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GMAT/Data Sufficiency - Clicks, Ticks, Albs, & Berks
Clicks, Ticks, Albs, & Berks
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 4.
(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
| ОТВЕТЫ И КОММЕНТАРИИ |
| Решение |
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 x 77, 7 x 11, 11 x 7, 77 x 1.
| Clicks Awarded | Albs Captured | Ticks Awarded | Berks Captured |
| 1 | 3, 4 or 5 | 77 | 308, 309, 310, or 311 |
| 7 | 21, 22, or 23 | 11 | 44, 45, 46 or 47 |
| 11 | 33, 34, or 35 | 7 | 28, 29, 30 or 31 |
| 77 | 231, 232 or 233 | 1 | 4, 5, 6, or 7 |
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 4. Again, looking at the chart, we see that the number of Albs captured must be 4 or 232. 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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Funball Match
In the game of Funball, each batter can either hit a home run, hit a single, or
strikeout, and the likelihood of each outcome is completely determined by the
opposing pitcher. A Funball batter scores a point for their team by advancing
sequentially through each of four "bases", according to the following rules:
Home run: The batter and any players already on a base advance through all four
bases.
Single: The batter advances to first base, and any players already on a base
advance one base each.
Strikeout: No one advances any bases, and the batter loses his/her turn.
If the batting team has a runner on first base, which pitcher (Roger or Greg)
is more likely to allow a point before recording a strikeout?
(1) Greg is twice as likely as Roger to allow a single, and four times as
likely as Roger to record a strikeout.
(2) Greg is twice as likely as Roger to allow a single, and one fourth as
likely as Roger to allow a home run.
(A) Statement (1) alone is sufficient, but statement (2) alone is not
sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not
sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
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