Question

2. What should be the values of a and b such that 1a8b is divisible by 2, 3, 4, 6, 7 and 8? (a) a = 3, b = 5 (b) a = 6, b = 0 (c) a = 4, b = 2 (d) None of these ​

Answer 1

Answer:

b

1680 is diviablw by 2,3,4,6and 7

Answer 2

Answer:

Step-by-step explanation:

(b) 1680 is divisible by 2, 3, 4, 6, 7, 8.

Proof:

{A number is divisible by another if it gives a zero remainder when divided by the latter}

==> 1680/2 = 840

==> 1680/3 = 560

==> 1680/4 = 420

==> 1680/6 = 280

==> 1680/7 = 240

==> 1680/8 = 210

Calculations:

#1

If a number has an even end – 0,2,4,6,8 – it is divisible by 2.

And since the end of 1a8b is "b", b should be an even integer.

"Hit and trial"

Let's see from the given options which one meets the requirements.

(a) says b = 5 – an odd value which is not acceptable, hence (a) gets discarded.

(b) says b = 0 – meets the requirement.

(c) says b = 2 – meets the requirement.

So either our number will be 1680 as per (b) or 1482 as per (c)

#2

If the sum of the digits of a number is divisible by 3, the number is divisible by 3.

(b) and (c) both meet this requirement, so moving further to check which one is divisible by 4.

#3

If the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4.

So, the last two digits!

80 from (b)

82 from (c)

{Check} Is 80 divisible by 4?

-- Yes! 4 × 20 = 80

{Check} Is 82 divisible by 4?

-- No! It leaves a remainder of 2 upon division by 4.

So, the number which is divisible by 4 is 1680 from (b) and NOT 1682 from (c).

And thus we have our number which is divisible by 2,3,4,6,7,8 ("the" "remarkable" number, I should say) – 1680.

Hope this helps! (Hope I'm not too late!!)^^"