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M21-07

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If \(x\), \(y\), and \(z\) are even positive integers, each of the following must be an even integer EXCEPT:

A. \(\frac{xyx}{4}\)
B. \(x^{(y + z)}\)
C. \((x+y)^{z-1}\)
D. \(x-y-z\)
E. \(y^{z-x}\)
[Reveal] Spoiler: OA

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Official Solution:

If \(x\), \(y\), and \(z\) are even positive integers, each of the following must be an even integer EXCEPT:

A. \(\frac{xyx}{4}\)
B. \(x^{(y + z)}\)
C. \((x+y)^{z-1}\)
D. \(x-y-z\)
E. \(y^{z-x}\)

If \(z=x\), then option E gives: \(y^{z-x}=y^0=1=odd\). All the other options are necessarily even.

Answer: E
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M21-07 [#permalink]

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New post 11 Apr 2015, 23:43
Bunuel wrote:
Official Solution:

If \(x\), \(y\), and \(z\) are even positive integers, each of the following must be an even integer EXCEPT:

A. \(\frac{xyx}{4}\)
B. \(x^{(y + z)}\)
C. \((x+y)^{z-1}\)
D. \(x-y-z\)
E. \(y^{z-x}\)

If \(z=x\), then option E gives: \(y^{z-x}=y^0=1=odd\). All the other options are necessarily even.

Answer: E



Sir Question says "Must be even integer". So either it can be odd or it can be 0 ( as it doesnt say the resultant will be positive)

If we take option D i.e. x-y-z (let x=4 y=2 and z=2), the resultant would be 0
this also satisfies the equation in my opinion.

Please clarify this doubt. Thanks

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New post 12 Apr 2015, 03:34
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saharshbagaria wrote:
Bunuel wrote:
Official Solution:

If \(x\), \(y\), and \(z\) are even positive integers, each of the following must be an even integer EXCEPT:

A. \(\frac{xyx}{4}\)
B. \(x^{(y + z)}\)
C. \((x+y)^{z-1}\)
D. \(x-y-z\)
E. \(y^{z-x}\)

If \(z=x\), then option E gives: \(y^{z-x}=y^0=1=odd\). All the other options are necessarily even.

Answer: E



Sir Question says "Must be even integer". So either it can be odd or it can be 0 ( as it doesnt say the resultant will be positive)

If we take option D i.e. x-y-z (let x=4 y=2 and z=2), the resultant would be 0
this also satisfies the equation in my opinion.

Please clarify this doubt. Thanks


ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: M21-07 [#permalink]

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New post 08 Nov 2015, 19:30
Quote:
If \(x\), \(y\), and \(z\) are even positive integers, each of the following must be an even integer EXCEPT:

A. \(\frac{xyx}{4}\)
B. \(x^{(y + z)}\)
C. \((x+y)^{z-1}\)
D. \(x-y-z\)
E. \(y^{z-x}\)


Hi Bunuel,

I have a doubt about choice C. In case z=0, it turns out to be the reciprocal of (x+y), which may not be an even integer, isn't it? Pls clarify. I had this Q as my 1st Q in quant section in a GmatClub test. Spent 2 full minutes and got demotivated :( Pls help :)

Thanks,

Binit

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New post 08 Nov 2015, 20:38
binit wrote:
Quote:
If \(x\), \(y\), and \(z\) are even positive integers, each of the following must be an even integer EXCEPT:

A. \(\frac{xyx}{4}\)
B. \(x^{(y + z)}\)
C. \((x+y)^{z-1}\)
D. \(x-y-z\)
E. \(y^{z-x}\)


Hi Bunuel,

I have a doubt about choice C. In case z=0, it turns out to be the reciprocal of (x+y), which may not be an even integer, isn't it? Pls clarify. I had this Q as my 1st Q in quant section in a GmatClub test. Spent 2 full minutes and got demotivated :( Pls help :)

Thanks,

Binit


You should read questions more carefully: If \(x\), \(y\), and \(z\) are even POSITIVE integers... 0 is not positive.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M21-07 [#permalink]

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New post 08 Nov 2015, 21:33
Quote:
You should read questions more carefully: If x, y, and z are even POSITIVE integers... 0 is not positive.


Yes. I should be more careful in reading. I unnecessarily got nervous on the first Q and wasted time. Thanks so much for ur suggestion.

Binit.

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M21-07 [#permalink]

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New post 13 Dec 2015, 05:05
HI BUNUEL ! this is my 1st post in gmatclub !..
i also answered E ; my thought process was : if z>x then option E would not be an integer
is it ok ?

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New post 13 Dec 2015, 05:16

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Re: M21-07 [#permalink]

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New post 14 Dec 2016, 05:03
Hi bunuel,

My question might be ridiculous but pls. reply. If x and z are same integers then why would the author name it differently? In questions like these, i should also consider the fact that all integers might be same?

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Re: M21-07 [#permalink]

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New post 14 Dec 2016, 05:06
Klenex wrote:
Hi bunuel,

My question might be ridiculous but pls. reply. If x and z are same integers then why would the author name it differently? In questions like these, i should also consider the fact that all integers might be same?


Unless it is explicitly stated otherwise, different variables CAN represent the same number.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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M21-07 [#permalink]

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New post 13 Nov 2017, 08:55
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Last edited by vrkr on 13 Nov 2017, 08:59, edited 1 time in total.

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New post 13 Nov 2017, 08:58

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Re: M21-07   [#permalink] 13 Nov 2017, 08:58
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