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# During a certain football season, Tom, Bela, and Amanda each scored at

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Math Expert
Joined: 02 Sep 2009
Posts: 51197
During a certain football season, Tom, Bela, and Amanda each scored at  [#permalink]

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01 Jul 2018, 20:17
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Difficulty:

45% (medium)

Question Stats:

67% (01:55) correct 33% (01:27) wrong based on 24 sessions

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During a certain football season, Tom, Bela, and Amanda each scored at least one goal, and they scored a total of 16 goals. If Bela scored fewer goals than Tom scored, how many goals did Tom score?

(1) Bela scored fewer than 3 goals during the season.
(2) Amanda scored 12 goals during the season

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
During a certain football season, Tom, Bela, and Amanda each scored at  [#permalink]

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04 Jul 2018, 21:34
Bunuel wrote:
During a certain football season, Tom, Bela, and Amanda each scored at least one goal, and they scored a total of 16 goals. If Bela scored fewer goals than Tom scored, how many goals did Tom score?

(1) Bela scored fewer than 3 goals during the season.
(2) Amanda scored 12 goals during the season

Given, Total goals of the season=16
Or, T+B+A=16 (T,B, and A are the goals scored by Tom, Bela, and Amanda respectively)
Each one scored at least one goal.
Or, $$T\geq1$$,$$B\geq1$$,$$A\geq1$$
Bela scored fewer goals than Tom scored.
Or, B<T
Question stem:- T=?
Statement-1
B<3.
So, B can have 2 values, i.e., 1 and 2.
When B=1, A & T can have more than one values. Similarly for B=2 too.
Hence, insufficient.

Statement-2
A=12

Now T+B+12=16
Or, T+B=4
Since $$B<T$$ & $$T\geq1$$,$$B\geq1$$
we have only one combination possible, T=3, and B=1 .

Therefore, sufficient.

Ans. (B)
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PKN

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Re: During a certain football season, Tom, Bela, and Amanda each scored at  [#permalink]

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04 Jul 2018, 21:52
Bunuel wrote:
During a certain football season, Tom, Bela, and Amanda each scored at least one goal, and they scored a total of 16 goals. If Bela scored fewer goals than Tom scored, how many goals did Tom score?

(1) Bela scored fewer than 3 goals during the season.
(2) Amanda scored 12 goals during the season

We are given that T + B + A = 16, and B < T. We have to find T such that each of T, B, A should be at least 1.

(1) B = either 1 or 2. This means T + A = either 14 or 15. This would give multiple values of T where T > B. Not sufficient.

(2) A = 12. This means T + B = 4. Now each of T/B should be at least 1 and T > B.
The only possibility here is if B=1 and T=3. Thus sufficient.

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Joined: 20 Feb 2015
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Re: During a certain football season, Tom, Bela, and Amanda each scored at  [#permalink]

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05 Jul 2018, 02:39
Bunuel wrote:
During a certain football season, Tom, Bela, and Amanda each scored at least one goal, and they scored a total of 16 goals. If Bela scored fewer goals than Tom scored, how many goals did Tom score?

(1) Bela scored fewer than 3 goals during the season.
(2) Amanda scored 12 goals during the season

T+B+A=16 goals
B >=1
and so is
B and A
also,
B < T
T= ?

1. B < 3 from question we have B >= 1 , which means
if B=1 ,T is between 2 and 14
if B=2 , T is between 3 and 14
insufficient

2. A =12
if B=1 then T=3
if B = 2 then T=2
but we are given T>B
so ,
T=3
Sufficient
B
Re: During a certain football season, Tom, Bela, and Amanda each scored at &nbs [#permalink] 05 Jul 2018, 02:39
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# During a certain football season, Tom, Bela, and Amanda each scored at

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