The Product of the First 10 Prime Numbers is Closest GMAT Problem Solving

Question: The product of the first 10 prime numbers is closest to which of the following?

  1. 6.5 x 10^7
  2. 6.5 x 10^8
  3. 6.5 x 10^9
  4. 6.5 x 10^10
  5. 6.5 x 10^11

Correct Answer: C

Solution and Explanation:
Approach Solution 1:

The problem statement asks to find the product of the first 10 prime numbers.

The first 10 primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Therefore, it is required to find the approximate value of 2*3*5*7*11*13*17*19*23*29.
A number of different approximations are possible. For instance:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667

2*3*5*7*11*13*17*19
=~10*50*100*200*667
=10^7*667
=6.67*10^9 =~ 6.5 x 10^9
Therefore, the product of the first 10 prime numbers = 6.5 x 10^9

Approach Solution 2:
The problem statement asks to find the product of the first 10 prime numbers.

The first 10 Prime Numbers- 2,3,5,7,11,13,17,19,23,29
Let Product of 1st 10 Prime Number =P
Therefore P=2∗3∗5∗7∗11∗13∗17∗19∗23∗29
Now approximating the following as
5∗13=65
2∗3∗7≈40
11≈10
13≈10
17≈20
19≈20
23≈20
29≈30

Therefore P=65∗40∗10∗10∗20∗20∗20∗30
P=\(65∗8∗10^7\)
P=\(65∗8∗10^7\) (as 8≈10)
P=\(65∗10^8\)
P=\(6.5∗10∗10^8\)
P=\(6.5∗10^9\)
Therefore, the product of the first 10 prime numbers = 6.5 x 10^9

“The product of the first 10 prime numbers is closest”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide 2021”. GMAT Problem Solving questions enable the candidates to evaluate information and solve numerical problems. GMAT Quant practice papers help the candidates to go through several sorts of questions that will enable them to improve their mathematical learning.

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