Tricky DS Please help

[mwaychowsky86]

If ab ≠ 0 and a + b ≠ 0, is ((1/(a+b))<(1/a) + (1/b)

(1) |a| + |b| = a + b

(2) a > b

[NL]

If ab ≠ 0 and a + b ≠ 0, is ((1/(a+b))<(1/a) + (1/b)

(1) |a| + |b| = a + b

(2) a > b

Manipulate the question: (a+b) < 1/a + 1/b?
--> 1/(a+b) < (a+b)/ab?

Leave it there because we don’t know a+b and ab are negative or positive (can’t do cross multiply).

(1) |a| + |b| = a + b
- What do we know about a and b?
* |a| + |b| = a + b means: |a| = a and |b| = b
* ab ≠ 0 means a # 0 and b # 0
--> So we know: a >0 and b >0

We now can manipulate the question:
(a+b) < (a+b)/ab?
--> ab < (a+b)^2 ?
--> 0 < a^2 + 2ab + b^2 -ab?
--> 0 < a^2 + ab +b^2? YES!
(because a >0 and b >0)


(2) a > b
This tells us that a and b can freely run in wide ranges of positive and negative values.
(a+b) < (a+b)/ab? YES and NO. In sufficient!


The answer is A.

[NL]

Any different thought that brings short cuts?

[RonPurewal]

To the original poster:
Do not simply reproduce a question without any commentary or specific questions.

If you don't tell us what you are actually having trouble with, we can't help you.

Thanks.

[RonPurewal]

Any different thought that brings short cuts?

For statement #1, once you realize that both variables are positive, you don't really have to slog through all that algebra.
Instead, you can just note that, for numbers with the same sign,
* 1/(bigger number) = smaller number
* 1/(smaller number) = bigger number

As a result, 1/a, all by itself, is already bigger than 1/(a + b). Likewise for 1/b by itself.
Both of these are bigger than 1/(a + b) before you even add them together, so that's a very solid Yes to the question.

[NL]

* 1/(bigger number) = smaller number
* 1/(smaller number) = bigger number

Hehe, my brain felt so shy when seeing your solution. Excellent! Got it!

- Do you have some other examples in that the bigger-smaller strategy can be used?
(This method is new to me, so I’m just curious to see common "faces" of similar problems)

[RonPurewal]

- Do you have some other examples in that the bigger-smaller strategy can be used?

Off the top of my head, no.

It may be instructive for you to see whether you can make up a few such problems yourself. If you're the one making the problems, you'll learn more than if you just solve problems written by other people.
(Note"”this does not extend to SC. It's not a good idea to try to write GMAT-style SC problems. You should write example sentences that illustrate one principle at a time, but you shouldn't try to weave them all togethe into long, complex sentences.)

[NL]

If you're the one making the problems, you'll learn more than if you just solve problems written by other people.

Good idea. It will be more fun!
I don't know the principle for building questions, so I imagine it looks like this:

I. Determining common criteria:

1- Main idea: comparison issues such as: faster-slower; bigger-smaller; deeper-shallower ; fatter-thinner; stronger-weaker; richer-poorer; thicker-lighter...

2- Finding/building rules that are absolutely true or pretended to be true within the scope of questions. These rules are the base bearing the situation or the "middle man" on which 2 things can be compared.

3- Solutions for problems: don’t require to use algebra or actual calculation. Just using reasoning or common sense.

4- The last step: tailor "clothes" for questions: For low level: sexy clothes (so it’s pretty easy to see the body inside); For medium level: elegant and thick clothes; For high level: super thick or shocking or weird clothes.

II. Examples:

E.g. 1: Bad a-Good a
(This problem has few words, and you also know the general way to tackle it, so 45 second for this. This is Thursday with Ron simulation.)

Is a >0?

(1) |2a| = a-8
(2) (a-1)^9 > -1


E.g. 2: Naughty triangles
(This question doesn’t look like gmat questions, but it can be used to illustrate the idea above. 1 minute for this because you have to draw a picture)

A trapezoid has two bases that are AB and CD.
What is the relationship between the area of the trapezoid and the sum of two triangles ABC and ACD?

A. The area of the trapezoid is bigger the sum of the two triangles
B. The area of the trapezoid is smaller the sum of the two triangles
C. The area of the trapezoid is equal the sum of the two triangles
D. It cannot be determined.


E.g.3 Ron and Rat.
(This problem has more words, so I give you 1 minute. If you find yourself in psychological conflict, I give you 10 more second. Remember, avoid information that is thrown there to distract you.)

