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# If x and y are positive integers, does x–y = 0? (1)

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Intern
Joined: 03 Nov 2016
Posts: 4
If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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02 Mar 2017, 11:59
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75% (hard)

Question Stats:

45% (01:55) correct 55% (01:16) wrong based on 160 sessions

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If x and y are positive integers, does x–y = 0?

(1) ( z^2)^(x)= (z)^(2y)

(2) z^2 = z
Director
Joined: 05 Mar 2015
Posts: 999
Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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02 Mar 2017, 12:16
Bhalla wrote:
If x and y are positive integers, does x–y = 0?

(1) ( z^2)^(x)= (z)^(2y)

(2) z^2 = z

(1) if x=y=2....yes
if x=3 , y=4 ......No
insuff

(2) clearly insuff

combining z^x =z^y*z^y
again if x=4 , y=2
but if z=0 then x=y
insuff

Ans E
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Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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02 Mar 2017, 12:26
rohit8865 wrote:
Bhalla wrote:
If x and y are positive integers, does x–y = 0?

(1) ( z^2)^(x)= (z)^(2y)

(2) z^2 = z

(1) if x=y=2....yes
if x=3 , y=4 ......No
insuff

(2) clearly insuff

combining z^x =z^y*z^y
again if x=4 , y=2
but if z=0 then x=y
insuff

Ans E

rohit8865 I have a doubt

(1) ( z^2)^(x)= (z)^(2y)
upon simplifying,
z^2x = z^2y
2x = 2y
x = y

where did i go wrong ?
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Remember, if it is a GMAT question, it can be simplified elegantly.
Intern
Joined: 03 Nov 2016
Posts: 4
If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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Updated on: 02 Mar 2017, 12:51
2
hotshot02 wrote:
rohit8865 wrote:
Bhalla wrote:
If x and y are positive integers, does x–y = 0?

(1) ( z^2)^(x)= (z)^(2y)

(2) z^2 = z

(1) if x=y=2....yes
if x=3 , y=4 ......No
insuff

(2) clearly insuff

combining z^x =z^y*z^y
again if x=4 , y=2
but if z=0 then x=y
insuff

Ans E

I have a doubt

(1) ( z^2)^(x)= (z)^(2y)
upon simplifying,
z^2x = z^2y
2x = 2y
x = y

where did i go wrong ?

You've not gone wrong! You have assumed that z is not equal to 0.
Where as no such information is given in question stem. Try it again!
The question says x and y are positive integers. It says nothing about 'z'
z can be 0 or greater than 1 or less than 1
Eg:0^3=0^4

I hope now you know where you went wrong.
Give it another shot! You'll get it right!
Cheers!

Originally posted by Bhalla on 02 Mar 2017, 12:46.
Last edited by Bhalla on 02 Mar 2017, 12:51, edited 1 time in total.
Director
Joined: 05 Mar 2015
Posts: 999
Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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02 Mar 2017, 12:46
hotshot02 wrote:
rohit8865 wrote:
Bhalla wrote:
If x and y are positive integers, does x–y = 0?

(1) ( z^2)^(x)= (z)^(2y)

(2) z^2 = z

(1) if x=y=2....yes
if x=3 , y=4 ......No
insuff

(2) clearly insuff

combining z^x =z^y*z^y
again if x=4 , y=2
but if z=0 then x=y
insuff

Ans E

rohit8865 I have a doubt

(1) ( z^2)^(x)= (z)^(2y)
upon simplifying,
z^2x = z^2y
2x = 2y
x = y

where did i go wrong ?

might be my explanation too short
i mean if z>0 then x=y holds
but if z=0 then no matter x or y values
Manager
Joined: 21 Feb 2017
Posts: 73
Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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02 Mar 2017, 13:06
Without any calculation can't we say E because we have 3 unknown vs 2 equations?

Sent from my XT1663 using GMAT Club Forum mobile app
Intern
Joined: 26 Mar 2013
Posts: 1
Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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02 Mar 2017, 14:44
(1) ( z^2)^(x)= (z)^(2y)

(2) z^2 = z

when Z^2 =Z

(1) becomes Z ^x= Z^2y
which means x=2y.

combining both we don't get answer, so E
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Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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03 Mar 2017, 06:40
goalMBA1990 wrote:
Without any calculation can't we say E because we have 3 unknown vs 2 equations?

Sent from my XT1663 using GMAT Club Forum mobile app

statment 1 is not simplified so we can't say that..
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Joined: 02 Feb 2016
Posts: 88
GMAT 1: 690 Q43 V41
Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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25 Jul 2017, 12:48
Am i right in my understanding?

Statement (1), either z=0 or x=y .. Thus, insufficient.
Statement (2), either z=0 or z=1 .. Thus, insufficient.

But when we combine both the statements, shouldn't it give a confirmation of z being equal to 0?
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Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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28 Jul 2017, 00:51
TheMastermind wrote:
Am i right in my understanding?

Statement (1), either z=0 or x=y .. Thus, insufficient.
Statement (2), either z=0 or z=1 .. Thus, insufficient.

But when we combine both the statements, shouldn't it give a confirmation of z being equal to 0?

Hi TheMastermind ,

There are actually three inferences from statement 1.

Either Z = 0 or Z = 1 or x = y.

Remember (1)^anything is also always 1.

Hence, even if you combine the two statements, you won't get any answer.

Does that make sense?
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Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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29 Jul 2017, 09:25
abhimahna wrote:
TheMastermind wrote:
Am i right in my understanding?

Statement (1), either z=0 or x=y .. Thus, insufficient.
Statement (2), either z=0 or z=1 .. Thus, insufficient.

But when we combine both the statements, shouldn't it give a confirmation of z being equal to 0?

Hi TheMastermind ,

There are actually three inferences from statement 1.

Either Z = 0 or Z = 1 or x = y.

Remember (1)^anything is also always 1.

Hence, even if you combine the two statements, you won't get any answer.

Does that make sense?

I must be missing something in the statement (1) then. How do we get z=1? Isn't it z^2*(z^x - z^y) = 0 ??
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Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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29 Jul 2017, 09:34
TheMastermind wrote:
I must be missing something in the statement (1) then. How do we get z=1? Isn't it z^2*(z^x - z^y) = 0 ??

Hi TheMastermind ,

Okay, I understand the way you simplified. Try to put Z = 1 and keep other things intact. You will still get LHS= RHS. Hence,

Z = 1 is also a possibility.

Also, I don't even need to make such conversions.

When I am given that Z^2x = Z^2y, I can conclude that Z could be 1 because (1)^anything is always one.

Does that make sense?
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Re: If x and y are positive integers, does x–y = 0? (1)  [#permalink]

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30 Jul 2017, 03:33
Bhalla wrote:
If x and y are positive integers, does x–y = 0?

(1) ( z^2)^(x)= (z)^(2y)

(2) z^2 = z

( z^2)^(x)= (z)^(2y) means that 2^x=2y or 2^(x-1)=y. If x=2 then y=2 or x=y. But if x=3 then y=4. Insufficient

Z^2=z means that z=0 or z=1. Tells nothing about x and y. Insufficient

Combine together: if we will have a look at ( z^2)^(x)= (z)^(2y) and say that z=0 or 1 it means that it really doesn't matter which values x and y will have (because x and y positive integers) it will hold for any values of x and y (it will be either 0=0 or 1=1). Therefore x can equal y and also there is the case when x<>y. Answer E
Re: If x and y are positive integers, does x–y = 0? (1)   [#permalink] 30 Jul 2017, 03:33
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