A diagram has exactly two black dots and one green dot for every two r

Question

A diagram has exactly two black dots and one green dot for every two red dots. There are no dots of any other color in the diagram. Which of the following could be the number of dots in the diagram?

A. 3
B. 18
C. 36
D. 45
E. 52

A. 3
B. 18
C. 36
D. 45
E. 52

A diagram has exactly two black dots and one green dot for every two red dots. There are no dots of any other color in the diagram. Which of the following could be the number of dots in the diagram?

A. 3
B. 18
C. 36
D. 45
E. 52

AP001 · Answer

Can anyone explain this question please? TIA

Regor60 · Answer

The question is saying that for every set of 2 red dots, there are also 2 black dots and 1 green dot.

So let's say there ARE just 2 red dots. That means there are also 2 black dots and 1 green.

These total to 5.

But we could have multiple sets of 2 red dots, say X of them, since the question doesn't limit to just 1 set

So then there would be 2X red dots, 2X black and 1X green, for a total of

5X.

So the total number of dots could vary but would always be a multiple of 5.

Which answer choice is a multiple of 5?

Posted from my mobile device

vishthedish · Answer

why is 3 incorrect? If there are 2(Block dots) and 1(Red dot) does this mean we can have 0(Green dots) ?

priyankagh · Answer

My line of reasoning for this question is that the total number of dots must be odd. That leaves me with options A & D, but since 3 seems unlikely ("exactly two black dots and exactly one green dot for every two red dots"), I chose to go with D. Can someone confirm if my process made logical sense?

IanStewart · Answer

No, that's not right -- we might have 4 black, 2 green and 4 red dots here, for example, for a total of 10 dots, which is even.

Regor60 above posted the correct solution: for every 1 green dot we have 2 red dots and 2 black dots. So we can divide all the dots into sets of 5, where each set has 1 green, 2 red and 2 black dots. So the total number of dots must be a multiple of 5 (and it could be any positive multiple of 5 at all, but of the answer choices, only 45 is possible).

A diagram has exactly two black dots and one green dot for every two r

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A diagram has exactly two black dots and one green dot for every two r

Prep Toolkit

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