You have a sample of a compound of molecular formula c11h15no2, which has a benzene ring substituted by two groups, (ch3)2n― and ―co2ch2ch3 and exhibits the given 13c nmr. what disubstituted benzene isomer corresponds to these 13c data?

The best way to predict the isomer of the given molecular information is to count the number of possible peaks present in spectra and compare it with the possible number of peaks given by each isomer. (Remember: This is not the final way to elucidate structure, but it is applicable in this question).

Explanation:
The number of peaks present in spectra are 8. Now, we will calculate the number of peaks given by each isomer.

ISOMER A: 
1 peak for two equivalent methyl C attached to N
1 peak for carbonyl C
1 peak for methylene C
1 peak for methyl C
and 4 peaks for benzene C's as 2 carbons at ortho position and meta position to any of the two functional groups are equivalent hence give single signal. 
So, 1+1+1+1+4 = 8
And it (Isomer A red) is the correct answer, because other two isomers give more than 8 peaks as they have no equivalent carbons in benzene ring.

8.7 degrees celsius and 15.6 degrees fahrenheit