If $M$ and $N$ are integers, is $\dfrac{10^M + N}3$ an integer?

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Fri Oct 02, 2020 12:53 am

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If $M$ and $N$ are integers, is $\dfrac{10^M + N}3$ an integer?

(1) $N = 5.$
(2) $MN$ is even.

Answer: E

Source: GMAT Club Tests

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Source: Beat The GMAT — Data Sufficiency | Fri Oct 02, 2020 12:53 am

DHRJ007: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Thu Sep 17, 2020 9:27 amFollowed by: 1 member

Re: If $M$ and $N$ are integers, is $\dfrac{10^M + N}3$ an integer?

by DHRJ007 » Fri Oct 02, 2020 1:56 am

1) M can be any integer coz 10/3 will always leave 1 as remainder.
since N=5 then 5/3 leaves 2 as remainder.
so 1+2/3 will leave NO remainder.
so the whole expression will be an integer.
SUFFICIENT.

2)with changing values of N, we will get different remainders.
so INSUFFICIENT.

IMO
ANS: A

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