rite2deepti wrote:
In a certain game played with red chips and blue chips, each red chip has a point value
of X and each blue chip has a point value of Y, where X>Y and X and Y are positive
integers. If a player has 5 red chips and 3 blue chips, what is the average (arithmetic
mean ) point value of the 8 chips that the player has?
(1) The average point value of one red chip and one blue chip is 5.
(2) The average point value of the 8 chips that the player has is an integer.
I am absolutely clueless about this question ...how to proceed ..Also please explain in detail
If algebra doesn't work for you, go on and use brute force.
Simply try to arrange the information you have:
Red - X points Blue - Y points
X > Y, X and Y are +ve integer (You kind of expect it from a regular game so nothing to remember here)
5 Red ..... 3 Blue
Statement 1: Average point value of 1 Red and 1 Blue chip is 5, their total point value will be 5*2 = 10
So only 4 cases possible:
1 Red (9).... 1 Blue (1)
1 Red (8).... 1 Blue (2)
1 Red (7).... 1 Blue (3)
1 Red (6).... 1 Blue (4)
Average of 5 reds and 3 blues will be different in each case so not sufficient.
Statement 2: Average of 8 chips is integer. Insufficient alone.
Both statements together:
Case 1: 1 Red (9).... 1 Blue (1): 5 Red + 3 Blue = 48 - Divisible by 8
Case 2: 1 Red (8).... 1 Blue (2): 5 Red + 3 Blue = 46 - Not div by 8
Case 3: 1 Red (7).... 1 Blue (3): 5 Red + 3 Blue = 44 - Not div by 8
See the pattern, next one will be 42 - Not div by 8
Since in only one case, we get the average of 8 chips an integer, both together are sufficient. Answer (C).
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