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705-805 (Hard)|   Arithmetic|   Exponents|                        
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JBoe2002
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The product of all the prime numbers less than 20 is closest to which 19 Feb 2025, 15:36
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Is this also a possible solution for the problem?

2,3,5,7,11,13,17,19 -->2*5=10
3*7*10*11*13*17*19 -->3+7+10+11+13+17+19=70
70/7=10 --> 10*10*10*10*10*10*10 =10^7
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The product of all the prime numbers less than 20 is closest to which 28 Nov 2025, 08:22
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GMATCoachBen hpw does 2^3 add up to another 0
GMATCoachBen
Short video solution here (1:39):


The key is that we can round quite aggressively, since the answers are a full power of 10 apart. (For example, \(10^7\) is an enormous 1000% of \(10^6\))

In this solution video, I knew that 13*17 would round to be close to 200, since \(13^2\) = 169.

However, it may be easier to round down the 13 to 10, and round up the 17 to 20, to make it 10*20.

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2023-12-17 18_06_49-(2) Problem Solving (OG 2020)_ _The product of all the prime numbers less than 2.png
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The product of all the prime numbers less than 20 is closest to which 30 Nov 2025, 12:31
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AditiDeokar 2^3 is 8, which is close enough to 10 for this approximation.

It's important to look at the answer choices and see how far apart they are.

Notice that the answer choices are all *10 from each other, which is a huge difference — that would be the difference between 8 and 80. With this much smaller difference between 8 and 10, it's totally fine to round up to 10.

Does that help?
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GMATCoachBen hpw does 2^3 add up to another 0

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The product of all the prime numbers less than 20 is closest to which 26 Mar 2026, 00:29
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Bunuel
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
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2*3*5*7*11*13*17*19

2*5 * 3*7 * 11*13 * 17*19

10 * 21 * 143 * 323

10 * 2.1 * 10 * 1.43 * 100 * 3.23 * 100

10^6 * 2.1 * 1.43 * 3.23

~ 10^6 * 2 * 1.5 * 3
~ 10^6 * 9
~ 10^7

Correct Answer C
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The product of all the prime numbers less than 20 is closest to which 29 Jul 2026, 01:39
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2*3*5*7*11*13*17*19
2*5*11*19*(10-3)*(10+3)*(10+7)*(10-7)
10*~10*~20*(100-~10)*(100-~50)
10*10*20*90*50
9*10^6 is closest to 10^7 (not 10^6)
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The product of all the prime numbers less than 20 is closest to which 31 Jul 2026, 09:34
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Consider all the primes less than 20 whic are

2*3*5*7*11*13*17*19

Now, make pairs of numbers so that the product is close to 10 or multiples of 10

2*5=10=10^1
7*3=21~20=2*10^1
13*17=220~ 200=2*10^2
11*19=209~200=2*10^2

so the total 10s required is 10^6* 8= 10^7 is the answer
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