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Divisibility

Problem Solving — algebra and arithmetic
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Junior | Next Rank: 30 Posts
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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: — Quantitative Reasoning |
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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Junior | Next Rank: 30 Posts
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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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Newbie | Next Rank: 10 Posts
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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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Junior | Next Rank: 30 Posts
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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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