After winning 80 percent of the first 40 games it played

Question

After winning 80 percent of the first 40 games it played, Team A lost all the remaining games it played. How many total games did Team A play?

(1) Team A lost all of its games against Team B, which won 75 percent of its total games.
(2) Team A lost exactly 1/3 of all the games it played.

Bunuel · Accepted Answer

After winning 80 percent of the first 40 games it played, Team A lost all the remaining games it played. How many total games did Team A play?

Team A lost 0.2*40=8 of the first 40 games and  all the remaining games , say x. So, total games lost is 8+x and total games played is 40+x.

(1) Team A lost all of its games against Team B, which won 75 percent of its total games. Clearly not sufficient.

(2) Team A lost exactly 1/3 of all the games it played --> 8+x=1/3*(40+x), only one unknown, hence we can solve for it. Sufficient.

Answer: B.

Hope it's clear.

boomtangboy · Answer

Hi,

I used a tabular format as mentioned below
- - 40 Games - - X-40 Games
Won - - 32 -------0
Lost- - 8 ---------X-40

Statement 1 : We have no clue if Team A played B C D E hence insufficient
Statement 2 : X/3 = 8 + X - 40 
Sufficient 
Thus B

Hope this helps

iamvishnu · Answer

Won-32 lost-8. Now, rest all loose then 8+X. Total-40+x. Stmt1 insufficient bcoz- no information about team B games.,….. stamnt-2 (40+x)/3=x+8. We can solve for x

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gemministorm · Answer

For statement A, as it's mentioned A lost all it's match against B so took it for only A and B existed and calculated
0.75(40+x) = x

and B was sufficient.... So I marked C....

how do I not make assumptions like above....

Bunuel · Answer

Your doubt comes from assuming that Team A played only against Team B. Statement (1) never says that. It only tells us that A lost all games vs B and that B won 75% of its total games. Since A could also have played other teams, we cannot solve for the total games from this information. That’s why Statement (1) is not sufficient.

mattisweb · Answer

It should say "Game can only be won or lost" for this solution to be valid. Else it is E.

abhikc3004 · Answer

Hey, the question doesn't specify whether a draw is a valid result or not, and that led me to select E once I charted out all cases (i.e if games can end in a draw vs if games can't end in a draw).

Should we always assume games to be a Win-Lose if a draw is not explicitly mentioned? 
   Bunuel

abhikc3004 · Answer

Is this a case of contrapositive? Can someone explain that to me pls - I seem to be struggling with similar questions.

kaustubhkohli12 · Answer

Hi , Isn't with B we can make the equation like x+8 = 0.25(x+40). But here we are assuming Team a and B are the only team. That assumption is wrong ?

egmat · Answer

Hi kaustubhkohli12,

You've accidentally mixed the two statements together, and that's the whole source of the confusion.

Everything about  Team B  and the  75%  lives in Statement (1). Statement (2) says nothing about Team B, about other teams, or about who beat whom. So when you write  x + 8 = 0.25(x + 40) , two things have slipped in that don't belong:

- The  0.25  - Statement (2) says Team A lost exactly  1/3  of all its games, not 1/4. There's no place to get  0.25  from Statement (2) itself.
- The  "only A and B" assumption  - that idea came from the Statement (1) discussion. Statement (2) is a plain fact about  all  of Team A's games, so no assumption about how many teams exist is needed at all.

So Statement (2) stands on its own.

From the stem, Team A won  80%  of the first  40  games ( 32  wins,  8  losses) and lost every remaining game (call it  x ). That gives:

- Total games =  40 + x 
- Total losses =  8 + x

Statement (2): losses are  1/3  of all games:

8 + x = (1/3)(40 + x)  →  24 + 3x = 40 + x  →  2x = 16  →  x = 8

One clean value, total =  48 games .  Sufficient  - and notice we never had to know anything about Team B or how many teams played.

The takeaway:  treat each statement in complete isolation. Only borrow numbers and conditions that appear  inside that statement  (plus the original stem). The moment a fraction or an assumption from the other statement sneaks in, you're solving a different problem.

Answer: B

egmat · Answer

Hi abhikc3004,

Good instinct to reach for a logical tool, but this one is actually a  numbers/algebra  question, not a formal-logic one, so  contrapositive doesn't apply here .

A contrapositive is a move you make on a conditional ("if-then") statement:

- Original:  If P, then Q 
- Contrapositive:  If not Q, then not P

Example: "If it rained, the ground is wet" becomes "If the ground is  not  wet, it did  not  rain." Same truth, flipped and negated. You use it in Critical Reasoning and pure-logic puzzles where the statements are conditionals.

This Data Sufficiency question has no if-then claims to flip. It just gives you quantities:  32  wins,  8  losses in the first  40  games, then  x  more losses. Everything runs on setting up and solving an equation - no logical negation involved.

What actually drives the answer

Statement (2):  "lost exactly  1/3  of all games" gives one clean equation with one unknown:

-  (8 + x) / (40 + x) = 1/3  →  x  =  8  → total games =  48 .

One unknown, one equation, one value →  sufficient .

Statement (1):  it never links Team B's schedule to A's total games (we don't know how many games A played against B, or how many B played overall), so  x  stays unknown →  not sufficient .

That's why the answer is  B  - and none of it needed contrapositive reasoning.

Takeaway for the "similar questions" you mentioned:  save contrapositive for stems built on conditional statements (mostly Verbal/CR). In DS quant, the real question is always  "does this statement pin the value (or the yes/no) down to exactly one answer?"  - pure sufficiency, not logic-flipping.

Answer: B

After winning 80 percent of the first 40 games it played

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After winning 80 percent of the first 40 games it played