Question

Q54

Please help me as soon as possible

Answer 1

G. 182

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According to the question, the number we are looking for has a form of:

• 9k + 2 or
• 10t + 2 or
• 12p + 2

If we subtract 2 form the number then it is divisible by 9, 10 and 12.

Find LCM of the three numbers:

• LCM (9, 10, 12) = LCM (3*3, 2*5, 2*2*3) = 2*2*3*3*5 = 180

Add 2 to the result to get the number we need:

• 180 + 2 = 182

The matching choice is G.

Answer 2

G. 182

Explanation:

To find the smallest number of bingo chips in the original pile that can be divided evenly among 9, 10, or 12 players with two chips left over, we need to find the least common multiple (LCM) of 9, 10, and 12, and then add 2 to that LCM.

To find the LCM of a set of numbers, first find the prime factorizations of these numbers (the prime numbers that multiply together to make the original number):

• 9 = 3²
• 10 = 2 × 5
• 12 = 2² × 3

Now, multiply each prime factor the maximum number of times it appears in any of the factorizations:

LCM(9, 10, 12) = 2² × 3² × 5 = 4 × 9 × 5 = 180

Therefore, the least common multiple (LCM) of 9, 10 and 12 is 180.

To account for the two extra chips, add 2 to the LCM:

180 + 2 = 182

So, the smallest number of bingo chips that could be in the original pile is 182.