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When 15 is divided by y, the remainder is y3. If y must be
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02 Jun 2012, 23:28
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When 15 is divided by y, the remainder is y3. If y must be an integer, what are all the possible values of y? OA:




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Re: When 15 is divided by y, the remainder is y3. If y must be
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03 Jun 2012, 02:32
AceofSpades wrote: When 15 is divided by y, the remainder is y3. If y must be an integer, what are all the possible values of y? OA: Note: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is nonnegative integer and always less than divisor).So, we have that \(15=qy+(y3)\) and \(remainder=y3\geq{0}\) > \(y\geq{3}\). From \(15=qy+(y3)\) > \(y(q+1)=18\) > \(y\) must be factor of 18 but greater than or equal to 3. Thus \(y\) can be: 3, 6, 9, or 18.
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Re: When 15 is divided by y, the remainder is y3. If y must be
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03 Jun 2012, 03:02
AceofSpades wrote: When 15 is divided by y, the remainder is y3. If y must be an integer, what are all the possible values of y? OA: Nice one. I had left out 3. Remainder 0 is a possibility too.



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Re: When 15 is divided by y, the remainder is y3. If y must be
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04 May 2017, 09:59
Bunuel wrote: AceofSpades wrote: When 15 is divided by y, the remainder is y3. If y must be an integer, what are all the possible values of y? OA: Note: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is nonnegative integer and always less than divisor).So, we have that \(15=qy+(y3)\) and \(remainder=y3\geq{0}\) > \(y\geq{3}\). From \(15=qy+(y3)\) > \(y(q+1)=18\) > \(y\) must be factor of 18 but greater than or equal to 3. Thus \(y\) can be: 3, 6, 9, or 18. I directly solved it. 18=y(q+1) As y is an integer, it should divide 18 i.e. it has to be a factor of 18. Total values y can take are 6 Why do we have to consider y>=3 ?



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Re: When 15 is divided by y, the remainder is y3. If y must be
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04 May 2017, 10:43
Shiv2016 wrote: Bunuel wrote: AceofSpades wrote: When 15 is divided by y, the remainder is y3. If y must be an integer, what are all the possible values of y? OA: Note: Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is nonnegative integer and always less than divisor).So, we have that \(15=qy+(y3)\) and \(remainder=y3\geq{0}\) > \(y\geq{3}\). From \(15=qy+(y3)\) > \(y(q+1)=18\) > \(y\) must be factor of 18 but greater than or equal to 3. Thus \(y\) can be: 3, 6, 9, or 18. I directly solved it. 18=y(q+1) As y is an integer, it should divide 18 i.e. it has to be a factor of 18. Total values y can take are 6 Why do we have to consider y>=3 ? Please reread the highlighted part. Hope it helps.
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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: When 15 is divided by y, the remainder is y3. If y must be
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04 May 2017, 13:52
15=ya+y3 18=y(a+1) factors of 18 are 1,2,3,6,9,18 y can take 3,6,9,18



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