What is the greatest five-digit which when divided by 4, 6, 10 and 15

Question

What is the greatest five-digit which when divided by 4, 6, 10 and 15 leaves the same remainder 3 in each case?

(A) 99,993 
(B) 99,963
(C) 99,063
(D) 90,093 
(E) 90,063

abuc0112 · Answer

My attempt

Looking through the answers we can eliminate A, B, & D because after subtracting 3, the numbers will not be divisible by 3 or 4

Now for the remaining answers C & E after subtracting 3, the resulting numbers are divisible by 4, 6, 10, 15. So the greatest number is 99,063

Answer C

VirFortis · Answer

Given -> 4, 6, 10 and 15 leaves the same remainder 3 
Target -> greatest number to satisfy given condition.

Check options ->
Divisibility with 4, should leave remainder 3.
A and D are not divisible by 4 but each leaves remainders 1. Discard.

Divisibility check with 6 -> divisible by 2 (none of the left options), divisibility by 3.
All leave remainder 3 when divided by 6.

Greatest among these -> B.

Ans. B.

rohitagr999 · Answer

This is trick question, I first tried option E and it worked, it gave reminder of 3 wen divided by 4,6,10 and 15

but later I realized even B gives same answer and question is asking for greater no, so I should not have tested lowest no at the first place.

Just in case someone repeats same mistake like me

parasma · Answer

As number leaves remainder 3 if divided by 4 and 6. So it must leave remainderof 3 if divide by 24.
Ie it must leave remainder of 3 if we divide the number by 8.
There is only one number which leaves remainder of 3 after dividing by 8.

Answer is B. 
Dear Bunuel seeking your input on my approach.

Posted from my mobile device

abhishumat · Answer

Here's my thought process for solving this particular question:

First, find a number that gives the same remainder when divided by the given numbers (4, 6, 10, 15), i.e look for their  HCF .
 HCF: 60

Next, find the  greatest five-digit multiple of the HCF . It can also be calculated by seeing how off the smallest 6 digit number (100,000) is from 60. (100000%60) 
Which will bring you to 99960.

Finally just  add the remainder , 3 in this case, to 99963, offsetting it by the amount required. 
 Answer : B

Checking all the options here by dividing might 
1. Be time-consuming as it might so happen that the last number that you check by the division process might be the one you were looking for.
2. There might be multiple options that would be divisible and you might just end up with the wrong one.

Cheers

chetan2u · Answer

Find LCM and then greatest 5-digit integer.

LCM(4,6,10,15)=60
Surely 99,900 is a multiple of 60, next number becomes 99,900+60=99,960.

Use options

Since the option-3 is a multiple of 4, last two digits must be divisible by 4.

We have two cases 60 and 90, out of which 60 is a multiple of 4.
The largest option with 60 as last two digits is 99,960, which is 3*33,320. 
So, 99,960 is multiple of 3, 4 and of course 5, so 3*4*5 or 60.

B

AnishTrivedi99 · Answer

I went with this way, look at the options and subtract 3,

Clearly the numbers that end with 90 wont be our solution as they wont be divisible by 4 (rule of divisibility)

A & D are out

Look for the biggest, 99963 (or 99960 after subtraction), it will be divisible by 4, 6, 10 and 15. (15's rule is the number should be divisible by both 3 & 5)

Hence, B

nikchopra · Answer

Did it in a different way , LCM is 60 and once you start adding 60 to each starting from 3- 
List becomes 3,63,123,183,243,......
|
Notice multiples of 6 are forming hence in options look for the same

B is the one which is the greatest satisfying that

Marcelo7 · Answer

My Attempt

Find the LCM of 4,6,10,15 = 60 and plus 3 (since every division must have the same remainder: 3).

Using letter A as an example, 99,993 = Q*60 +3 so 99,993 - 3 = Q*60 so Q = (99,993 - 3) / 60 and this operation must be an integer!!!

A) (99,993 - 3)/ 60 = 99,990 / 60 = 9,999/6 isn`t multiple X
B) (99,963 - 3)/ 60 = 99,960 / 60 = 9,996/6 is a multiple (possible answer)
C) (99,063 - 3)/ 60 ... same drill ... 9,906/6 is a multiple (possible answer)
D) same drill... = 9,009/6 not a multiple
E) same drill... = 9,006/6 is a multiple (possible answer)

Now we just need to find the greatest number between B, C and E, which is B, the answer.

It took me over 3 min to spot this solution, so any tips for how to quickly find solutions for this type of exercise are very welcome!

Thanks for reading.

What is the greatest five-digit which when divided by 4, 6, 10 and 15

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What is the greatest five-digit which when divided by 4, 6, 10 and 15

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