Which among the following is the smallest 7 digit number that is exact

Question

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

GMATinsight · Accepted Answer

1000000 divided by 43 leaves 35 remainder (i.e. 35-43=-8 remainder

i.e. we need more in 1,000,000 to make it divisible by 43

i.e. 1,000,008

Answer: Option B

freedom128 · Answer

First, let's divide 1,000,000 by 43. We get a quotient of 23,255 and a remainder of 35.

Adding (43-35)=8 to 1,000,000 to become 1,000,008 and dividing that 1,000,008 by 43, we will then have a zero remainder.

HENCE, the smallest 7 digit number that is exactly divisible by 43 is 1,000,008

FINAL ANSWER IS (B)

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nick1816 · Answer

10^3= 860+129+11

10^3= 11 mod 43

10^6 = (121-129) mod 43

10^6 = -8 mod 43.

Smallest 7- digit number that is divisible by 43 is  (10^6 + 8)

B

exc4libur · Answer

mult: 43 86 129 172 215 258

1,000,000/43=xxxx25(0)=not divisible
1,000,008/43=xxxx25(8)=divisible

ans (B)

unraveled · Answer

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

Option A is not divisible by 43 since 1000,000 is not divisible by 43 as
 \frac{1000,000}{43} + \frac{43}{43}

Out of other options only one needs to be checked as they all are near to each other.
Taking option C, we need to have a remainder of '37+6' from  \frac{1000,000}{43} + \frac{6}{43} .
 \frac{1000,000}{43} = \frac{860,000 + 140,000}{43}  
 \frac{1000,000}{43}  =  \frac{860,000}{43} + \frac{86,000 + 54000}{43} 
 \frac{1000,000}{43}  =  \frac{860,000}{43} + \frac{86,000}{43} + \frac{51,600 + 2400}{43}  
 \frac{1000,000}{43}  =  \frac{860,000}{43} + \frac{86,000}{43} + \frac{51,600}{43} + \frac{1,720 + 680}{43} 
 \frac{1000,000}{43}  =  \frac{860,000}{43} + \frac{86,000}{43} + \frac{51,600}{43} + \frac{1,720}{43} + \frac{645 + 35}{43}

From last term we have a remainder of 35 so a total of 41 as remainder which is not possible. Since we are short of '2' in remainder we add that to the 1000,006 to get 1000,008 which must be divisible by 43. Hence B is correct.

Answer B.

randomavoidplease · Answer

Thought about this question for far too long, started doing long division since middle numbers are all 0 but didn't work and was taking too long as well. My initial guess was that it can't be an even ending number, but that as turns out is wrong (Eventually used a calculator so not submitting answer). I am sure there is a completely simple logic to it which is why leaving this comment to finish off Bunuel's question and also so I can come back and check it.

Thanks

Thanks

monikakumar · Answer

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

take 1000000 and divide it by 43, remainder is 250, so next number divisible by 43 is 258, therefore adding 8 will be divisible by 43. so 1000008 is divisible by 43
AnsB

lacktutor · Answer

Let's take  1,000,000. 
-->  1000000-860000= 140000 
-->  140000-129000= 11000 
-->  11000- 8600= 2400 
-->  2400-2150= 250 
-->  \frac{250}{43} = 5 \frac{35}{43}

In order 7 digit number to be divisible by 43, 8 should be added to 1000000
-->  1000000+ 8 = 1000008.

Answer (B)

Kinshook · Answer

1000000mod43 = 35mod43 = -8mod43

1000008mod43 = 0

IMO B

abhish27 · Answer

This is largely embarrassing but would u please elaborate how is 10^3=11mod43 and the next step 10^6 = (121-129) mod 43.
I am fan of yours ,going through all your solutions i can say u have pretty sound basics and i am a fan of your approach.

nick1816 · Answer

Bhai Thanks for the kind words!

1000 = 860+129+11

1000= 43*20 +43*3 +11

1000= 43K+11

1000*1000 = (43K+11)^2

10^6 = (43k)^2 + 2*11*43K +121

10^6 = (43k)^2 + 2*11*43K +129 -8

10^6= (43k)^2 + 2*11*43K + 3*43 -8

(43k)^2 + 2*11*43K + 3*43  is a multiple of 43; Hence,

10^6 = 43X -8

So if you divide 10^6 by 43, remainder you'll get is -8.

If you still have doubt, you can ask.

matteotchodi · Answer

i have no idea what other people are talking about when they say MOD.....

but for those that prefer to apply logic.... since the test is about logic....

we can subtract multiples of 43 to 1000000..... and then figure out the divisibility

Bambi2021 · Answer

10^6 = 1000^2

1000 / 43 gives remainder 11 (20*43+3*43+ 11 )

Equation reduces to

11^2 / 43

121 / 43 gives remainder 35 (43*2+ 35 )

The integer therefore must be 8 bigger than 10^6.

rvgmat12 · Answer

100^3 = 14*14*14 mod 43 = 196* 14 mod 43 = 24*14 mod 43 = -8 mod 43 (14*3 = -1 mod 43)

gokul5544 · Answer

We can re write this question to see what is the remainder when 10^6 is divided by 43.

10^6/43 can be re written as 100^3/43 = (86+14)^3/43

Now we just have to find the reminder of 14^3/43.

This comes out to 35. If we add 8 to 10^6 it will be perfect multiple.

Abolnasr · Answer

Those who write the answer like "first we divide 1,000,000 by 43" need to elaborate their answer a little, we're not all masterminds like you and can't make such advanced mental calculations instantly بالراحة علينا ياعم عرفنا إن دماغك كمبيوتر

Abolnasr · Answer

WhatsApp Image 2023-08-24 at 5.05.20 PM.jpeg

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Which among the following is the smallest 7 digit number that is exact

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Which among the following is the smallest 7 digit number that is exact

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