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M08-26

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M08-26  [#permalink]

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New post 15 Sep 2014, 23:38
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Question Stats:

85% (00:46) correct 15% (01:59) wrong based on 102 sessions

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If \(x\) and \(y\) are positive integer and \(xy\) is divisible by 4, which of the following must be true?

A. If \(x\) is even then \(y\) is odd.
B. If \(x\) is odd then \(y\) is a multiple of 4.
C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer.
D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer.
E. \(x^y\) is even.

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Re M08-26  [#permalink]

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New post 15 Sep 2014, 23:38
1
Official Solution:

If \(x\) and \(y\) are positive integer and \(xy\) is divisible by 4, which of the following must be true?

A. If \(x\) is even then \(y\) is odd.
B. If \(x\) is odd then \(y\) is a multiple of 4.
C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer.
D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer.
E. \(x^y\) is even.


Notice that the question asks which of the following MUST be true, not COULD be true.

A. If \(x\) is even then \(y\) is odd. Not necessarily true, consider: \(x=y=2=\text{even}\);

B. If \(x\) is odd then \(y\) is a multiple of 4. Always true: if \(x=\text{odd}\) then in order \(xy\) to be a multiple of 4 \(y\) must be a multiple of 4;

C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer. Not necessarily true, consider: \(x=1\) and \(y=4\);

D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer. Not necessarily true, consider: \(x=2\) and \(y=4\);

E. \(x^y\) is even. Not necessarily true, consider: \(x=1\) and \(y=4\);


Answer: B
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Collection of Questions:
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Re: M08-26  [#permalink]

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New post 31 Aug 2015, 00:03
this question has to be reconsidered to clarify the users confusion on whether xy means x*y or xy a two digit number.
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Re: M08-26  [#permalink]

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New post 31 Aug 2015, 06:49
ramarao443 wrote:
this question has to be reconsidered to clarify the users confusion on whether xy means x*y or xy a two digit number.


xy always means x multiplied by y, if it's not stated otherwise. If it were two digit number xy, then it would be explicitly mentioned.
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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: M08-26  [#permalink]

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New post 09 Feb 2016, 22:40
Bunuel wrote:
Official Solution:

If \(x\) and \(y\) are positive integer and \(xy\) is divisible by 4, which of the following must be true?

A. If \(x\) is even then \(y\) is odd.
B. If \(x\) is odd then \(y\) is a multiple of 4.
C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer.
D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer.
E. \(x^y\) is even.


Notice that the question asks which of the following MUST be true, not COULD be true.

A. If \(x\) is even then \(y\) is odd. Not necessarily true, consider: \(x=y=2=\text{even}\);

B. If \(x\) is odd then \(y\) is a multiple of 4. Always true: if \(x=\text{odd}\) then in order \(xy\) to be a multiple of 4 \(y\) must be a multiple of 4;

C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer. Not necessarily true, consider: \(x=1\) and \(y=4\);

D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer. Not necessarily true, consider: \(x=2\) and \(y=4\);

E. \(x^y\) is even. Not necessarily true, consider: \(x=1\) and \(y=4\);


Answer: B


Hi Buneul,

As per the question, X and Y are positive number and XY is divisible by 4. Then we have to consider numbers which are only divisible by 4.

Then how Choice (B) can be correct.
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Re: M08-26  [#permalink]

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New post 09 Feb 2016, 23:10
msk0657 wrote:
Bunuel wrote:
Official Solution:

If \(x\) and \(y\) are positive integer and \(xy\) is divisible by 4, which of the following must be true?

A. If \(x\) is even then \(y\) is odd.
B. If \(x\) is odd then \(y\) is a multiple of 4.
C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer.
D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer.
E. \(x^y\) is even.


Notice that the question asks which of the following MUST be true, not COULD be true.

A. If \(x\) is even then \(y\) is odd. Not necessarily true, consider: \(x=y=2=\text{even}\);

B. If \(x\) is odd then \(y\) is a multiple of 4. Always true: if \(x=\text{odd}\) then in order \(xy\) to be a multiple of 4 \(y\) must be a multiple of 4;

C. If \(x+y\) is odd then \(\frac{y}{x}\) is not an integer. Not necessarily true, consider: \(x=1\) and \(y=4\);

D. If \(x+y\) is even then \(\frac{x}{y}\) is an integer. Not necessarily true, consider: \(x=2\) and \(y=4\);

E. \(x^y\) is even. Not necessarily true, consider: \(x=1\) and \(y=4\);


Answer: B


Hi Buneul,

As per the question, X and Y are positive number and XY is divisible by 4. Then we have to consider numbers which are only divisible by 4.

Then how Choice (B) can be correct.


We are given that \(x\) and \(y\) are positive integer and \(xy\) (the product of x and y) is divisible by 4.

(B) says that if \(x\) is odd then \(y\) is a multiple of 4. Now, if x is odd, then for xy to be divisible by 4, y must be a multiple of 4. So, option B must be true.
_________________

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

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Re: M08-26  [#permalink]

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New post 15 Mar 2018, 22:53
if x =1 and y=4 then none of the options r true
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Re: M08-26  [#permalink]

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New post 15 Mar 2018, 23:00
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Re: M08-26 &nbs [#permalink] 15 Mar 2018, 23:00
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M08-26

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