Two different sections of an economics class, designated A and B

Question

Two different sections of an economics class, designated A and B respectively, took a final exam. Each student received an integer score from 1 to 10 inclusive. If section A had 50 students and section B had 100 students, what was the median final exam score when sections A and B were combined?

(1) A section A student who scored a 7 was in the 90th percentile. A section B student who scored an 8 was in the 30th percentile.

(2) No student in Section B scored lower than any student in Section A.

Bunuel · Accepted Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=RAVTJPmkGSA

CrazyBlender123 · Answer

Since n(A)+n(B)=150
median=(75th term+76th term)/2
S2:
max(A)<=min(B)
With 50 students in A and 100 in B, the combined order is A1,A2,A3......B1,B2,B3....B100
75th and 76th terms are B25 and B26, then (B25+B26)/2 is the median.
Not Sufficient

S1:
A B student who scored 8 was in the 30th percentile.
Since B has 100 students, at least 30 students scored ≤8.
Not Sufficient

S1&S2:
But from Statement (2), every B score is at least every A score.
Also, in A, a score of 7 is at the 90th percentile, so there are students scoring above 7. Since scores are integers, some A score is at least 8.
max(A)≥8 
therefore, min(B)≥8.
So at least 30 students in Class B must have ≥8.
B25=B26=8
Median = 8

Answer is C

vasu1104 · Answer

class A = 50
class B = 100

score ranges from integer 1-10

we need median= 75th + 76th /2

C-1
A section A student who scored a 7 was in the 90th percentile. 
it means there are 90 people who scored 7 or less than 7.
total in A= 50
90% of 50 = 45

so 45 students scored 7 or less than 7. so other 5 more than 7.

now other part of statement, A section B student who scored an 8 was in the 30th percentile.
30% of 100 =30. so these 30 people scored 8 or less.
and other 70 scored > 8.

now we need 75th and 76th num for median. 
that means these numbers will be from class B. and 30% of B are with 8 or less.
but still we dont have definite num from here. becuase those remaining 5 from A can be higher than 30. and any of those 5 can be 75th or 76th.

so clearly this is not sufficient.

C-2
this means all 100 from B scored higher than all 50 of A.
but nothing about score num. so clearly not sufficient.

now combine 1 & 2.

we now 45 from A are with 7 or less. other 5 are with more than 7.
we know 30 from B are with 8 or less. and other 70 with more than 8.

now we also know that all B score are higher than all A.
so the first 30 from B cant have lower than top 5 from A.
top 5 from A can have more than 7 and the bottom 30 of B can have 8 or less. and all B scored higher than A.
that means top 5 of A cant have more than 8 as all B scored higher than A. so now those bottom 30 from B must have 8.
so 75th and 76th will have 8 as score.

so median = 16/2 = 8

both together are sufficient.

Choice C

Two different sections of an economics class, designated A and B

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GMAT Data Sufficiency (DS) Questions

Two different sections of an economics class, designated A and B

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