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The product of all the prime numbers less than 20 is closest
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10 Aug 2020, 11:33
10 Aug 2020, 11:33
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Question Stats:
38% (00:58) correct
61% (01:50) wrong based on 21 sessions
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The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
(A) \(10^9\)
(B) \(10^8\)
(C) \(10^7\)
(D) \(10^6\)
(E) \(10^5\)
(A) \(10^9\)
(B) \(10^8\)
(C) \(10^7\)
(D) \(10^6\)
(E) \(10^5\)
Re: The product of all the prime numbers less than 20 is closest
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10 Aug 2020, 11:34
10 Aug 2020, 11:34
Expert Reply
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Re: The product of all the prime numbers less than 20 is closest
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10 Aug 2020, 11:43
10 Aug 2020, 11:43
1
Carcass wrote:
The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
(A) \(10^9\)
(B) \(10^8\)
(C) \(10^7\)
(D) \(10^6\)
(E) \(10^5\)
(A) \(10^9\)
(B) \(10^8\)
(C) \(10^7\)
(D) \(10^6\)
(E) \(10^5\)
Don't even think about using a calculator!
Since the answer choices are very spread apart (each number is 10 times greater than the next answer choice), we can be somewhat AGGRESSIVE with our estimation.
We have the product (2)(3)(5)(7)(11)(13)(17)(19)
Let's see if we can group the numbers to get some approximate powers of 10
First (2)(5)=10, so we get (2)(3)(5)(7)(11)(13)(17)(19) = (10)(3)(7)(11)(13)(17)(19)
Next, 11 is close enough to 10, so we get: (10)(3)(7)(11)(13)(17)(19) ≈ (10)(3)(7)(10)(13)(17)(19) [approximately]
Next, (7)(13)=91, which is pretty close to 100. So we get (10)(3)(7)(10)(13)(17)(19) ≈ (10)(3)(100)(10)(17)(19) [approximately]
Finally, 3(17)=51, and (51)(19) is very close to (51)(20), which is very close to 1000
So,(10)(3)(100)(10)(17)(19) ≈ (10)(1000)(100)(10) ≈ 10,000,000
Since 10,000,000 = 10^7, the best answer is C
Cheers,
Brent
