How many zeros does 135^19 x 42^17 end with?

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sat Jan 06, 2018 3:54 am

How many zeros does 135^19 x 42^17 end with?

(a) 0
(b) 2
(c) 5
(d) 13
(e) 17

The OA is the option E.

How can I find the number of zeros fast? I want your explanation experts. Please.

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Source: Beat The GMAT — Problem Solving | Sat Jan 06, 2018 3:54 am

elias.latour.apex: Master | Next Rank: 500 Posts; Posts: 228; Joined: Thu Apr 20, 2017 1:02 amFollowed by: 3 members; Location: Global; Thanked: 32 times; GMAT Score:770

by elias.latour.apex » Sat Jan 06, 2018 10:02 am

To have a zero at the end, a number must be multiplied by 10. Another way to think of this is that the number must be multiplied by the prime factors 5 and 2.

135 can be factored into 5 and 27. There are no other factors of 5 or 2.
42 can be factored into 2 and 21. There are no other factors of 5 or 2.

So 135^19 will have 19 5s, and 42^17 will have 17 2s. So the answer will end in 17 zeros because there are more 2s than 5s.

Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622

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