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25 Jun 2021, 08:45
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B
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Difficulty:
65%
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Question Stats:
58% (01:59) correct
42%
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wrong
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A box contains 90 balls of different colours: 13 yellow, 19 green, 27 red, 10 black, 7 brown and 14 white. Find the smallest number V such that any V balls drawn from the box will contain at least 14 balls of the same colour.
(A) 69
(B) 70
(C) 72
(D) 76
(E) 79
(A) 69
(B) 70
(C) 72
(D) 76
(E) 79
25 Jun 2021, 09:08
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The question is asking for the amount of balls needed to be drawn that will guarantee that you will have 14 balls of a single colour.
To do this, let’s say that all the colours with less than 14 balls are drawn: brown (7), black (10) and yellow (13). The sum of this is 30.
Next we have 3 colours equal to or exceeding 14 balls. White, red and green. Let’s say that 13 of each is drawn: 13*3 = 39. This means that no matter what balls is drawn next, we will have a colour with 14 balls drawn.
So 30+39 = 69 and then +1 for the final ball which will give us a colour with 14 balls, gives us 70.
Answer B
Posted from my mobile device
To do this, let’s say that all the colours with less than 14 balls are drawn: brown (7), black (10) and yellow (13). The sum of this is 30.
Next we have 3 colours equal to or exceeding 14 balls. White, red and green. Let’s say that 13 of each is drawn: 13*3 = 39. This means that no matter what balls is drawn next, we will have a colour with 14 balls drawn.
So 30+39 = 69 and then +1 for the final ball which will give us a colour with 14 balls, gives us 70.
Answer B
Posted from my mobile device
27 Jun 2021, 20:01
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Bunuel
V has to ensure that we have at least 14 balls of same colour
For this we have to take the worst scenario wherein we pick up 13 of each before picking the 14th of any one colour.
Thus we pick up 13 of Y, G, R and W, and all of the others as they are less than 13.
So we pick 13*4+10+7=69.
We are left with G, R and W.
Now whatever we pick, it will give 14th of that colour, ( G, R or W).
So 69+1=70 will ensure 14 of one of the colors for sure.
B
