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GMAT Math: Data Sufficiency – Inequalities^(Exponents) – What You Need To Know

TheGMATPill | Questions & Strategies For GMAT Prep.

Step 1) The first thing I notice is that one exponent is odd and the other is even. So I immediately know what it’s testing.

Step 2) I know I need to check positive and negative…but I also need to check fractions as well.

Check positive/negative:
If x = 2, then of course x^3 > x^2 [GOOD]
If x= -2, then x^3 is NOT > x^2 [NO GOOD]

So (A) and (D) are no good since there’s inconsistency here with GOOD/NO GOOD.
For now, I don’t need to check fractions. Just evaluate (2) for now.

Step 3) Evaluating (2): x^2 > x
Genearlly, squaring a number means it gets bigger. BUT–I know there’s an exception–FRACTIONS!
If x = 1/2, then (1/2)^2 = (1/4)
So when you square a fraction, it actually gets smaller!
OK, so (2) is telling us: “Let’s use only non-fractions.”

Obviously, if we plug in a normal number like 3, it’s gonna be a [TRUE] statement.
What happens if we plugin a negative number to x^3 > x^2?
Try x=-2. Well, then you’d get -8>+4 [FALSE].
So with x=+2, you get TRUE, but with x=-2, you get FALSE. .

So since you sometimes get FALSE and sometimes get TRUE—then you know this conflict means (B) is NO GOOD!

Step 4) But what about if you combine (1) and (2) together.

Well, (1) basically tells us we can restrict x to be positive.
(2) basically tells us we can restrict x to be only non-fractions.

So what if we only use x values that are positive AND non-fractions. That means x>1.

Can we answer this original question definitively?

Is x^3 > X^2?

Well, when we only use x>1, then this statement is ALWAYS true. So voila!

When we combine (1) and (2) we can restrict the scope of possible X’s to only those that are POSITIVE and NON-FRACTIONS–which means x>1.

Turns out this works out great. So we can choose (C) is the final answer.

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Verbal Videos: Sentence Correction | Critical Reasoning | Reading Comprehension
Quant Videos: Problem Solving | Data Sufficiency

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Sentence Structure Clarifications – Email From Student

TheGMATPill | Questions & Strategies For GMAT Prep.

So I received some questions regarding sentence structure clarifications.

These questions this student is asking are actually pretty important to understand so make sure you take a look at these responses.

Email From Student:

Hi Zeke,

I was watching sentence correction, framework2 part 2.

Could you please confirm my understanding?

1)
My sister is more likely to study than ME ? (ME is incorrect because here is comparing the act of study)

GMATPill: yes

My sister is more likely to study than I DO? (adding DO is fine, right?)

GMATPill: Well, it should be:
My sister is more likely to study than I am.
or
My sister is more likely to study than I.

My weight is more than HIS. (in the video, you use “that of his”. can “his” refer to “his weight”? )

GMATPill: Yes.
My weight is more than his [weight].

2)
In framework3, you mentioned that descriptive phrase describes noun closest to the comma and ING-verb. what if the ING-verb is in the descriptive phrase? let say the sentences below are grammatically correct.

- The antique dealer displayed the cabinet in this window, beautifully RESTORING to its original condition. (does “beautifully restoring to its original condition” now describe antique dealer?)

GMATPill: STRUCTURALLY-YES.
You can flip it around:
“Beautifully restoring to its original condition, the antique dealer blah blah blah”

BUT remember you still need to evaluate the sentence to make sure it makes sense.
“Restoring to its original condition, the antique dealer blah blah blah”—the [its] is intending to refer to the cabinet but structurally it is describing the antique dealer. So it doesn’t make sense.

- I have no doubt the book is better than the film, RECENTLY having read the book. (does ” recently having read the book” still describe the subject “I” ?)

GMATPill: It’s kind of weird to have the word “recently” there–but yes—the phrase describes “I.”

3)
In framework 5, you explain that vs which.

I’m in the third study room that has a door knob. (how do you know she is not in the third study room? how do you know there are a lot of rooms?)

GMATPill: You don’t know how many different third study rooms there. The word “that” invites the possibility of multiple third study rooms.
Which third study room are you in?
I’m in the third study room that has the door knob–not that one that does not have the door knob.

The word “that” invites possibilities of multiple third rooms.

Do you mind using a simple example to illusrate the difference between that and which? i watched this slide many times. i still don’t understand.

“I am in the third study room, which is known to be the really quiet study room.”
Here it is clear that there is only one third study room. The phrase “known to be really quiet” DEFINITIVELY describes the third study room. There is NO other third study room that the author is referring to.

Contrast the above to:

“I am in the third study room that is known to be really quiet study room. There’s also another third study room that is really loud, but I’m in the one THAT is really quiet.

THAT implies that there are multiple possibilities because THAT restricts the scope of possibilities. Now you are referring to the scope of possibilities–not all of them–but just the one THAT is really quiet.

Sorry for asking so many stupid questions.

GMATPill: No problem!

Many thanks,
xxxxxxxx

GMAT Questions This is a history of selected GMAT Questions that GMATPill goes over with students.
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GMAT Reading Comprehension – Perhaps the best video guide to the GMAT reading comprehension section ever created.

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Verbal Videos: Sentence Correction | Critical Reasoning | Reading Comprehension
Quant Videos: Problem Solving | Data Sufficiency

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GMATPill Releases Reading Comprehension Pill – the first video guide to RC

TheGMATPill | announcements, Questions & Strategies For GMAT Prep.

The RC section is perhaps the MOST important part of your GMAT Verbal score!

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GMAT Reading Comprehension Passages

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RC Passage: Genetic Mutations
RC Passage: Caffeine
PDF: GMATPill’s RC Frameworks (accompanying video going over this is for members only)

GMATPill RC Pill Membership

General RC Passage Tips
RC Frameworks: Attack Strategy (17 Minutes)

RC Passage: Archaeology (from the Official Guide)
RC Passage: Austen
RC Passage: Avian Flu
RC Passage: Caffeine
RC Passage: Eatonville
RC Passage: Ecoefficiency
RC Passage: Farming
RC Passage: Federal
RC Passage: Free Market
RC Passage: Genetic Mutations
RC Passage: Industrial Revolution
RC Passage: Outsourcing
RC Passage: Oxygen
RC Passage: Predator (from the Official Guide)
RC Passage: Price-Reduction
RC Passage: Progressive Education
RC Passage: Portrait

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Good luck studying,
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The GMAT Pill Study Method

Related Resources:
Reading Comprehension Tips
RC Cut the Fluff

Table of Contents | See Pricing

Verbal Videos: Sentence Correction | Critical Reasoning | Reading Comprehension
Quant Videos: Problem Solving | Data Sufficiency

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