Is there an algebraic way to solve this problem?

[RonPurewal]

Is it advisable to use higher mathematics in dealing with questions which are purely in the set of gmat quant?

In general, I would say no. If you are too concerned with "higher" math, the most likely result is that you'll make more mistakes with the "lower" math.
I.e., if you are wasting your brainpower thinking about theorems from your senior-year honors course in abstract algebra, then you're much more likely to make silly ground-level mistakes. Like, say, thinking that the opposite of x > 0 is x < 0, rather than x ≤ 0.
Not because the higher-level principles have any direct adverse effect, of course, but merely because you'll be distracted by them.

The GMAT will never, ever, ever require any math past first-year high-school algebra and geometry.

On the other hand, IF you get a problem that can be easily solved using trigonometry or calculus, then you can use those things. If the application is not immediate and obvious, do not bother; stick with the basics.
It is EXTREMELY unlikely that you'll see a problem that can be facilitated by "advanced" math. It's pretty obvious that the writers try to filter such questions out of the pool.

[RonPurewal]

Just to put some statistics behind that "” Of the approximately 1000 official math questions I've seen, there have been only 1 or 2 that have been made substantially easier by calculus or trigonometry.
The only area of "higher" mathematics that might be actually useful to consider is "mod" arithmetic, which does, in fact, allow a decent fraction of the divisibility and remainder problems to be solved more efficiently.

[beakdas]

Hi Ron,
On a general note i have been struggling with geometry questions that i have come across on the manhattan CAT.I did review the questions and practiced from the OG but the OG geometry questions are definitely not at par nor do they test concepts more viscously.The result is my geometry hasn't improved much from those questions when i deal with manhattan cat quant.

Would you recommend using the Geometry Guide of manhattan because i feel the geometry in the OG is not that tricky or cumbersome if i may say.

[jlucero]

Hi Ron,
On a general note i have been struggling with geometry questions that i have come across on the manhattan CAT.I did review the questions and practiced from the OG but the OG geometry questions are definitely not at par nor do they test concepts more viscously.The result is my geometry hasn't improved much from those questions when i deal with manhattan cat quant.

Would you recommend using the Geometry Guide of manhattan because i feel the geometry in the OG is not that tricky or cumbersome if i may say.

Like every other topic covered in the OG, there's a few really difficult Geometry questions and a few easier questions. From my own experience, some of the hardest questions I remember from my actual GMAT were Geometry based (though that's just one person's experience), so I would encourage you to use the Geometry Guide to get some more practice (especially the chapter on extra geometry). Also, if you're in a course, you should have access to an e-book version of Advanced Quant. There's some really tricky problems in there you might want to check out as well.

Finally, keep in mind that no matter how many tests you take or practice questions you see, there will always be questions you get wrong on test day, unless you plan on scoring an 800. So when you say that you haven't improved in Geometry, it's possible that this is because you're doing really well in other topics and Geometry is bringing your score down. Don't be discouraged by this. If your overall score is trending upwards, that's what's most important. Learn from the mistakes you make, and focus on improving weaknesses.

[NL]

Here is another version (from MGMAT CAT) of the original question:

If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item’s final price (after both changes) greater than its original price?
(1) m > d
(2) m = 1.5d

------------------------------------

I don't have intuition about percentages, so I was exhausted with testing numbers at the first time.

When reviewing, I remember a special case: With a 100, if it’s increased by 25%, then decreased by 20%, then it turns back to origin (100)

- So, for (1), I can immediately see it’s insufficient. (If m=26, d=20, then yes; If m=25, d=20, then no)

- For (2),
* No: if d=20, then m=30 (over the “standard”, so no)
* To get yes, I still have to test m=15; d=10

- Combine (1)&(2):
* No: I re-use the case m=30; n=20
* Yes: I re-use m=15; d=10

I don’t know if this special case is randomly useful for only this question or it (any special case/standard case) can be developed as a supplemental method? (maybe for problems dealing with comparison, things moving around?)

