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Is 0 (zero) to be considered as a multiple of every number?
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03 Nov 2010, 06:45
I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT? Do we consider 0 to be a multiple of every number?
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Re: Is 0 (zero) to be considered as a multiple of every number?
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03 Nov 2010, 07:15
siyer wrote: I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?
Do we consider 0 to be a multiple of every number? An integer \(a\) is a multiple of an integer \(b\) means that \(\frac{a}{b}=integer\): so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself). Also on GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\). Hope it helps.
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Re: Is 0 (zero) to be considered as a multiple of every number?
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03 Nov 2010, 07:21
Here is very similar information and broad answer. http://www.manhattangmat.com/forums/num ... t4998.html
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Re: Is 0 (zero) to be considered as a multiple of every number?
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03 Nov 2010, 07:21
Wow!! Thanks guys!
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Re: Is 0 (zero) to be considered as a multiple of every number?
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03 Nov 2010, 07:56
WOW. I got my first KUDOS!!!! Need many to get free tests.
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Re: Is 0 (zero) to be considered as a multiple of every number?
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13 Mar 2014, 02:54
Bunuel wrote: siyer wrote: I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?
Do we consider 0 to be a multiple of every number? An integer \(a\) is a multiple of an integer \(b\) means that \(\frac{a}{b}=integer\): so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself). Also on GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\). Hope it helps. Dear Bunuel, And the first factor of any number(>=0) is 1. am I right? thanks Sid



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Re: Is 0 (zero) to be considered as a multiple of every number?
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13 Mar 2014, 03:17
sidpopy wrote: Bunuel wrote: siyer wrote: I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?
Do we consider 0 to be a multiple of every number? An integer \(a\) is a multiple of an integer \(b\) means that \(\frac{a}{b}=integer\): so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself). Also on GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\). Hope it helps. Dear Bunuel, And the first factor of any number(>=0) is 1. am I right? thanks Sid Yes, the smallest factor, the smallest positive divisor of any positive integer is 1.
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Re: Is 0 (zero) to be considered as a multiple of every number?
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05 Sep 2014, 04:16
Bunuel wrote: siyer wrote: I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?
Do we consider 0 to be a multiple of every number? An integer \(a\) is a multiple of an integer \(b\) means that \(\frac{a}{b}=integer\): so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself). Also on GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\). Hope it helps. Hi, Then why LCM of two numbers not zero?



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Is 0 (zero) to be considered as a multiple of every number?
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05 Sep 2014, 04:47
tushain wrote: Bunuel wrote: siyer wrote: I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?
Do we consider 0 to be a multiple of every number? An integer \(a\) is a multiple of an integer \(b\) means that \(\frac{a}{b}=integer\): so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself). Also on GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\). Hope it helps. Hi, Then why LCM of two numbers not zero? By definition the lowest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b.
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Is 0 (zero) to be considered as a multiple of every number?
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05 Sep 2014, 07:16
Quote: By definition the lowest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b. Thanks Bunuel One more doubt: Can LCM, HCF be stated for ve numbers: for eg. what is the LCM of 36,12 or HCF of 12,+36 ?



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Re: Is 0 (zero) to be considered as a multiple of every number?
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14 Feb 2017, 23:54
Bunuel wrote: siyer wrote: I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?
Do we consider 0 to be a multiple of every number? An integer \(a\) is a multiple of an integer \(b\) means that \(\frac{a}{b}=integer\): so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself). Also on GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\). Hope it helps. Dear Bunuel, Does zero (0) consider as consecutive even integers? (0)(2)(4)(6)(8)
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Re: Is 0 (zero) to be considered as a multiple of every number?
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15 Feb 2017, 00:33
ziyuenlau wrote: Bunuel wrote: siyer wrote: I just got a question on a practice test wrong because I didn't consider 0 (zero) to be a multiple of 5 (or any integer for that matter). So, what's the rule on the GMAT?
Do we consider 0 to be a multiple of every number? An integer \(a\) is a multiple of an integer \(b\) means that \(\frac{a}{b}=integer\): so, as 0 divided by any integer (except zero itself) yields an integer then yes, zero is a multiple of every integer (except zero itself). Also on GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:1. \(a\) is an integer; 2. \(b\) is an integer; 3. \(\frac{a}{b}=integer\). Hope it helps. Dear Bunuel, Does zero (0) consider as consecutive even integers? (0)(2)(4)(6)(8) 0 is an even integer, so it can be a part of the sequence of even numbers.
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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: Is 0 (zero) to be considered as a multiple of every number?
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31 Jul 2018, 19:48
Hi Bunuel , A quick one. Suppose a=4.5, b=1.5; a/b would still be an integer. So unless mentioned in the question about the nature of "a" and "b", shouldn't we consider fractions as well for Data Sufficiency questions? Really appreciate your time! Cheers, Sushil



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31 Jul 2018, 20:47




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