Stack of Cards

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A stack of colored cards is sorted such that x blue cards, y red cards, and z green cards are placed on top of each yellow card, and there are no cards left over. How many yellow cards are there?

(1) The numbers of blue, red, and green cards placed on a given yellow card are in the ratio 3:4:7, respectively.

(2) A total of 90 blue cards, 120 red cards, and 210 green cards are placed.

Review: Stack of Cards




Explanation

This is a ratio question. We prefer to express two-element ratios as fractions, but we have four elements here, so colon notation is better:



On to the statements, separately first.

Statement (1) looks like it's giving us exactly what we need, at first blush. But on closer inspection, it's not giving us the number of blue, red and green cards per yellow card, only a ratio of the cards. There could be 3, 4, and 7 cards per yellow card, in one case, or 6, 8, and 14 cards per yellow card, in another case. Therefore, Statement (1) is insufficient.

Statement (2) has a similar problem. The two cases we picked for Statement (1) are both possible here. That means that Statement (2) is insufficient, and both statements together will be insufficient.

The correct answer is (E).


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