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If x, y, and z are all distinct positive integers and the percent
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27 Mar 2016, 13:36
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If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x? (1) y is prime (2) z = 9
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Re: If x, y, and z are all distinct positive integers and the percent
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27 Mar 2016, 14:08
If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x? The percent increase from x to y is equal to the percent increase from y to z: \(\frac{(yx)}{x}*100 = \frac{(zy)}{y}*100\) > \(xz = y^2\) (\(0 < x < y < z\)) (1) y is prime: y = 2, then \(xz = 4\), and since \(0 < x < y < z\) and all of them are positive integers, then x = 1 and z = 4. y = 3, then \(xz = 9\), and since \(0 < x < y < z\) and all of them are positive integers, then x = 1 and z = 9. y = 5, then \(xz = 25\), and since \(0 < x < y < z\) and all of them are positive integers, then x = 1 and z = 25. y = 7, then \(xz = 49\), and since \(0 < x < y < z\) and all of them are positive integers, then x = 1 and z = 49. ... We can see a pattern there, in all cases x = 1. Sufficient. (2) z = 9 > \(9x = y^2\). Case 1: x = 1 and y = 3; case 2: x = 4 and y = 6. Not sufficient. Answer: A.
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Re: If x, y, and z are all distinct positive integers and the percent
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08 Jun 2016, 08:48
Hello Bunuel,
I couldnt understand why (0<x<y<z). We could have selected the values of x,y and z as 4,2 and 1 or 9,3 and 1. The percentage changes for the above 2 cases would be negative but the changes would be equal. It was based on these 2 different sets that I ruled out option A as a possibility.
Could you please suggest where I might be going wring?
Regards, Amit



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Re: If x, y, and z are all distinct positive integers and the percent
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08 Jun 2016, 09:01
gmat_for_life wrote: Hello Bunuel,
I couldnt understand why (0<x<y<z). We could have selected the values of x,y and z as 4,2 and 1 or 9,3 and 1. The percentage changes for the above 2 cases would be negative but the changes would be equal. It was based on these 2 different sets that I ruled out option A as a possibility.
Could you please suggest where I might be going wring?
Regards, Amit hi anit, the Q stem talks of % increase  "the percent increase from x to y", so we cannot take % decrease by taking x>y>z....
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Re: If x, y, and z are all distinct positive integers and the percent
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08 Jun 2016, 09:21
Oh right! My mistake! thanks a lot Chetan!



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If x, y, and z are all distinct positive integers and the percent
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04 Jul 2017, 17:52
sahilkak007@gmail.com wrote: If x, y, z are all distinct positive integers and percent increase from x to y is equal to the percent increase from y to z , what is x?
1) y is a prime 2) z=9 Hi.. I would simplify for myself by taking same % increase as multiplication by same numberAlthough Q becomes a bit easier with finding value of x, I'll answer it if say we were to find value of y as it would be a bit more challenging. For finding x as the Q presently states, statement I is sufficient as shown below. x will always be 1. A Say we were to find value of y1) y is prime.. Starting with 1, I can find various combinations. Say y is 2.... 1, 1*2, 2*2......1,2,4 Say y is 3.....1, 1*3, 3*3...... 1,3,9 Say y is 5......1,1*5,5*5.....1,5,25 Insufficient 2) z=9 Possible values.. 1,3,9.....1,1*3,3*3 4,6,9....4,4*(1.5),6*(1.5) Two possible ways.. Insuff Combined.. ONLY 1,3,9 remains. Sufficient C
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Re: If x, y, z are all distinct positive integers and percent increase
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04 Jul 2017, 19:10
sahilkak007@gmail.com wrote: If x, y, z are all distinct positive integers and percent increase from x to y is equal to the percent increase from y to z , what is x?
1) y is a prime 2) z=9 simplifying the stem as percent increase from x to y is equal to the percent increase from y to z (yx)/x = (zy)/y y^2xy = xzxy y^2 = xz(given in stem) so x=?? (1) if y =3 then x=1,z=9 or x=9 ,z=1 Not suff (2) no info of other integers clearly insuff.. Combined z=9 and y is prime then, y^2= x*9 as 9 = 3^2 = Prime ^2, then for x,any value but 1 leaves y not anymore a prime number rather x=1 leaves y =3 i.e Y^2(3^2) = x(1) * 9(z) thus x=1,y=3 ,z=9 suff Ans C sahilkak007@gmail.comPlease confirm OA



