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A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?
- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A bag is filled with blue, green, purple and red chips worth 2, 5, x a...
Since 13,689,000 is a multiple of 13 (the worth of a red chip), the product must have at least one red chip. Divide 13,689,000 by 13 to find the product of the other chips: 13,689,000 / 13 = 1,052,000.
Now, notice that 1,052,000 is a multiple of 5 (the worth of a green chip). Divide 1,052,000 by 5 to find the product of the other chips: 1,052,000 / 5 = 210,400.
Since all remaining chips are blue and purple, and blue chips are worth 2 points, the product of all remaining chip points must be a power of 2. The highest power of 2 that divides 210,400 is 2^4 = 16. Divide 210,400 by 16 to find the product of the purple chips: 210,400 / 16 = 13,150.
Now we just need to find what x could be for the purple chips. Since x must be greater than 5 and less than 13, our possible values for x are 6, 7, 8, 9, 10, 11, and 12. The only value of x that divides 13,150 without any remainder is 12. Divide 13,150 by 12 to see how many purple chips there are: 13,150 / 12 = 1095 / 6 = 365 / 2 = 182.5.
Since there must be a whole number of purple chips, there were 2 purple chips selected. The answer is B.
Now, notice that 1,052,000 is a multiple of 5 (the worth of a green chip). Divide 1,052,000 by 5 to find the product of the other chips: 1,052,000 / 5 = 210,400.
Since all remaining chips are blue and purple, and blue chips are worth 2 points, the product of all remaining chip points must be a power of 2. The highest power of 2 that divides 210,400 is 2^4 = 16. Divide 210,400 by 16 to find the product of the purple chips: 210,400 / 16 = 13,150.
Now we just need to find what x could be for the purple chips. Since x must be greater than 5 and less than 13, our possible values for x are 6, 7, 8, 9, 10, 11, and 12. The only value of x that divides 13,150 without any remainder is 12. Divide 13,150 by 12 to see how many purple chips there are: 13,150 / 12 = 1095 / 6 = 365 / 2 = 182.5.
Since there must be a whole number of purple chips, there were 2 purple chips selected. The answer is B.
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Community Answer
A bag is filled with blue, green, purple and red chips worth 2, 5, x a...
To solve this question, we need to find the number of purple chips selected. Let's break down the given information and the steps to solve the problem.
Given Information:
- A bag contains blue, green, purple, and red chips.
- The blue chip is worth 2 points.
- The green chip is worth 5 points.
- The purple chip is worth x points.
- The red chip is worth 13 points.
- The worth of a purple chip is more than the worth of a green chip but less than that of a red chip.
- The product of the points of the selected chips is 13,689,000.
Step 1: Setting up the equation:
Let's assume that the number of blue chips selected is a, green chips selected is b, purple chips selected is c, and red chips selected is d.
The equation can be set up as follows:
2^a * 5^b * x^c * 13^d = 13,689,000
Step 2: Determining the value of x:
From the given information, the worth of a purple chip is more than the worth of a green chip but less than that of a red chip. Therefore, x must be greater than 5 and less than 13.
Step 3: Prime factorization of 13,689,000:
Prime factorize the number 13,689,000 to find its prime factors. The prime factorization of 13,689,000 is:
13,689,000 = 2^3 * 5^4 * 7^2 * 13^2
Step 4: Analyzing the prime factors:
From the prime factorization, we can conclude the following:
- The power of 2 is a multiple of 3.
- The power of 5 is a multiple of 4.
- The power of 7 is a multiple of 2.
- The power of 13 is a multiple of 2.
Step 5: Analyzing the equation:
To make the equation balance, the powers of the prime factors on both sides of the equation must match.
From step 4, we can conclude the following:
- The power of 2 on the left side of the equation must be a multiple of 3.
- The power of 5 on the left side of the equation must be a multiple of 4.
- The power of 7 on the left side of the equation must be a multiple of 2.
- The power of 13 on the left side of the equation must be a multiple of 2.
Step 6: Determining the number of purple chips:
From step 5, we can determine the following:
- The power of 2 on the left side of the equation is a multiple of 3, which means the number of blue chips selected (a) is a multiple of 3.
- The power of 5 on the left side of the equation is a multiple of 4, which means the number of green chips selected (b) is a multiple of 4.
- The power of 7 on the left side of the equation is a multiple of 2, which means the number of purple chips selected (c) is a multiple of 2.
- The power of
Given Information:
- A bag contains blue, green, purple, and red chips.
- The blue chip is worth 2 points.
- The green chip is worth 5 points.
- The purple chip is worth x points.
- The red chip is worth 13 points.
- The worth of a purple chip is more than the worth of a green chip but less than that of a red chip.
- The product of the points of the selected chips is 13,689,000.
Step 1: Setting up the equation:
Let's assume that the number of blue chips selected is a, green chips selected is b, purple chips selected is c, and red chips selected is d.
The equation can be set up as follows:
2^a * 5^b * x^c * 13^d = 13,689,000
Step 2: Determining the value of x:
From the given information, the worth of a purple chip is more than the worth of a green chip but less than that of a red chip. Therefore, x must be greater than 5 and less than 13.
Step 3: Prime factorization of 13,689,000:
Prime factorize the number 13,689,000 to find its prime factors. The prime factorization of 13,689,000 is:
13,689,000 = 2^3 * 5^4 * 7^2 * 13^2
Step 4: Analyzing the prime factors:
From the prime factorization, we can conclude the following:
- The power of 2 is a multiple of 3.
- The power of 5 is a multiple of 4.
- The power of 7 is a multiple of 2.
- The power of 13 is a multiple of 2.
Step 5: Analyzing the equation:
To make the equation balance, the powers of the prime factors on both sides of the equation must match.
From step 4, we can conclude the following:
- The power of 2 on the left side of the equation must be a multiple of 3.
- The power of 5 on the left side of the equation must be a multiple of 4.
- The power of 7 on the left side of the equation must be a multiple of 2.
- The power of 13 on the left side of the equation must be a multiple of 2.
Step 6: Determining the number of purple chips:
From step 5, we can determine the following:
- The power of 2 on the left side of the equation is a multiple of 3, which means the number of blue chips selected (a) is a multiple of 3.
- The power of 5 on the left side of the equation is a multiple of 4, which means the number of green chips selected (b) is a multiple of 4.
- The power of 7 on the left side of the equation is a multiple of 2, which means the number of purple chips selected (c) is a multiple of 2.
- The power of
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A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer?
Question Description
A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer?.
A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer?.
Solutions for A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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ample number of questions to practice A bag is filled with blue, green, purple and red chips worth 2, 5, x and 13 points each, respectively. The worth of a purple chip is more than the worth of a green chip, but less than that of a red chip. A certain number of chips are selected randomly from the bag. If the product of the points of the selected chips is 13,689,000, how many purple chips were selected?a)1b)2c)3d)4e)5Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
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