GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 26 May 2019, 16:17

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Problem Solving Pack 4, Question 1) If -2 < t < 0...[

Author Message
TAGS:

### Hide Tags

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14209
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Problem Solving Pack 4, Question 1) If -2 < t < 0...[  [#permalink]

### Show Tags

19 Nov 2015, 17:32
2
8
00:00

Difficulty:

65% (hard)

Question Stats:

61% (02:04) correct 39% (02:06) wrong based on 258 sessions

### HideShow timer Statistics

QUANT 4-PACK SERIES Problem Solving Pack 4 Question 1 If -2 < t < 0...

If -2 < t < 0 and 0 < v < 2, then which of the following must be true?

I. tv - v < 0

II. $$t^{2}$$ – $$v^{2}$$ > 0

III. $$(t – v)^{2}$$< 4

A) I only
B) II only
C) III only
D) I and III
E) I, II and III

48 Hour Window Answer & Explanation Window
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation

_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Senior Manager Joined: 28 Feb 2014 Posts: 294 Location: United States Concentration: Strategy, General Management Problem Solving Pack 4, Question 1) If -2 < t < 0...[ [#permalink] ### Show Tags 19 Nov 2015, 18:55 If -2 < t < 0 and 0 < v < 2, then which of the following must be true? I. tv - v < 0 v(t-1)<0 this is always true as t-1 is always negative and v is always positive II. $$t^{2}$$ – $$v^{2}$$ > 0 if t=-1 and v=1 this statement is false III. $$(t – v)^{2}$$< 4 the square turns this equation positive. since t and v will always be less than 2 the statement will always be less than 4. Answer: D) I and III Manager Joined: 17 Oct 2013 Posts: 50 Re: Problem Solving Pack 4, Question 1) If -2 < t < 0...[ [#permalink] ### Show Tags 19 Nov 2015, 19:07 2 peachfuzz wrote: If -2 < t < 0 and 0 < v < 2, then which of the following must be true? I. tv - v < 0 v(t-1)<0 this is always true as t-1 is always negative and v is always positive II. $$t^{2}$$ – $$v^{2}$$ > 0 if t=-1 and v=1 this statement is false III. $$(t – v)^{2}$$< 4 the square turns this equation positive. since t and v will always be less than 2 the statement will always be less than 4. Answer: D) I and III I think answer is A for III, what if t = -1.9 and v =1.9 we have -1.9 -1.9 = -3.8, now square of this > 4. Intern Joined: 21 May 2015 Posts: 11 Concentration: Marketing, Nonprofit GMAT 1: 720 Q48 V41 WE: Analyst (Non-Profit and Government) Re: Problem Solving Pack 4, Question 1) If -2 < t < 0...[ [#permalink] ### Show Tags 19 Nov 2015, 21:58 1 (-2)-----(t)--------(0)----(1)-(v)------(2) I. v(t-1)<0: Always true. Because t<1, v>0. II. (t-v)(t+v)>0: * t-v < 0 always * t+v < 0 only when |t|>|v| because t<0. As we see in the number line this is not always the case. III. |t-v|<2: t could be further to -2 and v could be further to 2. Their maximum distance is 4, so nothing guarantees they would be at these respective positions for the inequality to hold. So only I is correct. CEO Joined: 20 Mar 2014 Posts: 2626 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: Problem Solving Pack 4, Question 1) If -2 < t < 0...[ [#permalink] ### Show Tags 23 Nov 2015, 09:17 3 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Problem Solving Pack 4 Question 1 If -2 < t < 0... If -2 < t < 0 and 0 < v < 2, then which of the following must be true? I. tv - v < 0 II. $$t^{2}$$ – $$v^{2}$$ > 0 III. $$(t – v)^{2}$$< 4 A) I only B) II only C) III only D) I and III E) I, II and III 48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4-Pack series Scroll Down For Official Explanation This is a type of question that can be solved either by taking certain values for t and v. As t<0 and v>0 --> v>t --> v-t>0 Now for a must be true question, ALL cases must satisfy for a TRUE!! i) $$tv-v^2<0$$ ---> v(t-1) < 0 and as v>0 , the only case possible for t is for t<1 and we have indeed been given that t<0 --> t<1 . Thus this is a must be true statement. Eliminate B and C. ii) $$t^2-v^2 > 0$$ ---> $$(t+v)(t-v) > 0$$ ---> t-v < 0 as v> 0 and t<0 (given). But is t+v <0 ? This may or may not be true. You can check it by taking the following values: t=-1.5 and v=0.5, t+v <0 but t=-1 and v=1.5, t+v >0 This makes this statement not always true. Eliminate E. iii) $$(t-v)^2>4$$ this statement can be negated by taking t=-1.5, v=1.5 --> $$(t-v)^2 = 3^2 = 9 > 4$$ making this statement false. Eliminate D A is the correct answer. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14209 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Problem Solving Pack 4, Question 1) If -2 < t < 0...[ [#permalink] ### Show Tags 24 Nov 2015, 00:46 2 1 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Problem Solving Pack 4 Question 1 If -2 < t < 0... If -2 < t < 0 and 0 < v < 2, then which of the following must be true? I. tv - v < 0 II. $$t^{2}$$ – $$v^{2}$$ > 0 III. $$(t – v)^{2}$$< 4 A) I only B) II only C) III only D) I and III E) I, II and III Hi All, In Roman Numeral questions, the answer choices can often be used to approach the prompt in the most efficient way possible (and sometimes avoid doing unnecessary work). Given the ranges for t and v (-2 < t < 0 and 0 < v < 2), we're asked 'which of the following MUST be true?' This essentially means "which of the following is ALWAYS TRUE no matter how many different examples we can come up with. This prompt can be beaten by TESTing VALUES and/or by using Number Properties. From the Roman Numeral frequencies in the answer choices, it looks like 1 or 3 should be dealt with first. Roman Numeral 1 looks relatively easy, so let's start there. I. tv - v < 0 Since t is NEGATIVE and v is POSITIVE, tv = (negative)(positive) = NEGATIVE. Thus, we have... tv - v = ? negative - positive = negative The end result of this calculation will ALWAYS be NEGATIVE, so Roman Numeral 1 is TRUE. The correct answer MUST include Roman Numeral 1. Eliminate Answers B and C. From the remaining 3 answers, Roman Numeral 3 should be dealt with next (if we can eliminate it, then we'll have the final answer...). III. $$(t – v)^{2}$$< 4 For this Roman Numeral, we should look to DISPROVE the idea that the calculation will always be less than 4. From the given ranges, t can get 'really close' to -2 (think -1.99999) and v can get 'really close' to +2 (think +1.999999). $$(-1.9999999 - 1.999999)^{2}$$= about $$(-2 -2)^{2}$$= about $$(-4)^{2}$$ = about 16. This is clearly NOT less than 4, so Roman Numeral 3 is NOT always true. Eliminate Answers D and E. With only one answer remaining, there's no need to deal with Roman Numeral 2. Final Answer: For the sake of working through Roman Numeral 2 though, we should take the same general approach that we used with Roman Numeral 3: try to prove that it's NOT always true... II. $$t^{2}$$ – $$v^{2}$$ > 0 IF.... t = -1 v = +1 $$(-1)^{2}$$ - $$(1)^{2}$$ = 1 - 1= 0 This result is NOT greater than 0, so Roman Numeral 2 is NOT always true. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Senior Manager
Joined: 02 Apr 2014
Posts: 477
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Re: Problem Solving Pack 4, Question 1) If -2 < t < 0...[  [#permalink]

### Show Tags

26 Jan 2018, 04:42
1
I. $$tv - v < 0$$
$$v(t-1)$$ < 0
as v is always positive,
$$(t-1) < 0$$
$$t < 1$$ ? yes always true

2. $$t^2 - v^2 > 0$$ ?
$$t^2 > v^2$$ ?
$$|t| > |v|$$ ?
need not be, if t = -0.5 and v = 1

3. $$(t-v)^2 < 4$$ ?
$$|t-v| < 2$$ ?
need not be if t = -1.8, v = 1.8

Re: Problem Solving Pack 4, Question 1) If -2 < t < 0...[   [#permalink] 26 Jan 2018, 04:42
Display posts from previous: Sort by