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# For all numbers x,

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For all numbers x, [#permalink]  16 Apr 2018, 15:27
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00:00

Question Stats:

57% (00:59) correct 42% (01:15) wrong based on 26 sessions

For all numbers x, $$\boxed {x}$$ denotes the value of $$x^3$$ rounded to the nearest multiple of ten.

 Quantity A Quantity B $$\boxed{x+1}+ 1$$ $$\boxed {x} + 1$$

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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Last edited by Carcass on 27 Dec 2018, 09:48, edited 2 times in total.
Edited by Carcass
Founder
Joined: 18 Apr 2015
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Kudos [?]: 2143 [0], given: 8371

Re: For all numbers x, [#permalink]  10 Mar 2019, 12:43
Expert's post
Bump for further discussion
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Re: For all numbers x, [#permalink]  17 Mar 2019, 16:34
Expert's post
This one's a little bit of an oddball. Clearly, quantity A is going to be larger for positive integers. For instance, if x = 2, then $$\boxed{2+1}$$ = $$\boxed{3}$$ = $$3^{3}$$ = 27, and the closest multiple of 10 is 30. So quantity A = 30 + 1 = 31. When x = 2 in quantity B, though, we get $$\boxed{2}$$ = $$2^{3}$$ = 8, and the nearest multiple of 10 is 10. So quantity B = 10 + 1 = 11. Hence, quantity A is larger.

However, when x = 0.0001, then each quantity's boxed value will be rounded down to 0 as the nearest multiple of 10. In that case, the quantities are equal.

And when say, x = -2, following the math before, we'd end up with quantity A = -31 and quantity b = -11, making quantity B bigger.

Since we don't know which case is true, the answer is D.
Re: For all numbers x,   [#permalink] 17 Mar 2019, 16:34
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