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Re: If x, y, z are all distinct positive integers and percent increase
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04 Jul 2017, 21:10
Wrong; Y= %increase* x= prime Prime= no. itself * 1 Comparing both, since x and y are distinct, x can only be 1, hence statement 1 is sufficient



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Re: If x, y, and z are all distinct positive integers and the percent
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05 Jul 2017, 03:53
Bunuel wrote: If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x?
The percent increase from x to y is equal to the percent increase from y to z: \(\frac{(yx)}{x}*100 = \frac{(zy)}{y}*100\) > \(xz = y^2\) (\(0 < x < y < z\))
(1) y is prime:
y = 2, then \(xz = 4\), and since \(0 < x < y < z\) and all of them are positive integers, then x = 1 and z = 4. y = 3, then \(xz = 9\), and since \(0 < x < y < z\) and all of them are positive integers, then x = 1 and z = 9. y = 5, then \(xz = 25\), and since \(0 < x < y < z\) and all of them are positive integers, then x = 1 and z = 25. y = 7, then \(xz = 49\), and since \(0 < x < y < z\) and all of them are positive integers, then x = 1 and z = 49. ...
We can see a pattern there, in all cases x = 1. Sufficient.
(2) z = 9 > \(9x = y^2\). Case 1: x = 1 and y = 3; case 2: x = 4 and y = 6. Not sufficient.
Answer: A. Great approach, Bunuel I have learnt so much from you!!
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Re: If x, y, and z are all distinct positive integers and the percent
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19 Aug 2018, 22:00
(yx)/x=(zy)/y >> y^2=x*z 1. if y is prime, y^2 has only 3 factors 1,y,y^2. since x<y<z, x must be 1 2. 3^2=1*9 3^6=3^4*3^2



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Re: If x, y, and z are all distinct positive integers and the percent
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28 Jun 2019, 16:56
+int x<y<z Let a% = some % increase a%*x = y a%*y = z
(1) y is prime Say y is 2, and a is 100% If x = 1, then y is 2 and z is 4, this works.
Say y is 3, and a is 100% x would have to be 1.5 for y to be 3, this is not possible due to int constraint.
Say y is 3 and a is 50% Then x could be 2, and a 50% increase gives us y=3 BUT, 50% increase of 3 gives z=4.5, which is again not possible.
We can conclude that the only way to get the same percent increase and to maintain all int values is if x starts at 1. Sufficient. This makes sense because only 1 is a multiple of every number so essentially 1*y=y and then y^2 = z. This works for many cases but only if x=1.
(2) z = 9 Say a is 200%, If x = 1 then y could be 3 and z could be 9 Say a is 50%, If x = 4 then y could be 6 and z could be 9 Not sufficient.



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Re: If x, y, and z are all distinct positive integers and the percent
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01 Jul 2019, 02:59
Another way to solve A let's say a is the percentage increase, y = x(100+a)/100 since y is prime, so either x is 1 or (100 + a)/100 = 1, (100 + a)/100 = 1 can't be true because it will yield a = 0 and x, y and z are unique, so x is equal to 1



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If x, y, and z are all distinct positive integers and the percent
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11 Jul 2019, 03:37
Question says percentage increase from \(x\) to \(y\) and from \(y\) to \(z\) is the same. Few solutions say that, hence, \(0<x<y<z\). I cannot completely agree. If \(x=4\), \(y=2\) and \(z=1\), where \(0<z<y<x\), Percentage increase from \(x\) to \(y\) = \((\frac{(24)}{4}) * 100\) = \(50\%\) Percentage increase from \(y\) to \(z\) = \((\frac{(12)}{2}) * 100\) = \(50\%\) So, \(0<x<y<z\) may not always hold. I can however conclusively say \(x\),\(y\) and \(z\) are in ascending or descending order. Percentage increase can be negative too, can it not?
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If x, y, and z are all distinct positive integers and the percent
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