If x is a number such that 0

Question

If x is a number such that 0 < x ≤ 20, for how many values of x is  \frac{20}{x}  an integer?

(A) Four
(B) Six
(C) Eight
(D) Ten
(E) More than ten

PKN · Accepted Answer

Given, 'x' is a number. (NOT integer)
And 0 < x ≤ 20.

\frac{20}{x}  is an integer:-
a) Prime factorization of 20, 20= 2^2*5^1 , (2+1)*(1+1)=6 factors of 20 . So, 6 values of x.
b) When  x=\frac{1}{2} ,  \frac{20}{x} =40. Similarly, we can choose, x=1/3,1/4,1/5,1/6,1/7,1/8,1/9 etc.

So, the no of values of x is more than 10.

Ans. (E)

Archit3110 · Answer

we have to consider value of x as both an integer and fraction integer will be ; factors of 20 ; 2^2*5 ; 3*2 ; 6
and reciprocal of values 1/2 to 1/20 ; so more than 10 possible 
IMO E

Kinshook · Answer

Asked: If x is a number such that 0 < x ≤ 20, for how many values of x is  \frac{20}{x}  an integer?

20 = 2^2*5
Factors of 20 = {1,2,4,5,10,20};

Since x can take values = .5, .25, .125 etc
There are infinite such solutions possible

IMO E

Batman117 · Answer

Here X is not INTEGER
SO 20/X IS INTEGER FOR MOERE THEN 10 VAKUE OF X

20/0.1
20/0.01
20/0.001 AND SO ON....

Posted from my mobile device

samarpan.g28 · Answer

Trick question! Even I got it wrong on the first attempt. It is not mentioned in the question that x is an integer so x can be either 1,2,4,5,10,20 as integers and 1/2,1/3,1/4,1/5,.... as float values. Either way, 20/x becomes an integer. So, answer is more than 10(E).

Rhitib · Answer

This is a tricky sum, when I first read it I was fooled thinking x is an Integer, but no. 20/x should be an integer but not x, so normally six values can divide 20 and give us an Integer (1,2,4,5,10,20).

Now if x is not an Integer, then fractional values from 1/2 till 1/20

so 1/2...1/20 ( 19 values including 20) plus the 6 values from above makes it more than 10 values. So Answer is E.

P.S: Be careful to consider the fractional values in this case.

If x is a number such that 0 < x ≤ 20, for how many values of x is

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