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Number system problem (solving & explanations)


riteshn

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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?

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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.

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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

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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.

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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).

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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).

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