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Re: If X, Y and Z are positive integers, is X greater than Z – Y?
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01 Oct 2019, 07:38
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1
Bunuel wrote:
If X, Y and Z are positive integers, is X greater than Z – Y?
(1) X – Z – Y > 0
(2) Z^2 = X^2 + Y^2
(1) X – Z – Y > 0 \(X – Z – Y > 0......X>Z+Y\) As All are positive integers, X is greater than SUM of Z and Y, so Surely gtreater than their difference too...X>Z-Y Suff
(2) Z^2 = X^2 + Y^2 This says that Z is a hypotenuse with X and Y as other two sides.. May not help here \(X^2=Z^2-Y^2=(Z+Y)(Z-Y)=X*X\) Surely for this to be true, one of (Z+Y) and (Z-Y) should be GREATER than X and other LESS than Y.. But Sum of Z and Y has to be greater than difference of Z and Y. So, so X<Z+Y, but X>Z-Y. Suff
D, although statement I says X is the greatest while II says Z is the greatest, but statement II is well written to deduce the answer.
_________________
Re: If X, Y and Z are positive integers, is X greater than Z – Y?
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01 Oct 2019, 07:48
chetan2u wrote:
Bunuel wrote:
If X, Y and Z are positive integers, is X greater than Z – Y?
(1) X – Z – Y > 0
(2) Z^2 = X^2 + Y^2
(1) X – Z – Y > 0 \(X – Z – Y > 0......X>Z+Y\) As All are positive integers, X is greater than SUM of Z and Y, so Surely gtreater than their difference too...X>Z-Y Suff
(2) Z^2 = X^2 + Y^2 This says that Z is a hypotenuse with X and Y as other two sides.. May not help here \(X^2=Z^2-Y^2=(Z+Y)(Z-Y)=X*X\) Surely for this to be true, one of (Z+Y) and (Z-Y) should be GREATER than X and other LESS than Y.. But Sum of Z and Y has to be greater than difference of Z and Y. So, so X<Z+Y, but X>Z-Y. Suff
D, although statement I says X is the greatest while II says Z is the greatest, but statement II is well written to deduce the answer.
Edited (1) so that the statements do not contradict. Thank you.
_________________
Re: If X, Y and Z are positive integers, is X greater than Z – Y?
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01 Oct 2019, 11:15
If X, Y and Z are positive integers, is X greater than Z – Y?
Among X, Y and Z which one is greatest or which one is smallest is unknown.
(1) X – Z + Y > 0 Let X = 1, Y = 2 and Z = 3. Then X – Z + Y = 2 > 0 Thus, X = Z - Y. Hence X > Z - Y NO.
Let X = 3, Y = 2 and Z = 1. Then X – Z + Y = 4 > 0 Thus, X > Z - Y. Hence X > Z - Y YES.
INSUFFICIENT.
(2) Z^2 = X^2 + Y^2 This implies that Z is the greatest of all the three positive integers in fact they represent sides of a right angle triangle. So,
X^2 = Z^2 - Y^2 X^2 = (Z - Y) * (Z + Y) In ether case here X would be such that Z - Y < X < Z + Y. Eg. in the set of 3,4,5 Z = 5 and X takes any value among 3 or 4.
Hence X > Z - Y Always.
SUFFICIENT.
Answer (B).
_________________
Ephemeral Epiphany..!
GMATPREP1 590(Q48,V23) March 6, 2019 GMATPREP2 610(Q44,V29) June 10, 2019 GMATPREPSoft1 680(Q48,V35) June 26, 2019
Statement2: \(Z^{2}= X^{2} + Y^{2}\) As chetan2u told, this equality is about right angled triangle (z is a hypotenuse and two other sides of a triangle) —> according to features of a triangle, X+Y> Z or X+Z> Y or Z+Y> X —> ——————- X+Y> Z —> X> Z—Y (Always Yes) Sufficient
Re: If X, Y and Z are positive integers, is X greater than Z – Y?
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01 Oct 2019, 20:50
lnm87 wrote:
If X, Y and Z are positive integers, is X greater than Z – Y?
Among X, Y and Z which one is greatest or which one is smallest is unknown.
(1) X – Z + Y > 0 Let X = 1, Y = 2 and Z = 3. Then X – Z + Y = 2 > 0 Thus, X = Z - Y. Hence X > Z - Y NO.
Let X = 3, Y = 2 and Z = 1. Then X – Z + Y = 4 > 0 Thus, X > Z - Y. Hence X > Z - Y YES.
INSUFFICIENT.
(2) Z^2 = X^2 + Y^2 This implies that Z is the greatest of all the three positive integers in fact they represent sides of a right angle triangle. So,
X^2 = Z^2 - Y^2 X^2 = (Z - Y) * (Z + Y) In ether case here X would be such that Z - Y < X < Z + Y. Eg. in the set of 3,4,5 Z = 5 and X takes any value among 3 or 4.
Hence X > Z - Y Always.
SUFFICIENT.
Answer (B).
Again a silly error. Either all of them are equal X = Y = Z = 1 then X > Z - Y or such that X – Z + Y > 0. Thus, X > Z - Y always
For foolproof method it is best to say that statement 1 states that one side of a triangle is less than sum of other two sides. X + Y > Z.
Hence Statement 1 is SUFFICIENT. Answer (D).
_________________
Ephemeral Epiphany..!
GMATPREP1 590(Q48,V23) March 6, 2019 GMATPREP2 610(Q44,V29) June 10, 2019 GMATPREPSoft1 680(Q48,V35) June 26, 2019
Re: If X, Y and Z are positive integers, is X greater than Z – Y?
[#permalink]
Show Tags
01 Oct 2019, 22:12
chetan2u wrote:
Bunuel wrote:
If X, Y and Z are positive integers, is X greater than Z – Y?
(1) X – Z – Y > 0
(2) Z^2 = X^2 + Y^2
(1) X – Z – Y > 0 \(X – Z – Y > 0......X>Z+Y\) As All are positive integers, X is greater than SUM of Z and Y, so Surely gtreater than their difference too...X>Z-Y Suff
(2) Z^2 = X^2 + Y^2 This says that Z is a hypotenuse with X and Y as other two sides.. May not help here \(X^2=Z^2-Y^2=(Z+Y)(Z-Y)=X*X\) Surely for this to be true, one of (Z+Y) and (Z-Y) should be GREATER than X and other LESS than Y.. But Sum of Z and Y has to be greater than difference of Z and Y. So, so X<Z+Y, but X>Z-Y. Suff
D, although statement I says X is the greatest while II says Z is the greatest, but statement II is well written to deduce the answer.
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