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13 Aug 2018, 04:47
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E
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Difficulty:
75%
(hard)
Question Stats:
42% (01:16) correct
58%
(01:03)
wrong
based on 598
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
(A) Four
(B) Six
(C) Eight
(D) Ten
(E) More than ten
13 Aug 2018, 09:04
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Bunuel
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
(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)
General Discussion
16 Dec 2019, 11:25
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Bunuel
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
(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
