riteshn Posted December 8, 2005 Share Posted December 8, 2005 1.) What is the product of positive integer factor of 15? A) 1 B)3 C)5 D)15 E)225 15 can only be factorised as 5 X 3 and they are not positive integers. Is the question correct? Ans given in the book: 225 2) How many different factors are there for 242 excluding one and itself? A)3 B)4 C)5 D)6 E)7 I am getting 2 ( 11 X 2 ) but the answer given is B :hmm: 3.) Two different numbers whgen divided by same divisor leave remainders 4 and 3 respectively and when their sum is divised by the same divisor, remainder is 1. What is the divisor? A) 4 B)5 C)6 D)7 E)8 How to do this? Answer is: C 4.) What is the least interger n such that 54/n^3 is positive. A) -3 B)-1 C)1 D)2 E)3 I am getting D but the answer is A :hmm: Any ideas? Quote Link to comment Share on other sites More sharing options...
bscout Posted December 8, 2005 Share Posted December 8, 2005 1.) What is the product of positive integer factor of 15? A) 1 B)3 C)5 D)15 E)225 Factors of 15: 1, 3, 5 and 15. 1*3*5*15=225 ==>Answer E 2) How many different factors are there for 242 excluding one and itself? A)3 B)4 C)5 D)6 E)7 Factors: -2, -11, 2 and 11 ===Answer B I hope this help. 1 Quote Link to comment Share on other sites More sharing options...
riteshn Posted December 8, 2005 Author Share Posted December 8, 2005 1.) What is the product of positive integer factor of 15? So by POSITIVE INTEGER they mean positive total or integers which are positive? Quote Link to comment Share on other sites More sharing options...
kronique Posted December 8, 2005 Share Posted December 8, 2005 1.) What is the product of positive integer factor of 15? A) 1 B)3 C)5 D)15 E)225 Ans is E)225. the positive factors are 3, 5, 15 & their product is 225. 2) How many different factors are there for 242 excluding one and itself? A)3 B)4 C)5 D)6 E)7 Ans. is B : 2, 11, 22, 121 1 Quote Link to comment Share on other sites More sharing options...
kronique Posted December 8, 2005 Share Posted December 8, 2005 So by POSITIVE INTEGER they mean positive total or integers which are positive? ritesh... positive integers mean integers that are positive... here for 15 the positive factors are 1, 3, 5, 15 and the negative factors if asked are -1, -3, -5, -15 Quote Link to comment Share on other sites More sharing options...
riteshn Posted December 8, 2005 Author Share Posted December 8, 2005 Aaah....now I understood POSITIVE INTEGERS. Thanks. I misunderstood the FACTOR term too. Any ideas on 3 & 4? Quote Link to comment Share on other sites More sharing options...
kronique Posted December 8, 2005 Share Posted December 8, 2005 4.) What is the least interger n such that 54/n^3 is positive. A) -3 B)-1 C)1 D)2 E)3 ? is the Q (54/n)^3 or 54/n^3?? Quote Link to comment Share on other sites More sharing options...
kronique Posted December 8, 2005 Share Posted December 8, 2005 anyways...should'nt it be 1 since the smallest value of n is req.??:hmm: Quote Link to comment Share on other sites More sharing options...
riteshn Posted December 8, 2005 Author Share Posted December 8, 2005 (54)/n^3. I think its a wrong one? 1 Quote Link to comment Share on other sites More sharing options...
kronique Posted December 8, 2005 Share Posted December 8, 2005 (54)/n^3. I think its a wrong one? Probably OA is wrong...:hmm: ... Q3. is driving me nuts!! Quote Link to comment Share on other sites More sharing options...
riteshn Posted December 8, 2005 Author Share Posted December 8, 2005 anyways...should'nt it be 1 since the smallest value of n is req.?:hmm: Yeah :hmm: Quote Link to comment Share on other sites More sharing options...
bscout Posted December 8, 2005 Share Posted December 8, 2005 3.) Two different numbers whgen divided by same divisor leave remainders 4 and 3 respectively and when their sum is divised by the same divisor, remainder is 1. What is the divisor? A) 4 B)5 C)6 D)7 E)8 x/n ==> remainder of 4 (*) y/n ==> remainder of 3 (x+y)/n ==> remainder of 1 x=r1*k+4 where k is the divisor that we want to find. y=r2*k+3 x+y=(r1+r2)*k+7 x+y=T*k+1 where T=r1+r2 ===> We have: (r1+r2)*k+7=T*k+1 ===> (T-r1-r2)*k=6 But for (*) we know that k must be more than 4. As (T-r1-r2) is an integer k only could be 6. Quote Link to comment Share on other sites More sharing options...
bscout Posted December 8, 2005 Share Posted December 8, 2005 The method stated before was proposed by José in this thread. Quote Link to comment Share on other sites More sharing options...
krishnakanthc Posted December 8, 2005 Share Posted December 8, 2005 1 3.) Two different numbers when divided by same divisor leave remainders 4 and 3 respectively and when their sum is divised by the same divisor, remainder is 1. What is the divisor? A) 4 B)5 C)6 D)7 E)8 it has to be C , bcoz divisor is always greater than remainder. (rules out A) now when your adding numbers, (a+3 and a+4 { a is acommon factor} ) youll add remainders also( remainder is 3+4= 7 say ) .since you get rem as 1. it means only one ans is left 6 ( i.e 6+ 1 is the remainder). Quote Link to comment Share on other sites More sharing options...
kronique Posted December 8, 2005 Share Posted December 8, 2005 ahhhhh...thanx guys... Q3 is clearer now..:tup: Quote Link to comment Share on other sites More sharing options...
Dkumar Posted December 8, 2005 Share Posted December 8, 2005 3.) Two different numbers whgen divided by same divisor leave remainders 4 and 3 respectively and when their sum is divised by the same divisor, remainder is 1. What is the divisor? A) 4 B)5 C)6 D)7 E)8 Let the two numbers be d1 and d2. given, d1+d2=(q)*n +1 d1= q1*n+4 d2=q2*n+3 Adding the above two eqns d1+d2=(q1+q2)*n +7 d1+ d2= ((q1+q2)*n +6)+1 n=6. 4.) What is the least interger n such that 54/n^3 is positive. A) -3 B)-1 C)1 D)2 E)3 54/n^3= (3^3 * 2)/n^3 It should be C (1). Quote Link to comment Share on other sites More sharing options...
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