A manufacturer produces a certain men's athletic shoe

[griffin.811]

A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe. If the largest size of this shoe is 20% longer than the smallest size, how long, in inches, is the shoe in size 15?

A. 12
B. 12.25
C. 12.5
D. 12.75
E. 13
Correct Answer:E

Hi,
I'm struggling quite a bit with understanding what this problem is trying to test/what the key take away here is. Can someone please advise?

Is the idea that sometimes we won't be eplicitly given two equations which we can use to solve for x?

Also, the solution says that when back testing, we should test B, then D, because since the numbers are listed in order, if the number is smaller than B, the correct answer must be A, etc...This is probably something really obvious, but after testing B, we arrive at the conclusion that the Sz.8 shoe is 10.5in and that 20% more than this would be 12.6in. Since we find that Under B, the sz.17 is 12.75, answer choice B is too small.

How do we know Choice B is too small, and not too big?

Thanks

[tim]

Yes, it is definitely true that the GMAT will often not give you explicit equations. You need to be prepared to create equations of your own whenever necessary based on the text in the problem.

As for the strategy of picking a middle value and using that to decide on which side the correct answer falls, if it is not immediately apparent which side you'll go to based on what happens when you plug in the value, you should play it safe and just plug in all the values. Coming up with a comprehensive algorithm to account for all types of situations is far more complicated than just plugging in values until you get the right one.

[griffin.811]

Thanks Tim!

[RonPurewal]

Thanks Tim!

More precisely, think about the costs and benefits of ...
... just plugging in more choices right away,
versus
... sitting there and wondering, "Which way should I go?"

In most problems, plugging in more choices takes an essentially negligible amount of time. If you've already laid the groundwork by plugging in one choice, then, essentially, you're just going to do exactly the same steps again.
If your work is organized, you should even be able to follow the steps you just did for the previous choice. If it's not ... well, it is, right? (:

So, unless you IMMEDIATELY know the answer to "Which way should I go?", you're going to hit negative returns pretty fast by sitting there pondering it. Just go one way or the other.
In most cases, you'll know if you went the wrong way, anyway—if you get even farther from the desired outcome, then you've probably gone up when you should've gone down (or vice versa).

As always, the two rules for success are ...
1/ Do stuff.
2/ Don't not do stuff.
Really, that's about half of your success on the quant section right there.

[griffin.811]

So true, too often I just freeze, and ponder. Helpful as always!

[RonPurewal]

So true, too often I just freeze, and ponder. Helpful as always!

Of note, this exam is debilerately designed to punish two specific mentalities:
• Indecision
• Perfectionism

This is why you have an adaptive test that has a relatively large number of problems in a short period.

The result is that "No patience, no perseverance" becomes an awfully good real-time strategy.
(You'll need a certain amount of both to overcome mental blocks while you're studying and reviewing problems—but both are VERY bad during timed exams.).

[ZiYuen]

L(8) = Length of size 8
L(17) = length of size 17

L(17) = 1.2 * L(8)

L(17) = L(8) + 0.25 *(17 - 8)
L(17) = L(8) + 0.25 * 9
L(17) = L(8) + 2.25

IF L(8) + 2.25 = 1.2 * L(8)
THEN 0.2 * L(8) = 2.25
L(8) = 2.25 / 0.2
L(8) = 11.25
L(15) = 11.25 + (15 - 8) * 0.25
L(15) = 11.25 + 7 * 0.25
L(15) = 11.25 + 1.75
L(15) = 13.00

[RonPurewal]

Zi YuenL --
Do you have a question?
If so, I can't figure out what you are trying to ask. Please clarify, thanks.

(If you don't have a question, then please do not post solutions on random forum threads that are several years old. thank you.)