Answer is D as the values of a,b,c,d are not specified .

It has not been fixed and how is the answer D when all the numbers are right to the 0 and choice B is further to the right than choice A.

If you observe the image, a,b,c,d are all greater than zero

Now there is no specification about a,b,c,d being Integers or fraction but we have following information

0<a<b<c<d

we have to compare axc and bxd

Assuming axc = Z

Now we know that b is greater than a and d is greater than c

So any value of b will be greater than a and any value of d will be greater than c

So if axc = Z then bxd will always be greater than Z.

You can try doing this assuming values as well. but based on the above calculation, axc = Z < bxd

Hence the Answer is B

Hope it helps.

Regards,
Mudit

That's a tricky example.
Test at least three scenarios for more accuracy:

For example if:
1) a=1 b=2 c=3 d=4
2) a=0,5 b=0,6 c=0,8 d=0,9
3) a=0,5 b=0,6 c=0,8 d=1

Now:
1) A=1*3=3 and B=2*4=8
2) A=0.5*0.8=0.4 and B=0.6*0.9=0.54
3) A=0.5*0.8=0.4 and B=0.6*1=0.6

In every case B is more than A

It was a simple one.
consider a=1, b=2, c=3, d=4
in this case quantity B is bigger

now consider decimals a=0.1, b=0.2, c=0.3, d=0.4
again quantity B is bigger

The key concept is number line i.e. numbers are greater than zero and in ascending order

We can also solve this question using matching operations (my favorite QC strategy)

Given: 0 < a < b < c < d

Given:
QUANTITY A: ac
QUANTITY B: bd

Since a is POSITIVE, we can safely divide both quantities by a to get:
QUANTITY A: c
QUANTITY B: bd/a

Since b is POSITIVE, we can safely divide both quantities by b to get:
QUANTITY A: c/b
QUANTITY B: d/a

Since d is the biggest number, and a is the smallest number, we know that d/a > c/b

Answer: B

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For quantity B,
(a+1) (c+1) = ac + a + c + 1

in Quantity A,
ac
so, B > A

1st, note that the only thing we can assume from this problem is 0 < a < b < c < d. In other words, we know they're all positive numbers but we don't know if they're greater than 1 or anything.

Consider a * c, we know b is greater than a so ==> a * c < b * c, we know d is greater than c so ==> b * c < b * d.

Therefore b*d > a*c.

If the a =1 , b = 2, c = 3, d = 4, a * c = 3 and b * d = 8, meaning column B is bigger.
This would be true for all integers since a < b < c < d.

However, numbers between 0 and 1 act differently when multiplied.
If a = 1/4, b = 2/4, c = 3/4, and d = 1, a * c = 1/4 * 3/4 = 3/16 and b * d = 2/4 * 1 = 1/2. 1/2 > 3/16 which means column B is bigger again.

From this, Choice B is the right answer.