Hi joannaecohen,
One way you will know that you have mastered (or are at least on the road to mastering) a concept is if, upon seeing a GMAT question, you have an immediate (and sound) plan of attack for that problem. Let me illustrate this idea with an example:
20^2 + 21^2+ 22^2+ 23^2+ 24^2+ 25^2 = ?
A) 3,055
B) 2,060
C) 3,066
D) 3,704
E) 3,077
Upon seeing this question, what is the first thing that comes to your mind? Do you want to grab a calculator and add up the values in the expression? Are you spending 20 to 30 seconds thinking about how this question should be solved? Or do you quickly recognize that you are likely being tested simply on patterns in units digits?
If you were able to recognize that you are being tested on patterns units digits, it’s a good sign that you have mastered (or are at least on the road to mastering) some concepts related to units digits.
Solution:
Because each answer choice has a different units digit, instead of finding the actual sum, we can just find the units digit of the sum. Let’s use the units digits of each square to determine the units digit of the sum.
- The units digit of 20^2 must be 0, since 0^2 = 0
- The units digit of 21^2 must be 1, since 1^2 = 1
- The units digit of 22^2 must be 4, since 2^2 = 4
- The units digit of 23^2 must be 9, since 3^2 = 9
- The units digit of 24^2 must be 6, since 4^2 = 16
- The units digit of 25^2 must be 5, since 5^2 = 25
With this, we can sum the units digits: 0 + 1 + 4 + 9 + 6 + 5 = 25. Thus, the units digit of the correct answer is 5.
Answer: A
Although this is just one example (of many), you see that you must have the tools in your toolbox to efficiently attack each GMAT quant and verbal question that comes your way.
If you would like to practice more questions similar to one the above, I welcome you to take my free
37-question quant diagnostic. After completing the diagnostic, you will be provided with a detailed analysis of your proficiency level of all GMAT quant topics, as well as an opportunity to discuss your diagnostic results with me or another
TTP instructor/coach.
If you have any further questions, feel free to contact me directly.