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If n is a positive integer and r is the remainder when (n1) [#permalink]
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03 Jul 2010, 22:19
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hI Everyone
Can someone, please explain to me, the following problem:
PROBLEM 2: If n is a positive integer and r is the remainder when (n1)(n+1) is divided by 24, what is the value of r?
1) n is not divisible by 2.
2) n is not divisible by 3.
Thanks for your help. I hope someone can explain to me.
regards



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Re: DS from GMATPrep [#permalink]
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27 Jun 2010, 21:26
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If n is a positive integer and R is the remainder when (n1)(n+1) is divided by 24, what is the value of r?Number plugging method: \((n1)(n+1)=n^21\) (1) n is not divisible by 2 > pick two odd numbers: let's say 1 and 3 > if \(n=1\), then \(n^21=0\) and as zero is divisible by 24 (zero is divisible by any integer except zero itself) so remainder is 0 but if \(n=3\), then \(n^21=8\) and 8 divided by 24 yields remainder of 8. Two different answers, hence not sufficient. (2) n is not divisible by 3 > pick two numbers which are not divisible by 3: let's say 1 and 2 > if \(n=1\), then \(n^21=0\), so remainder is 0 but if \(n=2\), then \(n^21=3\) and 3 divided by 24 yields remainder of 3. Two different answers, hence not sufficient. (1)+(2) Let's check for several numbers which are not divisible by 2 or 3: \(n=1\) > \(n^21=0\) > remainder 0; \(n=5\) > \(n^21=24\) > remainder 0; \(n=7\) > \(n^21=48\) > remainder 0; \(n=11\) > \(n^21=120\) > remainder 0. Well it seems that all appropriate numbers will give remainder of 0. Sufficient. Algebraic approach: (1) n is not divisible by 2. Insufficient on its own, but this statement says that \(n=odd\) > \(n1\) and \(n+1\) are consecutive even integers > \((n1)(n+1)\) must be divisible by 8 (as both multiples are even and one of them will be divisible by 4. From consecutive even integers one is divisible by 4: (2, 4); (4, 6); (6, 8); (8, 10); (10, 12), ...). (2) n is not divisible by 3. Insufficient on its own, but form this statement either \(n1\) or \(n+1\) must be divisible by 3 (as \(n1\), \(n\), and \(n+1\) are consecutive integers, so one of them must be divisible by 3, we are told that it's not \(n\), hence either \(n1\) or \(n+1\)). (1)+(2) From (1) \((n1)(n+1)\) is divisible by 8, from (2) it's also divisible by 3, therefore it must be divisible by \(8*3=24\), which means that remainder upon division \((n1)(n+1)\) by 24 will be 0. Sufficient. Answer: C. Hope it helps.
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If n is a positive integer and r is the remainder when (n1) [#permalink]
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27 Jun 2010, 20:31
If n is a positive integer and R is the remainder when (n1)(n+1) is divided by 24, what is the value of r? (1) n is not divisible by 2 (2) n is not divisible by 3 OA:



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Re: NEED HELP  2 DATA SUFFICIENCY PROBLEMS [#permalink]
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03 Jul 2010, 22:54
Question 2:
To be divisible by 24, a number must be divisible by 8 and by 3.
Statement 1: n is not divisible by 2. This basically says that n is an odd number. So if n is an odd number, both n1 and n+1 are even numbers, which means that (n1)(n+1) must be divisible by 4.
n1 = 2k n+1 = 2p
Between any two consecutive even integers, one has to be divisible by 4, so we know that the given number is divisible by 8.
Statement 2: n is not divisible by 3. However, between any three consecutive numbers one has to be divisible by 3. Considering the consecutive numbers (n1)(n)(n+1) we know that n isn't divisible by 3, so either (n1) or (n+1) should be divisible by 3.
Combining both together, we know that (n1)(n+1) is divisible by 8 and 3 and hence 24. So reminder = 0. Hence answer is C.



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Re: NEED HELP  2 DATA SUFFICIENCY PROBLEMS [#permalink]
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04 Jul 2010, 05:21
in question 2, statement 2 alone will not be sufficient unless taken in conjunction with stmt 1 because if we consider ONLY stmt 2  then 10 is a value which is NOT divisible by 3 and (101)*(10+1) = gives 99 which does not leave a remainder 0 when divided by 24. Thus IMO the answer to problem 2 should be A  stmt 1 alone is sufficient... pls correct me if I am wrong.



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Re: DS from GMATPrep [#permalink]
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06 Jul 2010, 12:45
@bunuel... 3 divided by 24 yields remainder of 3???



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Re: DS from GMATPrep [#permalink]
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06 Jul 2010, 17:34
bunnel: i am too confused....how come 3 divided by 24 the remainder is 3?



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Re: NEED HELP  2 DATA SUFFICIENCY PROBLEMS [#permalink]
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06 Jul 2010, 23:58
whiplash2411 wrote: Question 2:
To be divisible by 24, a number must be divisible by 8 and by 3.
Statement 1: n is not divisible by 2. This basically says that n is an odd number. So if n is an odd number, both n1 and n+1 are even numbers, which means that (n1)(n+1) must be divisible by 4.
n1 = 2k n+1 = 2p
Between any two consecutive even integers, one has to be divisible by 4, so we know that the given number is divisible by 8.
Statement 2: n is not divisible by 3. However, between any three consecutive numbers one has to be divisible by 3. Considering the consecutive numbers (n1)(n)(n+1) we know that n isn't divisible by 3, so either (n1) or (n+1) should be divisible by 3.
Combining both together, we know that (n1)(n+1) is divisible by 8 and 3 and hence 24. So reminder = 0. Hence answer is C. n is not divisble by 2 implies n1 and n+1 are even , this implies the product of these two numbers i divisible by 4 and not 8. both the statements taken together say that the number is not even and not divisible by 3 , meaning all odd numbers not divisible by 3 . these are 1,5,7,11,13,17 , if u (square of any of these minus 1 )/24 = 1 and not 0



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Re: DS from GMATPrep [#permalink]
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07 Jul 2010, 03:46
utin wrote: @bunuel... 3 divided by 24 yields remainder of 3??? ruchichitral wrote: bunnel: i am too confused....how come 3 divided by 24 the remainder is 3? THEORY: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 when divisor (24 in our case) is more than dividend (3 in our case) then the reminder equals to the dividend: 3 divided by 24 yields a reminder of 3 > \(3=0*24+3\); or: 5 divided by 6 yields a reminder of 5 > \(5=0*6+5\). Hope it's clear.
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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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