bipolarbear wrote:

In the game Cako, a player is awarded one tick for every third Alb captured, and one click for every fourth Berk captured. The total score is equal to the product of clicks and ticks. If a player has a score of 77, how many Albs did he capture?

(1) The difference between Albs captured and Berks captured is 7.

(2) The number of Albs captured is divisible by 5.

OFFICIAL EXPLANATION

Every third Alb gives a click. This means no click is awarded until the third Alb is captured. The second click is not awarded until the sixth Alb is captured. Similarly, a tick is not awarded until the fourth Berk is captured.

We are told that the product clicks x ticks = 77. Thus, there are four possibilities: 1 × 77, 7 × 11, 11 × 7, 77 × 1.

Statement (1) tells us that the difference between Albs captured and Berks captured is 7. Looking at the chart, the only way to get a difference of 7 between Albs captured and Berks captured is with 35 Albs and 28 Berks. Therefore, statement (1) is sufficient to answer the question--there must have been 35 Albs captured.

Statement (2) says the number of Albs captured is divisible by 5. Again, looking at the chart, we see that the number of Albs captured must be 5 or 35. Therefore, statement (2) is not sufficient to answer the question--we do not know how many Albs were captured.

The correct answer is A: Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

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