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If x is a number such that 0 < x ≤ 20, for how many values of x is
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Bunuel
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If x is a number such that 0 < x ≤ 20, for how many values of x is [#permalink] New post  13 Aug 2018, 03:47
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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
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PKN
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Re: If x is a number such that 0 < x ≤ 20, for how many values of x is [#permalink] New post  13 Aug 2018, 08:04
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Bunuel wrote:
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


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)
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Re: If x is a number such that 0 < x ≤ 20, for how many values of x is [#permalink] New post  16 Dec 2019, 10:25
Bunuel wrote:
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


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
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If x is a number such that 0 < x ≤ 20, for how many values of x is [#permalink] New post  06 Jun 2020, 22:56
Bunuel wrote:
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


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
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Re: If x is a number such that 0 < x ≤ 20, for how many values of x is [#permalink] New post  06 Jun 2020, 23:10
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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....

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Re: If x is a number such that 0 < x ≤ 20, for how many values of x is [#permalink] New post  08 Jul 2021, 22:57
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Re: If x is a number such that 0 < x ≤ 20, for how many values of x is [#permalink]
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