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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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Math Expert
Joined: 02 Sep 2009
Posts: 51035
If x is a number such that 0 < x ≤ 20, for how many values of x is  [#permalink]

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13 Aug 2018, 03:47
00:00

Difficulty:

65% (hard)

Question Stats:

40% (01:08) correct 60% (00:51) wrong based on 45 sessions

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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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Re: If x is a number such that 0 < x ≤ 20, for how many values of x is  [#permalink]

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13 Aug 2018, 08:04
1
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 &nbs [#permalink] 13 Aug 2018, 08:04
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