Question about Chess tactics problem

I've been reading "Tactics Time 2" by Tim Brennan and Anthea Carson and I'm wondering about problem 294, which looks like this:

What's Black's best move from this position?

The book gives the answer "13...Rb8 14.Qd3 Rxb2" and my Chess engine agrees. My question is: why would White play 14.Qd3 when 14.Qa4 or 14.Qa6 allows 15.Qxa7, reducing White's loss by snatching a pawn, at least? Does anyone have any ideas?

Qa6 followed by Qxa7 is possible, but white is losing in any case. The queen is well out of the action on a7 and doesn't influence things. Qd3 vs Qxa7 is probably not too different in terms of evaluation, on d3 it's centralised and can at least affect the game, on a7 it wins a pawn but stands badly. But anyway, the main point of the problem is to see the key move Rb8 which wins the Bb2. After this black should win regardless. 

Thank you for your response. I'm afraid I'm not convinced, though. Yes, White is losing in any case, and yes, I understand that the main point is 13...Rb8, but even then, I must assume that White will make it as hard as possible for Black to win. And it seems to me that a centralised queen, in this case, isn't any worse than a queen invading Black's home by reaching the 7th rank. I don't see that as "standing badly" at all. With 15.Qxa7 it could take Black dozens and dozens of moves to get further ahead; Black might blunder in all that time.

Again, I expect that the book - and my Chess engine - have good reason to expect 14.Qd3, but I'm still failing to see why.

On a7 the queen does not invade blacks home, it visits his garden and gets stuck behind the shed. What can it do from here? Engine likes this line to highlight whites helplessness... 

Ra8 is threatening to trap the white queen and forces some move like Rab1 when after exchanging rooks black can grab the c pawn if he wants. 

Okay, I'm beginning to see your point of view.

No, I should say more than "okay". I should say "thank you" for helping me to understand.

I mean... I still disagree. My philosophy lately has been that when I'm losing a game, so that any move I could possibly make can let my opponent win, then I should be aggressive. (Seriously, on more than one occasion, I won a game I should have lost because my opponent failed to figure out the right way to fend off my attack. An occasional opponent actually gets frightened by my offensive and proceeds to blunder - or even resign - even when I'm a bit behind in material!) But I can see why one would take the opposite approach. At the very least, I found this conversation to be fascinating.

For tactics problems that involve material imbalances, the pawns are almost never considered. A knight for a pawn should be a tactical win at all levels. Even if we consider the position after the tactic, White's a and c pawns are weak and should eventually be captured.

As to why Qa4 or Qa6 isn't played, my guess is that White's best try is to cover his weaknesses. Taking on a7 temporarily gains a pawn, but in the future Black will recapture a3 pawn due to its exposed nature and the newly opened a-file.

It's a good question, but it's not easy to answer rigorously.

First of all the fundamental currency of a chess position (so to speak) is piece activity. Notice that Qd3 centralizes the queen, and it has high mobility there. You can think of mobility as the probability that a piece will find something useful to do in the future. Putting the queen on a7 semi-traps it on the queenside.

Secondly the 'a' pawn is not worth much (rook pawns are worth less to begin). Plus by removing the 'a' pawn the 'a' file is opened to attack white's isolated 'a' pawn... this plus white's backward c pawn means black will easily win a pawn (probably more than one) at some point in the future.

As a counter example... if you can win a central pawn (a pawn on the 'e' or 'd' file) then it's usually worth some risk... but the 'a' pawn is not worth it.

Those are good points. Thank you.

1 question: what is the queen doing on a7?

white just takes away his queen from defense, attack, and everything else

on a7, the queen is attacking nothing and also defending nothing (basically)

it is useless on a7

and it will just get trapped

on d3 the queen has more attacking possibilities than a7

and blunders aren't included in the objective analysis of a position

on a7 the queen is not aggressive

aggressivity doesn't just mean how far away into the opponent's position the piece is.

it means how much it can attack that position, not how much it is in it.

and if the queen were on d3, actually kinda aggressive, then defending is also better.

i.e. a queen on a7 isn't going to help on a defense of a kingside

the cost of taking the a7 pawn is white's queen is relatively weaker at being useful

hope this helps