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What percentage of odd prime numbers lying between 1 and 30 divide 7,700 completely?

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by VJesus12 » Sun Jan 17, 2021 4:59 am

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Answers

A

B

C

D

E

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What percentage of odd prime numbers lying between 1 and 30 divide 7,700 completely?

A. 20%
B. 25%
C. 30%
D. 33%
E. 40%

Answer: D

Source: e-GMAT
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Re: What percentage of odd prime numbers lying between 1 and 30 divide 7,700 completely?

by deloitte247 » Fri Jan 22, 2021 10:41 am
Odd prime numbers between 1 and 30 => 3, 5, 7, 11, 13, 17, 19, 23, and 29
So, there are 9 odd prime numbers between 1 and 30.
Odd prime numbers that can divide 7700 completely can be gotten from the prime factors of 7700 which is $$2^2\cdot5^2\cdot7\cdot11.$$
$$The\ odd\ ones\ are\ 5^2\cdot7\cdot11.$$
So, that means there are 3 odd prime numbers that divide 7700 completely, and they are 5, 7, and 77.
Hence, out of the total odd prime numbers between 1 and 3, the % that can divide 7700 completely will be
$$\frac{3}{9}\cdot100=33.33\%$$

Answer = option D
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