Divisibility

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himadeepm: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Jun 22, 2020 11:34 am

by himadeepm » Sun Jul 05, 2020 9:12 am

Which among the following is the smallest 7 digit number that is exactly divisible by 43?

A. 1,000,043
B. 1,000,008
C. 1,000,006
D. 1,000,002
E. 1,000,001

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Source: Beat The GMAT — Quantitative Reasoning | Sun Jul 05, 2020 9:12 am

terminator12: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jul 28, 2020 9:01 pm

Re: Divisibility

by terminator12 » Tue Jul 28, 2020 9:50 pm

The way to solve these kinds of questions is:
Divide 1,000,000 by 43 and find the remainder.
Then subtract the remainder from 43, and add the result to 1,000,000

1,000,000 = 43 x 23,255 + 35
43 - 35 = 8
Adding 8 to 1,000,000 gives 1,000,008
Hence, answer is B

You may also notice that:
1,000,008 = 43 x 23,256

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Ignite: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sat Aug 01, 2020 9:03 pm

Re: Divisibility

by Ignite » Sat Aug 01, 2020 11:30 pm

Let's consider 1000000

We can find out that 1000000 = 43 * 23255 + 35

43 * 23255 = 999965
999965 + 43 = 1000008

Thus, B

Thanks,
Ignite

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NahidulRaffi: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sat Apr 15, 2023 3:27 pm

Re: Divisibility

by NahidulRaffi » Sat Apr 15, 2023 3:33 pm

Could anyone guide me to calculate this 1000000 = 43 * 23255 + 35 faster?

Thanks in advance.

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GMATJourneyman: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Wed May 24, 2023 7:40 am

Re: Divisibility

by GMATJourneyman » Wed May 24, 2023 7:57 am

NahidulRaffi wrote: ↑
Sat Apr 15, 2023 3:33 pm
Could anyone guide me to calculate this 1000000 = 43 * 23255 + 35 faster?

Thanks in advance.

Round 23255 up to 23300, then multiply by 43 for a pretty quick estimate.

Just add 35 after that.

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