Final Exam: Are You a Great GMAT Guesser? - Part 4
Okay, youve had several weeks to practice your GMAT guessing. Lets put your newfound skills to the test!
(If youre reading all these articles at once, stop here. Give yourself a few weeks to practice these concepts and look for more opportunities to guess on other problems. Then come back here.)
Ive got three problems for you from the GMATPrep software. The first and third are from the free problem set that comes with the software and the second one is from the free practice tests.
First, set your timer for about 2 minutes. Total, not just for the first question! Give yourself about 30 to 45 seconds per question to figure out what you would NOT pick. Pretend the test is about to end! Make a choice and go.
Then, if you like, re-set your timer for 6 minutes and really try these problems.
* If [pmath]{x/y}={2/3}[/pmath], then [pmath]{x-y}/x[/pmath] =(A)[pmath]-1/2[/pmath]
(B)[pmath]-1/3[/pmath]
(C)[pmath]1/3[/pmath]
(D)[pmath]1/2[/pmath]
(E) [pmath]5/2[/pmath]
*Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
* A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If the rabbits diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?(A) 100
(B) 140
(C) 150
(D) 160
(E) 200
So, what did you guess? And why did you guess that?
In general, its a good idea to glance at the answers on problem solving before you even consider solving the question. Notice anything in the answers for the first one?
(A)[pmath]-1/2[/pmath](B)[pmath]-1/3[/pmath]
(C)[pmath]1/3[/pmath]
(D)[pmath]1/2[/pmath]
(E) [pmath]5/2[/pmath]
There are two pairs of answers: (A) and (D) are a pair, and (B) and (C) are a pair. The pairs have the same number, but one is positive and one is negative. Apparently, negative vs. positive is a common trap or mistake on this problem.
Answer (E) doesnt have a pairing. And that fact alone is enough to eliminate this choice if you have to guess. If one of the answers is clearly the odd man outthat is, it doesnt have a trap pairingthen what are the chances that that one is going to be the right answer? Very slim. Traps are set off of the correct answer and (E) doesnt have a trap. Eliminate it.
Sometimes on problems like this one, you can also estimate whether the answer should be positive or negative; if so, you can knock off two more answers. I dont see a way to do that on this one that doesnt also involve knowing how to do the problem in the first place, but if you have any ideas, let me know!
Want to know how to do this one for real? See the series Reorient Your View on Math Problems. The full solution to this problem can be found in part 2 of the series. The correct answer is (A), by the way.
On to our second problem. Ive got 6 machines all working away to do a job in 12 days. How many more machines do I need to add in order to finish the job in 8 days instead of 12?
So if the 6 machines take 12 days what would happen if I tossed in another 6 machines?
Theyd get twice as much work done, so it would only take 6 days to do the job. Oh, but the problem says that I can take 8 days, not just 6 days. So I dont need 6 more machinesI can get away with fewer machines.
Boom! Eliminate answers (D) and (E).
Want to learn an awesome method to solve this problem for real, but without annoying algebraic equations? Your wish is my command: Make Stories Real. The correct answer on this one is (B).
All right, were up to the third and final problem about that pesky rabbit with his annoying food requirements. Hes got to have exactly 300 grams of food, made up of Food X and Food Y. The X food has 10% protein and the Y food has 15% protein, and the rabbit gets exactly 38g of protein total in his 300 grams of food. And we have to figure out how much X is in the mix.
On mixture questions, its smart to start by considering what youd have if you had an exactly equal mix of whatever the problem is talking about. If you had 150 grams of X and 150 grams of Y (for 300 grams total), how would the rest of the numbers work out?
X is 10% protein, so youd have (150)(0.1) = 15 grams of protein from X.
Y is 15% protein, so youd have (150)(0.15) = 22.5 grams of protein from Y.
(How can you do that second calculation fast? 15% = 10% + 5%. You already calculated that 10% = 15. Next, 5% is half of that, or 7.5. So 15 + 7.5 = 22.5.)
Total, the rabbit would have 15 + 22.5 = 37.5 grams of protein.
Hey, that doesnt match the problem. In the problem, the rabbit has 38 grams of protein.
Ah, so (C) cant be right. Further, since the rabbit has more protein than expected, the mixture must contain more of the food that has the higher protein percentage: Food Y. If theres more Food Y, then theres less Food X, so X must be less than half of the mixture.
Answers (D) and (E) are gone, too.
If you want to get really sophisticated: 37.5 is lower than 38but its awfully close. So the X portion is less than 150, but it should be pretty close. Only one of the two remaining answers fulfills that requirement: answer (B).
But don't take my word for it! See the full solution in this article on Weighted Averages.
Key Takeaways to Become a Great Guesser
(1) I want takeaways from you this time. What have you learned over the course of this series? How have you become a better guesser? How can you keep developing that skill?
(2) Note that guessing tactics are sometimes actually solving tactics. We got all the way to the correct answer on that last one. Dont view guessing as merely a last resort if the clock is about to run out. Sometimes, guessing is really a better and faster approach to the right answer than the textbook math.
* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.