In a laboratory, a race is organized for Ron and Rat. They are fed the same nutrients, bathed twice a day, and not allowed to meet girlfriends or some sort of. They run the same round trip. Rat runs at a constant rate of 6 miles per hour, but during the return, he slips on a banana’s peel (that Ron secretly throws out), so slows down to an average speed of 2 miles per hour. Ron’s average speeds are more stable than Rat’s, with a constant rate of the going-trip is 4 miles per hour and 3 miles per hour in average when return.

What is the closest difference between average speeds of Ron and Rat?
A. 0
B. ½
C. 1
D. 2 ½
E. 3


Please present your solutions if you don't discover something wrong with the questions :))

[jnelson0612]

Interesting, NL. Would you provide the answers after this post for those reading this forum? I'm sure that people will be curious!

[NL]

Thanks Jamie, I will. I just want to see whether Ron can answer my super...hard questions correctly :))

[RonPurewal]

I like these. They're insightful; I can tell that you're learning more about what goes on in GMAC's ateliers (or else applying what you've already absorbed).

Two notes of caution:

1/
Please start a new thread with these. (Ideally, you'd start a separate thread for each problem"”per the forum rules"”but, for problems of your own creation, it seems acceptable for you to post them together.)

2/
Especially in the case of #2 (and #3, if you actually meant to include the ambiguity I'm going to describe below), you're veering too far toward "tricky".
One of the most important hallmarks of GMAC's problems is that they are NOT "trick questions", ever. Sure, there will be problems that require close attention"”but that's not the same as a "trick".
GMAC's problems will not contain words that are ambiguous but made to look straightforward, nor will they make you come up with obscure exceptions to things (e.g., the fact that 1 is not a prime number).

Still, the effort is appreciated.

Responses below.

[RonPurewal]

I. Determining common criteria:

1- Main idea: comparison issues such as: faster-slower; bigger-smaller; deeper-shallower ; fatter-thinner; stronger-weaker; richer-poorer; thicker-lighter...

Interesting. Totally different from how I'd start a problem.

I wouldn't start with a general category (as you do here). Instead, I'd start from some very specific mathematical observation"”something that seems salient enough to be the basis of a good problem.
For instance... "Traditional algebra doesn't solve problems whose solutions are restricted to whole numbers."

From that, I'd make a problem like this one:
If m and n are positive integers, what is the value of 2m + n?
(1) 5m + 7n = 48
(2) 6m + 3n = 36
(If I were feeling less lazy today, I'd make it a word problem; the math would ultimately be the same. The only advantage of a word problem is the ability to make "positive integers" emerge organically from whatever m and n actually represent in the problem.)

You can try that problem if you want. You have to watch your assumptions and refrain from jumping to conclusions, but this is not a "trick question".

[RonPurewal]

2- Finding/building rules that are absolutely true or pretended to be true within the scope of questions. These rules are the base bearing the situation or the "middle man" on which 2 things can be compared.

I think I get what you mean here. When I see "pretend to be true", I interpret that as "People don't think about the exceptions".

If that's what you mean, then, yes, this is one of the core principles of data sufficiency.
I.e., by minimizing calculations and staying focused on "sufficient"/"insufficient", the DS format probes this whole kind of thing more deeply than the multiple-choice probelms do.

[RonPurewal]

3- Solutions for problems: don’t require to use algebra or actual calculation. Just using reasoning or common sense.

Well... no. Almost all official problems require some "grabbing the shovel and digging". And, even when there is a cute shortcut, brute force still tends to work pretty well"”as long as you don't spend too long staring at the problem first.

GMAT problems that can be solved by pure "lightbulb" insight are rare; among multiple-choice problems, practically nonexistent.

[RonPurewal]

4- The last step: tailor "clothes" for questions: For low level: sexy clothes (so it’s pretty easy to see the body inside); For medium level: elegant and thick clothes; For high level: super thick or shocking or weird clothes.

As a fashion-obsessed person, I am appalled by your casual equating of "sexy" and "revealing"... but let's not digress.

[b]Is a >0?

(1) |2a| = a-8
(2) (a-1)^9 > -1

This is a non-problem, because statement 1 has no solutions at all.
Every DS statement has just one solution (= sufficient) or else more than one (= not sufficient).

Statement 2 is well written.
Odd powers increase as the value increases, and (-1)^9 is still -1. So, statement 2 just means a - 1 > -1, or, equivalently, a > 0.