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If x, y, and z are all distinct positive integers and the percent

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If x, y, and z are all distinct positive integers and the percent  [#permalink]

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New post 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  [#permalink]

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New post 27 Mar 2016, 14:08
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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?

The percent increase from x to y is equal to the percent increase from y to z: \(\frac{(y-x)}{x}*100 = \frac{(z-y)}{y}*100\) --> \(xz = y^2\) (\(0 < x < y < z\))

(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  [#permalink]

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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 04 Jul 2017, 17:52
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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 number

Although 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 y
1) 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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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x, y, z are all distinct positive integers and percent increase  [#permalink]

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New post 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

(y-x)/x = (z-y)/y
y^2-xy = xz-xy
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.com
Please confirm OA
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Re: If x, y, z are all distinct positive integers and percent increase  [#permalink]

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New post 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  [#permalink]

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New post 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: \(\frac{(y-x)}{x}*100 = \frac{(z-y)}{y}*100\) --> \(xz = y^2\) (\(0 < x < y < z\))

(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!! :shock: :)
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Re: If x, y, and z are all distinct positive integers and the percent  [#permalink]

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New post 19 Aug 2018, 22:00
(y-x)/x=(z-y)/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
Re: If x, y, and z are all distinct positive integers and the percent &nbs [#permalink] 19 Aug 2018, 22:00
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