If n is the product of the integers from 1 to 8...

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swerve: Legendary Member; Posts: 2548; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue Dec 19, 2017 10:39 am

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A) Four
B) Five
C) Six
D) Seven
E) Eight

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Dec 19, 2017 10:39 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Tue Dec 19, 2017 10:49 am

If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A) Four
B) Five
C) Six
D) Seven
E) Eight

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

Hi Swerve,
Let's take a look at your question.

n is the product of the integers from 1 to 8, inclusive.

$$n=1\times2\times3\times4\times5\times6\times7\times8$$ $$n=1\times2\times3\times\left(2\times2\right)\times5\times\left(2\times3\right)\times7\times\left(2\times2\times2\right)$$ $$n=1\times2\times2\times2\times2\times2\times2\times2\times3\times3\times5\times7$$

We can see that the product n has four different prime factors, 2, 3, 5, 7.

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Jan 10, 2020 5:29 am

swerve wrote:If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?

A) Four
B) Five
C) Six
D) Seven
E) Eight

n = (1)(2)(3)(4)(5)(6)(7)(8)
= (1)(2)(3)(2)(2)(5)(2)(3)(7)(2)(2)(2)
The prime factors are 2, 3, 5 and 7

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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