[RonPurewal]

what do you propose?
if you have something specific already in mind, then let us know what it is.

if you don't, then trying to 'chase' generalizations is mostly a bad idea, for two reasons:
1/ you may not find any
2/ you may undermine more important skills

here, for instance, there's no real advantage in having memorized the %25/%20 case, IF you have at your fingertips the (much more generally useful) concept of TESTING EXTREMES.

one extreme is trivial. if m = 99 and d = 1, for instance, it should be clear, without any calculations, that the result will be higher than the starting value.

so then you would just try the other extreme-- 'numbers that are really close together'.
think about, say, m = 99 and d = 98.
if you start with 100 and mark it up by 99 percent, that's 199.
if you take 98 percent AWAY from 199... well, i don't really care exactly what that is, because it's obviously a lot less than 100.

[RonPurewal]

...so, my point is this: when you see something like this problem, the idea of testing extremes should occur IMMEDIATELY to you.
if you 'chase' too many rules that are extremely particular, you might NOT think of 'testing extremes' right away because you're too busy dithering with minutiae.

one thing is for sure: the gmat exam will NEVER contain a problem that DEPENDS on some 'weird', hard-to-find exception.
the whole point of this exam is NOT to be 'tricky' in obscure, nit-picky ways.

[RonPurewal]

if you DO notice what seems like a pattern, though, there's one super-useful thing you can do.
if you see a pattern (that's actually a valid pattern—i.e., you genuinely tried to find exceptions and couldn't find any), see whether you can develop an intuitive understanding of what's causing the pattern.

for instance:
if you increase something by %25 and then decrease it by %20 (your 'special' case), then you get the original number back.
same if you increase something by %50 and then decrease by %33.3333...
or if you increase something by %100 and then decrease by %50.

eventually you'll notice that the INCREASE is always a HIGHER percentage. THIS is the kind of thing you can use to develop your intuition.
• think about WHAT you're taking percentages of. i.e., "%25 of WHAT? and then %20 of WHAT?"
• think about how those two compare to each other.
• then you'll understand why the increase has to be bigger.

this is the kind of thing that actually has 'value added'.
the point is not "the increase is bigger". that could be useful if you win the lottery, so to speak (= if you get a problem about exactly that concept)... but not otherwise.
on the other hand, if you gain a better intuition about "...percent of WHAT?" then that is extraordinarily useful.

[NL]

one extreme is trivial. if m = 99 and d = 1, for instance, it should be clear, without any calculations, that the result will be higher than the starting value.

so then you would just try the other extreme-- 'numbers that are really close together'.
think about, say, m = 99 and d = 98.
if you start with 100 and mark it up by 99 percent, that's 199.
if you take 98 percent AWAY from 199... well, i don't really care exactly what that is, because it's obviously a lot less than 100.

That's a great "collection". Understandable for my brain

[NL]

if you DO notice what seems like a pattern, though, there's one super-useful thing you can do.
if you see a pattern (that's actually a valid pattern—i.e., you genuinely tried to find exceptions and couldn't find any), see whether you can develop an intuitive understanding of what's causing the pattern.

for instance:
if you increase something by %25 and then decrease it by %20 (your 'special' case), then you get the original number back.
same if you increase something by %50 and then decrease by %33.3333...
or if you increase something by %100 and then decrease by %50.

Cool, cool, cool! Why didn’t I think about this?
The distances between % increase & % decrease also correlate:
12.5----12 (smaller increase, smaller distance)
25------------20
50-------------------33.33
100--------------------------------50
200-----------------------------------------66.7% (bigger increase, bigger distance)

if you gain a better intuition about "...percent of WHAT?" then that is extraordinarily useful.

Yes, that’s kind of: Bigger % of smaller number = smaller % of bigger number = original modification.

[NL]

if you don't, then trying to 'chase' generalizations is mostly a bad idea, for two reasons:
1/ you may not find any
2/ you may undermine more important skills

Yes, it's as bad as an idea about gyms for only women
That's a trick of my brain. It tries to avoid calculation as much as possible. Hmm.

[RonPurewal]

'avoiding calculation' is not necessarily a bad thing; i generally do the same.

i.e., if i can think of any other method that circumvents the need for calculation, i'll use that method. but, if not, i'll just pick up the metaphorical shovel and start to dig.

...but 'avoiding calculation' is not what i was talking about.
i mean that basic, widely applicable strategies might be undermined if you try to memorize too many 'special rules'.

again, consider the example of testing extremes, which is the only thing you really need to solve the DS problem in this thread.
the point is that, if your mind is too cluttered with 'special cases' and 'rules', you might not think of testing extremes--to your ultimate detriment.