QTY A = \({\frac{1}{4 + \frac{1}{3 + \frac{1}{2}}} = {\frac{1}{4 + \frac{2}{7}}} = {\frac{1}{28 + \frac{2}{7}}} = {\frac{1}{\frac{30}{7}}} = {\frac{7}{30}}\)


QTY B = \({\frac{1}{2 + \frac{1}{3 + \frac{1}{4}}} = {\frac{1}{2 + \frac{4}{13}}} = {\frac{1}{26 + \frac{4}{13}}} = {\frac{1}{\frac{30}{13}}} = {\frac{13}{30}}\)


Therefore QTY A < QTY B

Option B
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We need only recognize that 1/(3 + 1/2) is less than 1
So, 4 + 1/(3 + 1/2) = 4.something

Likewise, 1/(3 + 1/4) is less than 1
So, 2 + 1/(3 + 1/2) = 2.something

So, we get:
Quantity A: 1/(4.something)
Quantity B: 1/(2.something)

Answer: B

Cheers,
Brent
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Hi Brent, how do we "recognize that 1/(3 + 1/2) is less than 1
So, 4 + 1/(3 + 1/2) = 4.something

Likewise, 1/(3 + 1/4) is less than 1
So, 2 + 1/(3 + 1/2) = 2.something" specifically?

I could benefit from seeing how it was worked out fully. Thank you!

Key concept: If x > 1, then 1/x has a value that's less than 1
For example:
1/2 is less than 1
1/4 is less than 1
1/3.1 is less than 1
1/6.5 is less than 1

Conversely, if 0 < x < 1, then 1/x has a value that's greater than 1
For example:
1/0.5 is greater than 1
1/0.1 is greater than 1
1/0.25 is greater than 1
etc.

3 + 1/4 = 3.25, and 1/3.25 is less than 1
2 + 1/2 = 2.5, and 1/2.5 is less than 1

So, 4 + 1/(3 + 1/4) = 4 + (some number that's less than 1)
= 4.something

And, 2 + 1/(3 + 1/2) = 2 + (some number that's less than 1)
= 2.something

Does that help?

Cheers,
Brent
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No but I got it now. Thanks!

Sir, do you have any doubt ??

Regards
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This sum can be done orally ,the only common number in both the quantities is 3 .
For Qty A , 3 + 1/2 will always be more than 3 + 1/4 for Qty B.
Alos 4 is added additionally to qty A and 2 is added to qty B.

Hence denominator of A will be greater.

Hence B > A