The question is about finding the divisor given remainders. Number Theory and Number Properties are hot favorites in GMAT.
You can solve this problem if you know one basic rule about remainders.
Let us say a number x, divides the product of A and B.
The remainder that you will get will be the product of the remainders when x divides A and when x divides B.
Using this information,
The remainder when 33 divides 1044 is 21.
The remainder when 33 divides 1047 is 24
The remainder when 33 divides 1050 is 27 and
The remainder when 33 divides 1053 is 30.
The net remainder is 21*24*27*30.
However, as the value of 21*24*27*30 is more than 33, the final remainder will be the remainder when 33 divides 21*24*27*30.
When 33 divides 21*24, the remainder is 9.
Similarly when 33 divides 27*30, the remainder is 18.
The final remainder is the remainder when 9*18 is divided by 33 = 30.
Topicwise List of Questions
This eBook covers all the topics in Number Theory related to GMAT. Concepts covered in this eBook include LCM, HCF, remainder theorem, units digits, remainders and factorials in number theory. 
This eBook has 80 Problem Solving questions and 49 Data Sufficiency questions in Number Properties and Number Theory. Concepts covered include LCM, HCF, remainder theorem in number theory, factors, factorials and numerous word problems. Detailed explanatory answers provided to each question.
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