The Product of All the Prime Numbers Less than 20 is Closest GMAT Problem Solving

Question: 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. \(10^5\)

Answer:
Approach Solution (1):
We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10
# of different approximations is possible
2*5 = 10;
3*7 = 20 (actually more than 20);
11*19 = 200 (actually more than 200);
13*17 = 200 (actually more than 200);
2*3*5*7*11*13*17*19 = 10*20*200*200 = 8*\(10^6\)\(≈ {10^7}\)
Correct option: C

Approach Solution (2):
We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10
# of different approximations is possible
2*5 = 10;
3*7 = 50 (actually more than 50);
7*13 = 100 (actually less than 100);
11*19 = 200 (actually more than 200);
2*3*5*7*11*13*17*19 = 10*50*100*200\(≈ {10^7}\)
Correct option: C

Approach Solution (3):
Product of Prime no between 1 & 20 =
(2*3*5*7)*(11*13)* (17*19)
210 * 143 * 323
(\(10^2\)+10)∗( \(10^1\)+43)∗(\(10^3\)+23)
(\(10^3\)+4300+\(10^2\)+430)∗( \(10^3\)+23)
5830∗(\(10^3\)+23)
5830000 + 134090
= 6974090 this is near to\(10^7\)
Correct option: C

“The product of all the prime numbers less than 20 is closest to which of the following powers of 10?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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