60 students

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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Sat Oct 31, 2015 1:05 pm

98. Is the average age of a class of 60 students more than 30 years?
(1) 59 students in the class are exactly 30 years of age each.
(2) The average age of 5 of the students in the class is less than 30 years.

Please read explanation below. I dont understand why it is possible to combine the two statements eventhough statement 2 contradicts the total number of students in the class. Will GMAT do this? What is your approach?

Explanation:
Statement 1 is insufficient as it provides the data for 59 students, but does not provide any information about the last student; NOT SUFFICIENT.
Statement 2 provides information about the average age of 5 students but tells nothing about the remaining students; NOT SUFFICIENT.
Combining statements 1 and 2, the average age of first 59 students = 30 years and the average age of 5 students < 30 years. This implies that the age of the last student is less than 30 years. Hence the average age of all 60 students will be less than 30 years; SUFFICIENT.
The correct answer is C;
both statements together are sufficient.

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 31, 2015 1:05 pm

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Oct 31, 2015 4:52 pm

Can you explain why you think "statement 2 contradicts the total number of students in the class"?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Nov 01, 2015 3:50 am

oquiella wrote:98. Is the average age of a class of 60 students more than 30 years?
(1) 59 students in the class are exactly 30 years of age each.
(2) The average age of 5 of the students in the class is less than 30 years.

If the average age of the students = 60, then the sum of the ages = (number of students)(average age) = 60*30 = 1800.
Implication:
For the average age to be GREATER THAN 30, the sum of the ages must be GREATER THAN 1800.
Question stem, rephrased:
Is the sum of the ages greater than 1800?

Statement 1:
Let x = the 60th student.
If x=30, then the sum of the ages of all 60 students = (60)(30) = 1800.
If x=100, then the sum of the ages of all 60 students = (59)(30) + (1)(100) = (60 - 1)(30) + 100 = 1800 - 30 + 100 = 1870.
Since the sum is greater than 1800 in the second case but not greater than 1800 in the first case, INSUFFICIENT.

Statement 2:
Since 5*30 = 150, the sum of the ages for these 5 students < 150.
If each of the remaining 55 students is 1 year of age, then the sum of the ages of all 60 students < 1800.
If each of the remaining 55 students is 100 years of age, then the sum of the ages of all 60 students > 1800.
Since the sum is greater than 1800 in the second case but not greater than 1800 in the first case, INSUFFICIENT.

Statements combined:
Since 59 students are each 30 years old, 5 of the students can have an average age that is LESS than 30 only if x < 30.
Thus, the greatest possible value for x is 29.
Implication:
The maximum possible sum for all of the ages = (59)(30) + 29 = (60 - 1)(30) + 29 = 1800 - 30 + 29 = 1799.
Since the greatest possible sum is less than 1800, SUFFICIENT.

The correct answer is C.

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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Mon Nov 02, 2015 5:18 am

theCEO wrote:Can you explain why you think "statement 2 contradicts the total number of students in the class"?

Combined the 2 statements would infer there is more than 60 students. right?

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Mon Nov 02, 2015 5:26 am

oquiella wrote:
theCEO wrote:Can you explain why you think "statement 2 contradicts the total number of students

Combined the 2 statements would infer there is more than 60 students. right?
No it doesn't. When we combine we have:
1) 59 students (missing 1 student from total)
2) 5 students (the missing student from above + 4 of the 59 students from above

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Mon Nov 02, 2015 3:21 pm

Eventhough this question didnt have any contradicting choices, I did see some other posts recently with contracting statements!!

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