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Founder  Joined: 18 Apr 2015
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Expert's post 00:00

Question Stats: 52% (01:02) correct 47% (00:57) wrong based on 34 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
Posts: 13309
Followers: 286

Kudos [?]: 3370 , given: 12174

Re: For all numbers x, [#permalink]
Expert's post
Bump for further discussion
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Manager Joined: 04 Feb 2019
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Re: For all numbers x, [#permalink]
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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