Minimize Your Math: Avoiding Calculations on the GMAT
A while back, we talked about how to avoid calculations on both Problem Solving and Data Sufficiency problems. Ive found another good one for you from the free GMATPrep exams.
Fair warning: this is a tough one. But there is a way to solve it that doesn't involve the textbook math. (It does still involve some math. As I said, its a tough one!)
Try it out.
*If each term in the sum [pmath]a_1+ a_2+[/pmath] [pmath]+ a_n[/pmath] is either 7 or 77 and the sum equals 350, which of the following could be equal to [pmath]n[/pmath]?(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Ready? Lets go!
Glance at the problem. PS. Sequence ugh. And the answers are really close, so I wont be estimating. Double ugh.
Lets get this down on paper.
Now what? That math seems pretty ugly. Dont just dive into it. Think about whats going on here (reflect!). Is there some other way to look at this math?
Whats the significance of the numbers being either 7 or 77? First, those are both multiples of 7. And since every number in the sum is a multiple of 7, the sum itself is also a multiple of 7. Can we use that somehow?
Check it out. When youre dealing with numbers that are all multiples of the same number (7, in this case), you can think of the numbers as consisting of a certain number of 7s.
For example, the number 7 consists of one 7. The number 77 consists of eleven 7s, since (7)(11) = 77.
What about the number 350?
Use a factor tree to break it down. Get the 7 by itself and then combine all of the other factors. 350 = (7)(50). In other words there are fifty 7s in 350.
Now, how can we use that to solve?
First, notice that 50 is not in the answersbut its also not that far from the answers. So we dont have 50 sevens
but maybe the next possibility will be the one that works. What is the next possibility?
We cant take out just one 7, because then wed have to add an entire 77, and wed have a sum thats larger than 350. So we have to take out enough 7s to equal one 77:
So if we introduce one 77, how many 7s do we have to take out?
Remember that 77 represents eleven 7s. So take out 11 of them from the plain 7s:
Now, do we still have fifty 7s, total?
Yes! There are thirty-nine 7s and then one 77but that one 77 represents eleven 7s, remember. So there are 39 + 11 = 50 of those 7s.
How many terms are there? We have 39 of the 7s and 1 of the 77s. 39 + 1 = 40 terms. Bingo! Thats the answer.
The correct answer is (C). (Careful. Answer (B) is a big trap!)
You can, of course, use traditional math to solve this one. If you really want to. :)
If you feel super-comfortable with sequences, feel free. But if you, like me, find them annoying, then take some time to think about what the pattern represents. Sequences are always about some patternthe task is to find it.
Key Takeaways for Minimizing Your Math:
(1) Dont just assume that you must use textbook math. The GMAT isnt really a math test at heart. Its a reasoning test.
(2) When a problem looks especially mathy, theres a good chance theyre actually using that harder-looking math to disguise some underlying principle. In this case, they were hiding the concept of factors. If you know that you can think of a sum (in this case, 350) as a number that contains a certain number of the starting factor (in this case, 7s), then you have a shot at being able to break down the pattern and solve without all of that textbook math.
* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.