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

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Math Expert
Joined: 02 Sep 2009
Posts: 51097
If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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27 Jun 2018, 21:51
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Difficulty:

45% (medium)

Question Stats:

58% (01:16) correct 42% (01:19) wrong based on 201 sessions

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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

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Posts: 2269
Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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27 Jun 2018, 22:08

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.

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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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28 Jun 2018, 02:28
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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28 Jun 2018, 09:51
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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02 Jul 2018, 08:44
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!

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Joined: 26 Jan 2018
Posts: 1
Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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13 Jul 2018, 07:02
1
What if x is negative?
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Joined: 16 Apr 2018
Posts: 7
Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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14 Jul 2018, 00:02
1
What if we take the value of X to be negative ?
Can anyone please clear my doubt?
Thanks!

Sent from my vivo 1611 using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 51097
Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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14 Jul 2018, 00:52
Insiya wrote:
What if we take the value of X to be negative ?
Can anyone please clear my doubt?
Thanks!

Sent from my vivo 1611 using GMAT Club Forum mobile app

You are right. The word "positive" was missing in the stem.
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If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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14 Jul 2018, 02:13
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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Joined: 02 Aug 2009
Posts: 7100
Re: If 2/x^3 < 0.02 what is the least positive integer value of x?  [#permalink]

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14 Jul 2018, 04:20
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, 04:20
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