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M28-37

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M28-37 [#permalink]

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New post 16 Sep 2014, 01:31
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Question Stats:

35% (00:40) correct 65% (00:48) wrong based on 40 sessions

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If \(x\) is not equal to 0 and \(x^y=1\), then which of the following must be true?
I. \(x=1\)

II. \(x=1\) and \(y=0\)

III. \(x=1\) or \(y=0\)


A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 01:31
Official Solution:

If \(x\) is not equal to 0 and \(x^y=1\), then which of the following must be true?
I. \(x=1\)

II. \(x=1\) and \(y=0\)

III. \(x=1\) or \(y=0\)


A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)


Notice that if \(x=-1\) and \(y\) is any even number, then \((-1)^{even}=1\), thus none of the options must be true.


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

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Re: M28-37 [#permalink]

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New post 16 Jul 2015, 04:25
Bunuel wrote:
Official Solution:

If \(x\) is not equal to 0 and \(x^y=1\), then which of the following must be true?
I. \(x=1\)

II. \(x=1\) and \(y=0\)

III. \(x=1\) or \(y=0\)


A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)


Notice that if \(x=-1\) and \(y\) is any even number, then \((-1)^{even}=1\), thus none of the options must be true.


Answer: E

Dear Bunuel,

Please explain why C is incorrect. Even that satisfies the must condition.

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Re: M28-37 [#permalink]

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New post 16 Jul 2015, 04:38
shanti47 wrote:
Bunuel wrote:
Official Solution:

If \(x\) is not equal to 0 and \(x^y=1\), then which of the following must be true?
I. \(x=1\)

II. \(x=1\) and \(y=0\)

III. \(x=1\) or \(y=0\)


A. \(I\) only
B. \(II\) only
C. \(III\) only
D. \(I\) and \(III\) only
E. \(None\)


Notice that if \(x=-1\) and \(y\) is any even number, then \((-1)^{even}=1\), thus none of the options must be true.


Answer: E

Dear Bunuel,

Please explain why C is incorrect. Even that satisfies the must condition.


III says \(x=1\) or \(y=0\). This is NOT necessarily true: consider x = -1 and y = 2 --> (-1)^2 = 1.
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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

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Re: M28-37 [#permalink]

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New post 12 Feb 2016, 00:22
x=1, y=1 discards 3d option
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Re: M28-37 [#permalink]

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New post 18 Jun 2017, 03:33
Hi Bunuel, I didn't understand why B is incorrect. When x=1 and y=0, then the answer is always 1. Please clarify.

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New post 18 Jun 2017, 03:37
Romannepal wrote:
Hi Bunuel, I didn't understand why B is incorrect. When x=1 and y=0, then the answer is always 1. Please clarify.


The question asks which of the following MUST be true? Not COULD be true.

II says: \(x=1\) and \(y=0\).

This is not necessarily true. Consider x = -1 and y = 0.
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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

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Re: M28-37 [#permalink]

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New post 05 Oct 2017, 07:58
Hi Bunuel, why is C incorrect. It says X=1 or Y=0. Now if X=1, x^y will always be 1 irrespective of Y and if Y = 0, then x^y will be 1 as well since X cannot be 0. Can you please explain.

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Re: M28-37 [#permalink]

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New post 05 Oct 2017, 08:00
mansi20081990 wrote:
Hi Bunuel, why is C incorrect. It says X=1 or Y=0. Now if X=1, x^y will always be 1 irrespective of Y and if Y = 0, then x^y will be 1 as well since X cannot be 0. Can you please explain.


This is explained above:

III says \(x=1\) or \(y=0\). This is NOT necessarily true: consider x = -1 and y = 2 --> (-1)^2 = 1.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128752 [0], given: 12182

Re: M28-37   [#permalink] 05 Oct 2017, 08:00
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