Col. A: (40076)(90042)
Col. B: (40075)(90043)

Col. A: (40000 + 76)(90000 + 42)
Col. B: (40000 + 75)(90000 + 43)

Col. A: 3600000000 + (40000)(42) + (76)(90000) + (76)(42)
Col. B: 3600000000 + (40000)(43) + (75)(90000) + (75)(43)

Subtracting 36000000000 from both the sides;

Col. A: (40000)(42) + (76)(90000) + (76)(42)
Col. B: (40000)(43) + (75)(90000) + (75)(43)

Col. A: (168)(\(10^4\)) + (684)(\(10^4\)) + 3192
Col. B: (172)(\(10^4\)) + (675)(\(10^4\)) + 3225

Col. A: (852)(\(10^4\)) + 3192
Col. B: (847)(\(10^4\)) + 3225

Hence, Col. A

Can I just calculate 476*942 vs. 475*943?

Sir, it will be clearly wrong. You can't neglect zeros in between EVER!

Let x = 40076 and y = 90042

Then: xy > (x-1)(y+1) <=> xy > xy +x -y -1 <=> x < y + 1

Which is definitely the case. Thus, A.

Here's a trick for such questions.

The multiplication of 2 numbers is maximum when the difference between the 2 numbers is minimum.

In A- 90042-40076= 49966
In B- 90043-40075= 49968

So, The difference of quantity A is lesser than B, hence, its multiplication is greater than B.
We choose A.

A. (40076)(90042) = (40K + 76)(90K + 42) = 40K*90K + 76*90K + 42*40K +76*42

B. (40075)(90043) = (40K + 75)(90K + 43) = 40K*90K + 75*90K + 43*40K + 43*75

Looking at the four expanded terms, 40K*90K appears in both A and B, so we can subtract it from both (ie. ignore it). And the last term on both A and B is very small relative to a whole number that will be in the tens of thousands, so we can ignore it. So what we really need to compare is:

A. 76*90K + 42*40K --> divided by 10,000 we get 76*9 + 42*4 = 852
B. 75*90K + 43*40K --> divided by 10,000 we get 75*9 + 43*4 = 847

So A is bigger.

Quantity A
(40075+1)(90043-1) [here the first product will be cancelled with the value in Quantity B]
Quantity B
(40075)(90043)

Quantity A
(40075 x 90043) - 40075 + 90043 - 1
Quantity B
(40075 x 90043)

Subtracting (40075 x 90043) from both sides

Quantity A
- 40075 + 90043 - 1
Quantity B
0

Quantity A
[Positive Value]
Quantity B
0

Option A

40075 = x and 90042 = y.

(x+1)y = xy+y

x(y+1) = xy+x

Comparing both y=90042 >x=40075

So, A > B.

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