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# White and black blocks are stacked in a vertical column so that no two

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Math Expert
Joined: 02 Sep 2009
Posts: 58325
White and black blocks are stacked in a vertical column so that no two  [#permalink]

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14 Mar 2018, 23:36
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Difficulty:

35% (medium)

Question Stats:

79% (01:16) correct 21% (01:15) wrong based on 52 sessions

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White and black blocks are stacked in a vertical column so that no two blocks of the same color are adjacent. If there are 247 blocks in the stack, how many white blocks are there in the stack?

(1) The top block in the stack is white
(2) There are 5 white blocks in the 10 blocks at the bottom of the stack.

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Joined: 07 Dec 2017
Posts: 1140
Re: White and black blocks are stacked in a vertical column so that no two  [#permalink]

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15 Mar 2018, 02:22
Bunuel wrote:
White and black blocks are stacked in a vertical column so that no two blocks of the same color are adjacent. If there are 247 blocks in the stack, how many white blocks are there in the stack?

(1) The top block in the stack is white
(2) There are 5 white blocks in the 10 blocks at the bottom of the stack.

We'll use a simpler case and a drawing to help show us the logic.
This is an Alternative approach.

(1)
Say we had a smaller, odd number of blocks, say 5:
Then w-b-w-b-w would give 3 whites, that is, half of 5 rounded up.
Similarly 7 blocks would give w-b-w-b-w-b-w, or 4 whites, again half rounded up.
So we have 247/2 (rounded up) white blocks.
Sufficient!

(2) Well, in this case we can have
w-b-w-b-w-b-w-b-w-b or b-w-b-w-b-w-b-w-b-w.
Both have 5 white blocks in the lower 10.
But, as we saw in (1), if we start from white we have (half of 247 rounded up) whites meaning that if we start from black we have (half of 247 rounded down).
Insufficient!

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Joined: 01 Feb 2017
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White and black blocks are stacked in a vertical column so that no two  [#permalink]

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16 Mar 2018, 04:42
Total Blocks: 247, arranged alternatively

So, there are 123 blocks of color1 and 124 blocks of color2.

To determine the colors, we need the start point. I.e. Color of first block at the bottom or top.

Hence, Statement 1 is sufficient and Statement 2 is not.

Ans A
White and black blocks are stacked in a vertical column so that no two   [#permalink] 16 Mar 2018, 04:42
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