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If x is a number such that 0 < x ≤ 20, for how many values o
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12 Aug 2018, 15:29
12 Aug 2018, 15:29
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Question Stats:
36% (00:54) correct
63% (00:43) wrong based on 77 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
Re: If x is a number such that 0 < x ≤ 20, for how many values o
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15 Aug 2018, 05:07
15 Aug 2018, 05:07
6
Expert Reply
Explanation
Notice that the problem did not say that x had to be an integer. Therefore, the factors of 20 will work (1, 2, 4, 5, 10, 20), but so will 0.5, 0.1, 0.25, 2.5, etc. It is possible to divide 20 into fractional parts—for instance, something 20 inches long could be divided evenly into quarter inches (there would be 80 of them, as \(\frac{20}{0.25}= 80\)). There are an infinite number of x values that would work (it is possible to divide 20 into thousandths, millionths, etc.), so the answer is (E).
It is very important on the GRE to notice whether there is an integer constraint on a variable or not! Any answer like “More than 10” should be a clue that this problem may be less straightforward than it seems.
Notice that the problem did not say that x had to be an integer. Therefore, the factors of 20 will work (1, 2, 4, 5, 10, 20), but so will 0.5, 0.1, 0.25, 2.5, etc. It is possible to divide 20 into fractional parts—for instance, something 20 inches long could be divided evenly into quarter inches (there would be 80 of them, as \(\frac{20}{0.25}= 80\)). There are an infinite number of x values that would work (it is possible to divide 20 into thousandths, millionths, etc.), so the answer is (E).
It is very important on the GRE to notice whether there is an integer constraint on a variable or not! Any answer like “More than 10” should be a clue that this problem may be less straightforward than it seems.
General Discussion
Re: If x is a number such that 0 < x ≤ 20, for how many values o
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05 Apr 2021, 16:19
05 Apr 2021, 16:19
All factors of 20 ike 1,2,4,5,10,20 and 1/2,1/4,1/5,1/6,1/7
Answer - E
Answer - E
