Last season, a football team scored 35 more goals than it conceded.

Question

Last season, a football team scored 35 more goals than it conceded. Was the difference between the number of goals the team scored and the number of goals it conceded greater this season than it was last season?

(1) This season, the team scored 10% more goals than it scored last season.
(2) This season, the team conceded 20% more goals than it conceded last season.

Bunuel · Accepted Answer

GMAT Club Official Solution:

Last season, a football team scored 35 more goals than it conceded. Was the difference between the number of goals the team scored and the number of goals it conceded greater this season than it was last season?

Let last season’s numbers be:

s = goals scored
c = goals conceded

We are told:

s - c = 35

We need to know whether this season’s difference was greater than 35.

(1) This season, the team scored 10% more goals than it scored last season.

So this season’s goals scored = 1.1s. But we do not know this season’s goals conceded, so we cannot determine this season’s goal difference. Not sufficient.

(2) This season, the team conceded 20% more goals than it conceded last season.

So this season’s goals conceded = 1.2c. But we do not know this season’s goals scored, so we cannot determine this season’s goal difference. Not sufficient.

(1) + (2) This season’s goal difference would be 1.1s - 1.2c. So, we need to know whether 1.1s - 1.2c > 35. Since s - c = 35, substitute s = c + 35 into the question:

Is 1.1(c + 35) - 1.2c > 35?

Is 1.1c + 38.5 - 1.2c > 35?

Is 35 > c?

So the answer depends on last season’s number of goals conceded.

Example 1: If c = 25, then s = 60. This season’s difference = 1.1(60) - 1.2(25) = 66 - 30 = 36, which is greater than 35.

Example 2: If c = 45, then s = 80. This season’s difference = 1.1(80) - 1.2(45) = 88 - 54 = 34, which is less than 35.

So even together, the statements are not sufficient.

Answer: E.

Adit_ · Answer

Statement 1:
Clearly INSUFFICIENT.
We dont know how much was conceded last season.

Statement 2:
Clearly INSUFFICIENT.
We dont know how much was scored last season

Combining the two:
This season goals scored = 1.1x
This season goals conceded = 1.2y
x = 35+y
Substituting:
1.1(35+y) - 1.2y
= 38.5 - 0.1y
This value can be greater than or lesser than 35.
INSUFFICIENT.

Answer:  Option E

NidhiYad · Answer

S1 - C1 = 35 The question asks: Is (S2 - C2) > 35?

Statement 1: S2 = 1.10 times S1.
However, we have no information about C2 (goals conceded this season). If the team conceded 100 more goals this season, the difference would decrease. If they conceded fewer goals, the difference would increase. -> Statement (1) is insufficient.

Statement 2: This tells us C2 = 1.20 times C1. We have no information about S2 (goals scored this season). If the team scored significantly more goals, the difference would increase. If they scored the same amount, the difference would decrease. -> Statement (2) is insufficient.

Combining Both Statements: When we combine them, we have the following:
S2 = 1.10 S1 and C2 = 1.20 C1. We want to know if 1.10 S1 - 1.20 C1 > 35. We know from the original equation that S1 = C1 + 35. Let’s substitute that into our new expression:
1.10(C1 + 35) - 1.20 C1 > 35 => 1.10 C1 + 38.5 - 1.20 C1 > 35 => -0.10 C1 + 38.5 > 35 => -0.10 C1 > -3.5 => C1 < 35.
If C1 = 10: Then -0.10(10) + 38.5 = 37.5. Since 37.5 > 35, the answer is Yes.
If C1 = 40: Then -0.10(40) + 38.5 = 34.5. Since 34.5 < 35, the answer is No.
Because we don't know the specific number of goals conceded last season (C1), we cannot determine if the difference increased or decreased.

Conclusion: E: Statements (1) and (2) together are NOT sufficient.

BongBideshini · Answer

Let S1 and C1 be goals from last season. We know: S1 - C1 = 35 
We need to find out (S2 - C2) >35?

Statement (1) Alone  S2 = 1.10 * S1. We have no info on C2.  Insufficient.

Statement (2) Alone  C2 = 1.20 * C1. We have no info on S2.  Insufficient.

Combine (1) and (2)  S2 = 1.1(S1) ; C2 = 1.2(C1)

We have to find whether 
S2-C2=1.1(C1 + 35) - 1.2(C1) > 35?
1.1(C1) + 38.5 - 1.2(C1) > 35?
 -0.1(C1) + 38.5 > 35?
 3.5 > 0.1(C1)
  35 > C1?

The answer depends on whether the team conceded fewer than 35 goals last season (C1). Since we don't know the value of C1, we cannot determine if the difference is greater or smaller.

Last season, a football team scored 35 more goals than it conceded.

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