Powerprep 2 Test 2,Q 12.

[hasibul212003]

In the first half of last year a team won 60% of the games it played. In the 2nd half of last year the team played 20 games and won three. If the team won 50% of the games it played last year, what was the total number of games it played last year.?
A. 60
B. 70
C. 80
D. 90
E. 100
The answer is D 90 but can anyone plz explain how the answer was derived.

[n00bpron00bpron00b]

Back solving looks efficient

Given :

1)Total games played in 2nd half - 20
So, total games played in 1st half will be (total games played minus 20)

2) Games won in 2nd half = "3"

3) Team won 50% of all the games (1st half + 2nd half) played last year

4) Team won 60% of all the games played in the 1st half

Lets start with option "C"
If the total number of games played last season were to be 80

Games played in 2nd half - 20 (given)
Games played in 1st half => 80 - 20 = 60

50% of total games were won => 50/100 * 80 = 40 games (when we add the wins from both halves, this criteria should be satisfied)

Now, they won 60% of the games played in 1st half => 60/100 * 60 = 36

Combining wins from both halves : 36 + 3 which is not equal to 40

Since 80 does not satisfy the condition, nor will the values below it (so we can strike out option A,B,C)

The answer has to be either "D" or "E" (just test one condition and you know the answer)

lets try "D"

If total games played = 90

Games played in 2nd half = 20
Games played in 1st half = 70

50% of the total games were won = 50/100 * 90 = 45 (total wins)

Wins from 2nd half = 3
Wins from 1st half = 60% of games played = 60/100 * 70 = 42

Combining both 42 + 3 = 45 (meets the above criteria)

If "C" would have not worked then obviously the answer would have been "D"..that's the only option left.

Hope this helps

[skmitterkol]

Total games played in 1st half = x(let)
Won=60% of x= 6x/10.
So eqn is :-
6x/10+3= 50%of (x+20);
or, 6x/10+3= 1/2(x+20);
or,6x/10-x/2=10-3;
or x/10=7=>x=70;
Total games=x+20=70+20=90

[tommywallach]

Great conversation everyone. I like both methods, but I do think the algebra is significantly faster on this one. (Not that backsolving isn't totally useful sometimes, but it's a stretch on this one!).

-t

[irs031]

The key on solving this problem is actually paying attention to what the problem is asking you to find. Once we solve for x=70, we have to remember what the problem actually wants us to find, which is x+20 = ? ; 70 is conveniently placed as one of the answer choices for those who did not pay attention.

[tommywallach]

Indeed, that's a favorite GRE trick. You've done a ton of work and come up with a number that you see in the answer choices, and you end up picking it before you notice that you were meant to do one more step. Tricksy!