Let b and x be positive integers. If b is the greatest divisor of x th

Question

Let b and x be positive integers. If b is the greatest divisor of x that is less than x, is the sum of the divisors of x, which are less than x itself and greater than one, greater than 2b?

(1) b^2 = x
(2) 2b = x

kpshabare · Answer

Ans is C.
Considering question stem, we have b as greatest divisor of x. For any no, it's greatest divisor will be half or less than half of itself, for it being a non prime.
Consider st1.
B^2=x

5x5 =25, sum of divisors = 5 lesser than 5.
6×6=36,sum of divisors = 2+3+4+6+9+18 greater than 6.cant answer. Not sufficient

Consider st2
2b=x
Eg 
2x4=8
Sum of divisors of 8 = 2+4 less than 8
2×6=12
Sum of divisors of 12 = 2+3 less than 12.
2x8=16
Sum of divisors of 16 = 2+4+8 less than 16
2x9=18
Sum of divisors of 18 =2+3+6+9 greater than 18.
Not sufficient.

Considering both st1 n st2

b^2=2b gives b=2
For b=2 sum of divisors of 2b is 2 which is less that 2b=4. Hence sufficient.

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Madhavi1990 · Answer

I picked D: Why is it A? 
St 1 - x^2 = b -->x = b * b 
Thus,x > 2b > b (as asked by the question. I think I have made a mistake here in the interpretation of the question). Thus x is the largest value here.

St 2 --> 2b = x--> 2b/b = 2. So, one factor is 2. b = x/2. What I got was --> x > b and x = 2b. So I am not sure why its not suff

niks18 · Answer

Statement 1:   b  is the greatest divisor of  x  and  x=b^2 , so  b  must be prime.

For eg.  b=7 , then  x=49 . Divisors of  x=1,7,49 . Greatest divisor  7=b

b  cannot be a composite number. for eg. if  b=4 , then  x=16 . Divisors of  x= 1,2,4,8,16 . Greatest divisor  8  which is not equal to  b .

So if  b =p_1 , a prime number and as  x  is square of a prime number,  x={p_1}^2 , divisors of  x  will be  1 ,  p_1  &  {p_1}^2  only.

Now the divisors of  x , which are less than  x  itself and greater than one is  p_1=b  which is not greater than  2b=2p_1 .  Sufficient

Statement 2:  if  b=3 ,  x=6 . Divisors of  x= 1,2,3,6 . sum of divisors of  x , which are less than  x  itself and greater than one is  2+3=5<2*3

if  b=6 ,  x=12 . Divisors of  x=1,2,3,4,6,12 . sum of divisors of  x , which are less than  x  itself and greater than one is  2+3+4+6=15>2*6 . Hence  Insufficient

Option  A

niks18 · Answer

Hi  Madhavi1990

I think you interpreted the question wrongly. we need to calculate sum of divisors of x but you are focusing only on the greatest divisor of x i.e b. for statement 2 if b=6, then x=12 and it will have other factors as well apart from 2.

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Let b and x be positive integers. If b is the greatest divisor of x th

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Let b and x be positive integers. If b is the greatest divisor of x th

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