The marks scored by 50 students of

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The marks scored by 50 students of

by raj44 » Fri Dec 12, 2014 6:11 am
2. The marks scored by 50 students of a class are m1, m2, m3 ...m50 where m1<m2<....m50. Student 1 scored 40 and student 50 scored 90. What is the average score of the class?
1. No two students scored the same marks and m25=62
2. The marks of the students follow an arithmetic progression.
OAB
Source: — Data Sufficiency |

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by GMATGuruNY » Fri Dec 12, 2014 7:34 am
raj44 wrote:2. The marks scored by 50 students of a class are m1, m2, m3 ...m50 where m1<m2<....m50. Student 1 scored 40 and student 50 scored 90. What is the average score of the class?
1. No two students scored the same marks and m25=62
2. The marks of the students follow an arithmetic progression.
OAB
Statement 1:
Since marks m₂...m₂₄ and m₂₆...m₄₉ are not known, the average of the 50 marks cannot be determined.
INSUFFICIENT.

Statement 2:
In an arithmetic progression, the distance between successive terms is a CONSTANT.
The result is that the values are EVENLY SPACED.
For any evenly spaced set, average = (biggest term + smallest term)/2.
Thus, the average of the 50 marks = (90+40)/2 = 65.
SUFFICIENT.

The correct answer is B.

This DS is not reflective of an actual GMAT problem.
The GMAT does not expect us to know the definition of the term arithmetic progression.
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by mbawisdom » Wed Dec 17, 2014 8:05 am
What do we need to know to solve this problem? We need to know the marks of all 50 students to get the average.

Statement 1: This doesn't give us the marks of all the students so it is INSUFFICIENT.
Statement 2: This tells us that the marks follow an arithmetic progression (that the marks are evenly spaced out by a constant). An arithmetic progression could be 1, 2, 3... or 2, 4, 6... here we know the marks start at 40 and end at 90. Since the marks follow an arithmetic progression they must be 40, 41, 42... 90. Hence, we now know all the marks and can work out the average. SUFFICIENT.