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Which of the following expressions is equivalent to 17,640?
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29 Oct 2018, 17:07
29 Oct 2018, 17:07
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Which of the following expressions is equivalent to 17,640?
Indicate all such expressions.
A. \(2^3 \times 3^2 \times 5 \times 7^2\)
B. \(2^3 \times 3^2 \times 7^2 \times 11\)
C. \((2 \times 3 \times 7)^2 \times 10\)
D. \(5 \times 7 \times 7 \times 8 \times 9\)
E. \(7 \times 7 \times 8 \times 9 \times 11\)
Indicate all such expressions.
A. \(2^3 \times 3^2 \times 5 \times 7^2\)
B. \(2^3 \times 3^2 \times 7^2 \times 11\)
C. \((2 \times 3 \times 7)^2 \times 10\)
D. \(5 \times 7 \times 7 \times 8 \times 9\)
E. \(7 \times 7 \times 8 \times 9 \times 11\)
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Re: Which of the following expressions is equivalent to 17,640?
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26 Nov 2018, 08:02
26 Nov 2018, 08:02
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sandy wrote:
Which of the following expressions is equivalent to 17,640?
Indicate all such expressions.
A. \(2^3 \times 3^2 \times 5 \times 7^2\)
B. \(2^3 \times 3^2 \times 7^2 \times 11\)
C. \((2 \times 3 \times 7)^2 \times 10\)
D. \(5 \times 7 \times 7 \times 8 \times 9\)
E. \(7 \times 7 \times 8 \times 9 \times 11\)
Indicate all such expressions.
A. \(2^3 \times 3^2 \times 5 \times 7^2\)
B. \(2^3 \times 3^2 \times 7^2 \times 11\)
C. \((2 \times 3 \times 7)^2 \times 10\)
D. \(5 \times 7 \times 7 \times 8 \times 9\)
E. \(7 \times 7 \times 8 \times 9 \times 11\)
Most of the answer choices feature products of prime numbers.
This suggests that we may benefit from finding the prime factorization of 17,640
17,640 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 7 = 2³ x 3² x 5 x 7²
So, one answer is A
We can also write:
17,640 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 7
= 2 x 2 x 3 x 3 x 7 x 7 x 2 x 5
= [2 x 3 x 7][2 x 3 x 7] x 2 x 5
= [2 x 3 x 7]² x 10
So, another answer is C
We can also write:
17,640 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 7
= 8 x 9 x 5 x 7 x 7
= 5 x 7 x 7 x 8 x 9
So, another answer is D
Since there are no 11's in the prime factorization of 17,640, we can ELIMINATE B and E
Answer: A, C, D
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Re: Which of the following expressions is equivalent to 17,640?
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10 Jul 2023, 16:07
10 Jul 2023, 16:07
1
Which of the following expressions is equivalent to 17,640?
Indicate all such expressions.
A. 2^3×3^2×5×7^2
B. 2^3×3^2×7^2×11
C. (2×3×7)^2×10
D. 5×7×7×8×9
E. 7×7×8×9×11
Another way to look at this question is to understand what the question is asking and what help the given options can provide:
Since 17,640 has unit digits ending in 0 , so there must be at least one factor of 2 and 5 to give us the solution.
if we look closely at option B and E , they do not have any 5 as the prime factor so they can be straight away eliminated.
For all the other options if you see they are just a form of expressing the same Prime factorization - 2^3×3^2×5×7^2
Indicate all such expressions.
A. 2^3×3^2×5×7^2
B. 2^3×3^2×7^2×11
C. (2×3×7)^2×10
D. 5×7×7×8×9
E. 7×7×8×9×11
Another way to look at this question is to understand what the question is asking and what help the given options can provide:
Since 17,640 has unit digits ending in 0 , so there must be at least one factor of 2 and 5 to give us the solution.
if we look closely at option B and E , they do not have any 5 as the prime factor so they can be straight away eliminated.
For all the other options if you see they are just a form of expressing the same Prime factorization - 2^3×3^2×5×7^2
