What is the value of M and N respectively? If M39048458N is

Question

What is the value of M and N respectively? If M39048458N is divisible by 8 & 11; Where M & N are single digit integers?

(a) 7, 8
(b) 8, 6
(c) 6, 4
(d) 5, 4
(e) 3,2

nakib77 · Answer

it is a long one.

first I tried to see what would be the last digit if the number is divisible by 8

becasue the hundreds digit is odd ,

so the reminder after dividing the hundreds will obviously be odd.

so 8 *A = odd tens are 16, 32, 56 and 72

so reminder after divions on tens will be 8 - 6 = 2 or 8 -2 = 6

in order to be divisible by 8 the ones has to be 4 because only 24 and 64 is divisible by 8.

so only C and D remains.

I don't have any shortcut rules for divisibility by 11, so i will plug both 5 and 6 and see which one is divisible by 11,

so after spending almost 5 minutes :twisted:

I got C as the answer.

does anyone else has better way to solve this problem :?:

I got C as the answer. does anyone else has better way to solve this problem :?:

laxieqv · Answer

Consider an integer a

 a = an10n + an-110n-1 +...+ a1101 + a0 
Criteria of divisibility by 11
 a is divisible by 11 if and only if the alternating sum of the digits (-1)nan + (-1)n-1an-1 + ... -a1 + a0 is divisible by 11

nakib77 · Answer

Thanks Lexi for the short cut. Can you please give an example and illustrate it further. I am still not certain how to use it.

thanks.

laxieqv · Answer

it's C 
we have 6390484584 = 6*10^9 + 3^10^8 + 9*10^7 + .....8*10^1 + 4*10^0

apply the 11 divisibility trick here: 
we have : (-1) ^9 * 6 + (-1)^ 8 *3 + .....+ (-1)^1*8 + (-1)^0*4 = -11 , which is divisible by 11.

nakib77 · Answer

Wow this is the cooles trick ever :wow

thanks buddy.

GMATT73 · Answer

This is definately going into my flashcards. Nice trick Laxie. Tricks like these separate Q50 from Q40 level test takers.

cool_jonny009 · Answer

yup OA is C ..

here is OE

If the last three digits of a number is divisible by 8, then the number is divisible by 8 (test of divisibility by 8).

Here, last three digits 58N is divisible by 8if N = 4. (Since 584 is divisible by 8.)

so down to C D

For divisibility by 11. If the digits at odd & even places of a given number are equal or differ by a number divisible by 11, then the given number is divisible by 11.

Therefore, (M+9+4+4+8)-(3+0+8+5+N)=(M+5) should be divisible by 11 => when M = 6

hence C

:done

rigger · Answer

I don't think C is right. It should be b.

Here is how I did it

add up digit 1, 3, 5 ..... we get M+25
add up digit 2, 4, 6 ..... we get N+16

Both M+25 and N+16 must be divisible by 11. Therefore M = 8 and N = 6.

Hence the last two digits are 86, which is divisible by 4.

The answer should be B.

rigger · Answer

Opps read the question wrong... should be divisible by 8.

the answer is C.

What is the value of M and N respectively? If M39048458N is

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