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For how many positive integers, x, is it true that x^3 ≤ 3x? 29 Nov 2018, 01:29
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72% (00:59) correct 28% (01:12) wrong based on 183 sessions

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For how many positive integers, x, is it true that x^3 ≤ 3x?

A. None
B. One
C. Two
D. Four
E. More than four
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B
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For how many positive integers, x, is it true that x^3 ≤ 3x? 29 Nov 2018, 04:14
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Bunuel
For how many positive integers, x, is it true that x^3 ≤ 3x?

A. None
B. One
C. Two
D. Four
E. More than four
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x^3 ≤ 3x
or x^2<=3

at x=1 only it will stand out to be true .. IMO B
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For how many positive integers, x, is it true that x^3 ≤ 3x? 29 Nov 2018, 06:22
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Bunuel
For how many positive integers, x, is it true that x^3 ≤ 3x?

A. None
B. One
C. Two
D. Four
E. More than four
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First , Since x is positive , we can eliminate x on both sides , so the equation becomes x2 ≤ 3 => |x| ≤ sqrt(3), since x is positive 0< x ≤ 1.732, Since x is integer x = 1 , and has only one value
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For how many positive integers, x, is it true that x^3 ≤ 3x? 06 Jun 2019, 03:55
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Archit3110
Bunuel
For how many positive integers, x, is it true that x^3 ≤ 3x?

A. None
B. One
C. Two
D. Four
E. More than four


x^3 ≤ 3x
or x^2<=3

at x=1 only it will stand out to be true .. IMO B
Show more

why not 0
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For how many positive integers, x, is it true that x^3 ≤ 3x? 06 Jun 2019, 04:45
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Neha2050
Archit3110
Bunuel
For how many positive integers, x, is it true that x^3 ≤ 3x?

A. None
B. One
C. Two
D. Four
E. More than four


x^3 ≤ 3x
or x^2<=3

at x=1 only it will stand out to be true .. IMO B

why not 0
Show more

“0” is not a positive integer. Positive integers start from 1 and so on. Hope this helps :)

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For how many positive integers, x, is it true that x^3 ≤ 3x? 06 Jun 2019, 05:17
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Neha2050
Archit3110
Bunuel
For how many positive integers, x, is it true that x^3 ≤ 3x?

A. None
B. One
C. Two
D. Four
E. More than four


x^3 ≤ 3x
or x^2<=3

at x=1 only it will stand out to be true .. IMO B

why not 0
Show more

We consider 0 as a "non-negative" integer but it does not belong to the group of "positive integers". :)
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For how many positive integers, x, is it true that x^3 ≤ 3x? 09 Jun 2019, 19:14
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Bunuel
For how many positive integers, x, is it true that x^3 ≤ 3x?

A. None
B. One
C. Two
D. Four
E. More than four
Show more

If x = 1, 1 ≤ 3

If x = 2, 8 is not less than 6.

If x = 3, 27 is not less than 9.

As we can see, as the value of x increases, x^3 will be always greater than 3x. Thus, we see that only one positive integer (the integer 1) fits the given criteria.

Alternate Solution:

Because x is positive, we can divide each side of the inequality x^3 ≤ 3x by x:

x^2 ≤ 3

Since 2^2 = 4 > 3, and since increasing x will only make x^2 greater, we see that the only positive integer that satisfies the given inequality is 1.

Answer: B
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For how many positive integers, x, is it true that x^3 ≤ 3x? 22 Sep 2021, 14:09
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Archit3110
Bunuel
For how many positive integers, x, is it true that x^3 ≤ 3x?

A. None
B. One
C. Two
D. Four
E. More than four


x^3 ≤ 3x
or x^2<=3

at x=1 only it will stand out to be true .. IMO B
Show more

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