \(x\geq{y}\) (see my solution to see why this must be true) then there can be 4 scenarios as you've written: A. \(x=y\) > \(xy=0=xz+zy\) > \(x=y=z\). Which means that \(xy = xz+zy\) is true when \(x=y=z\). B. \(z<y<x\) zyx \(xy=xz+zy\) > \(xy=xzz+y\) > \(z=y\). Which means that \(xy = xz+zy\) is also true when \(y={z}<x\). Two points \(z\) and \(y\) must coincide. C. \(y<z<x\) yzx \(xy=xz+zy\) > \(xy=xz+zy\) > \(0=0\). Which means that \(xy = xz+zy\) is always true for any values of x, y, and z, when \(y<z<x\). You can see this on diagram: if x, y, and z are placed on number line as above then the distance between two points \(x\) and \(y\), on the number line, equals to the sum of the distances between \(x\) and \(z\) AND \(z\) and \(y\). D. \(y<x<z\) yxz \(xy=xz+zy\) > \(xy=x+z+zy\) > \(z=x\). Which means that \(xy = xz+zy\) is true when \(y<z=x\). Two points \(z\) and \(x\) must coincide. So we've got that statement as \(xy = xz+zy\) is true, only following 4 scenarios are possible: A. \(x=y=z\); B. \(z=y<x\); C. \(y<z<x\); D. \(y<z=x\). Among the above scenarios there is no case when \(z<y<x\). Hence the answer to the question "is \(z<y<x\)" is NO. Hope it's clear.
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Re: is x>y>z
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24 Sep 2010, 00:18
Bunnel, can you please explain why in the algebraic approach for st1 the signs have not been changed for solving xy = lxzl + lzyl , as your solution shows that this equation becomes (after removing the modulus signs) xy = xzz+y > z=y
Look forward to your reply.



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Re: is x>y>z
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24 Sep 2010, 00:36
abhi758 wrote: Bunnel, can you please explain why in the algebraic approach for st1 the signs have not been changed for solving xy = lxzl + lzyl , as your solution shows that this equation becomes (after removing the modulus signs) xy = xzz+y > z=y
Look forward to your reply. We know that for \(x\): When \(x\leq{0}\), then \(x=x\); When \(x\geq{0}\), then \(x=x\). So if \(x>y>z\) is true, then: As \(x>z\) (\(xz>0\)) > \(xz=xz\) AND as \(y>z\) (\(zy<0\)) > \(zy=(zy)=z+y\). So \(xy=xz+zy\), will become \(xy=xzz+y\) > \(z=y\). Hope it's clear.
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Re: is x>y>z
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24 Sep 2010, 11:59
Bunnel, thanks as always for the explanation! was considering (xz) as a negative number..It's clear now..



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Re: is x>y>z
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24 Sep 2010, 15:44
great explanation.
i think the algebraic method is easier to understand in this one.



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Re: is x>y>z
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01 Jun 2011, 06:27
xyztroy wrote: Whether x>y>z? 1. xy = xz+zy 2. x > y 1) xy = x+z+zy x = z so x>y>z is not true. Sufficient 2) no information is given about z. Insufficient.
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Re: is x>y>z
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06 Jun 2011, 03:07
good question indeed.
assuming the stem to be correct and then solving A is a cool approach.



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Re: is x>y>z
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06 Jun 2011, 18:55
I agree with slightly different approach for solving. You rock Bunuel!



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Re: is x>y>z
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10 Jun 2011, 12:56
xyztroy wrote: Whether x>y>z? 1. xy = xz+zy 2. x > y Alternative approach: Stmnt 1: xy = xz+zy If the RHS has to be equal to x  y, we have to get rid of 'z'. That will happen only when EITHER xz = x  z and zy = z  y i.e. x  z and z  y are both positive which implies x > z and z > y OR xz = (x  z) and zy = (z  y) i.e. x  z and z  y are both negative which implies x < z and z < y. (Anyway, in this case, RHS becomes y  x instead of x  y) In both the cases, the relation between x, y and z is not x>y>z. Hence statement 1 is sufficient to say "No, x>y>z does not hold." Statement 2 doesn't say anything about z so is obviously not sufficient alone. Hence A.
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Re: Whether x>y>z?
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09 Oct 2013, 00:06
xyztroy wrote: Whether x>y>z?
(1) xy = xz+zy (2) x > y We need to answer this question in YES or NO. Statement 2 gives us no information about z, so Insufficient. Statement 1 : xy >= 0 ; since the RHS term will always be 0 or positive. Hence, there can be 3 scenarios with 1st statement. Imagining a number line : 1) yzx : x>z>y and xy (Distance between x and y) is equal to the distance between x and z & z and y. So False. since y<z 2) z,y  x : x > z ; x > y ; y = z , Therefore distance between y and z is 0. Still gives us false since y = z and not greater than that. 3) yx,z : x = z ; x > y ; y < z , Therefore distance between x and z is 0. Still gives us false since y < z. In all the 2 scenarios we get FALSE. Hence sufficient. So only A is sufficient. Consider Kudos if the post helps anyone. Its a good way to motivate



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Re: Whether x>y>z?
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14 Apr 2014, 09:59
what about the scenario when X=Y=Z



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Re: Whether x>y>z?
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14 Apr 2014, 10:04
ongy wrote: what about the scenario when X=Y=Z The answer will remain the same. The question asks whether x>y>z. If x=y=z, then the answer to the questions "is x>y>z" is still NO.
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Re: Whether x>y>z?
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27 Nov 2019, 01:41
Bunuel wrote: xyztroy wrote: Whether x>y>z? 1. xy = xz+zy 2. x > y Q: is \(x>y>z\)? (1) \(xy=xz+zy\) First of all as RHS is the sum of two nonnegative values LHS also must be nonnegative. So \(xy\geq{0}\). Now, we are told that the distance between two points \(x\) and \(y\), on the number line, equals to the sum of the distances between \(x\) and \(z\) AND \(z\) and \(y\). The question is: can the points placed on the number line as follows zyx. If you look at the number line you'll see that it's just not possible. Sufficient. OR algebraic approach: If \(x>y>z\) is true, then \(xy=xz+zy\), will become \(xy=xzz+y\) > \(z=y\), which contradicts our assumption \(x>y>z\). So \(x>y>z\) is not possible. Sufficient. (2) \(x>y\) > no info about \(z\). Not sufficient. Answer: A. Bunuel Can we assume what the question is asking to be true and solve for each statement as done here for statement 1?? Posted from my mobile device




Re: Whether x>y>z?
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