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If 2/x^3 < 0.02 what is the least positive integer value of x?

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If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 27 Jun 2018, 22:51
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

58% (00:58) correct 42% (01:06) wrong based on 190 sessions

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Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 27 Jun 2018, 23:08

Solution



Given:
    • \(\frac{2}{x^3} < 0.02\)

To find:
    • The least integer value of x

Approach and Working:
We can rewrite the given expression in the following manner:
    • \(\frac{2}{x^3} < 0.02\)
    Or, \(\frac{2}{x^3} < \frac{2}{100}\)

If this is true, then \(x^3\) must be greater than 100
    • If x = 4, then \(4^3\) = 64 < 100
    • If x = 5, then \(5^3\) = 125 > 100

Therefore, the least integer value of x must be 5

Hence, the correct answer is option D.

Answer: D
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Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 28 Jun 2018, 03:28
Bunuel wrote:
If \(\frac{2}{x^3}< 0.02\)what is the least integer value of x?

A. No such least value exists.
B. 101
C. 100
D. 5
E. 4



Note: we are asked to determine the least value of x.

what if \(x^3\) = 100

\(\frac{2}{100} = 0.02\)

then we can take care x = 5

\(x^3\) = 125

it is clear that

\(\frac{2}{125}\) < 0.02..........as we know\(\frac{2}{100}= 0.02\)

Thus the best answer is D.
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Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 28 Jun 2018, 10:51
By substitution,

2/64 = 1/32 > 0.02 - Incorrect
2/125 < 0.02 - Correct.
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Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 02 Jul 2018, 09:44
Bunuel wrote:
If \(\frac{2}{x^3}< 0.02\)what is the least integer value of x?

A. No such least value exists.
B. 101
C. 100
D. 5
E. 4


We can test the values given in the answer choices, starting with 4 (choice E):

2/4^3 < 0.02 ?

2 < 0.02 x 4^3 ?

2 < 0.02 x 64 ?

2 < 1.28 ? → No!

Now let’s test 5:

2/5^3 < 0.02 ?

2 < 0.02 x 5^3 ?

2 < 0.02 x 125 ?

2 < 2.5 ? → Yes!

Answer: D
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Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 13 Jul 2018, 08:02
1
What if x is negative?
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Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 14 Jul 2018, 01:02
1
What if we take the value of X to be negative ?
Can anyone please clear my doubt?
Thanks!

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Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 14 Jul 2018, 01:52
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If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 14 Jul 2018, 03:13
Since x must be a positive integer, both sides of the inequality can be multiplied by \(x^3\)

\(\frac{2}{x^3} < 0.02\)

\(2 < 0.02x^3\)

\(200 < 2x^3\)

\(100 < x^3\)

\(x^3 > 100\)

In the resulting inequality, the least positive integer value for x is 5.


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Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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New post 14 Jul 2018, 05:20
Bunuel wrote:
If \(\frac{2}{x^3}< 0.02\) what is the least positive integer value of x?

A. No such least value exists.
B. 101
C. 100
D. 5
E. 4


\(\frac{2}{x^3}< 0.02...............2<x^3*0.02......100<x^3\)
Now x is integer, 4^3=64 and 5^3=125
So minimum is 5

D
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Re: If 2/x^3 < 0.02 what is the least positive integer value of x? &nbs [#permalink] 14 Jul 2018, 05:20
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