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

It is currently 19 Oct 2019, 03:06

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If b < 1 and 2x - b = 0, which of the following must be true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 02 Oct 2008
Posts: 48
If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post Updated on: 06 Feb 2018, 21:58
2
5
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

58% (01:30) correct 42% (01:40) wrong based on 395 sessions

HideShow timer Statistics

If b < 1 and 2x - b = 0, which of the following must be true?

A. x > -1
B. x < -2
C. x = 2
D. x < 3
E. x > 3

Originally posted by tania on 06 Dec 2009, 11:29.
Last edited by Bunuel on 06 Feb 2018, 21:58, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58452
If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 06 Dec 2009, 12:02
2
2
Manager
Manager
User avatar
Joined: 29 Oct 2009
Posts: 177
GMAT 1: 750 Q50 V42
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 06 Dec 2009, 12:13
tania wrote:
For the following question, it is indicated that option D is correct.

I am not able to understand why ? can anyone explain to me in detail about this one

if b< 1 and 2x-b = 0, which of the following must be true?

A.X>-1
B.x<-2
C.X=2
D.X<3
E.X>3

Regards,
Tania


The two statements we have been given are :

1) b < 1

2) 2x - b = 0


Now notice that all the answer choices ask us something relating to the value of 'x'. This is our cue for rearranging the given information so that we can cross check its validity with the answer choices.

Let us write the equation as : x = b/2

Since we know that 'b < 1', we can safely conclude that x must be less that 1/2 or 'x < 0.5'

Now let us compare the answer choices to see which one of them must be true with the information we have at hand.

(A) x > -1 --> We know that x < 0.5 but there is no restriction on its lower limit. Thus it can hold values that are less than -1. Hence this statement is not necessarily true.

(B) x < -2 --> Again since x can hold any values less than 0.5 (such as 0, -0.5 etc.) this statement is not always true.

(C) x = 2 --> Since we know that x < 0.5, this statement can never be true.

(D) x < 3 --> If x < 0.5, then x MUST be less than 3. Therefore this statement MUST be true.

(E) x > 3 --> Since we know that x < 0.5, this statement can never be true.

Answer : D

_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!
1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html
Intern
Intern
avatar
Joined: 24 Sep 2012
Posts: 26
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 26 Oct 2012, 22:12
Hello All,

X < 1/2 is correct, two answer choices seems to be correct
B.x<-2
D.X<3
It is not given than X is a postive or negative, integer or fraction.
In my opinion, if we consider D it can have possible answer as X = 2 or X = 1, but X has to be less than 1/2.
If we consider X < -2 for all values of X, X < 1/2 holds true.
Hence my answer was B.

Please feel free to correct me.

REgards,
Pritish
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 563
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 26 Oct 2012, 22:57
pritish2301 wrote:
Hello All,

X < 1/2 is correct, two answer choices seems to be correct
B.x<-2
D.X<3
It is not given than X is a postive or negative, integer or fraction.
In my opinion, if we consider D it can have possible answer as X = 2 or X = 1, but X has to be less than 1/2.
If we consider X < -2 for all values of X, X < 1/2 holds true.
Hence my answer was B.

Please feel free to correct me.

REgards,
Pritish


Hi Pritish,

Question says : if b< 1 and 2x-b = 0 , which of the following must be true?or in simple words ,
"if x<1/2 , which of the following must be true?"

Option B doesnt hold good for any value of x where,
\(-2 <=x <1/2\)

Consider for example, if x =0,
x<1/2 is true but x <-2 is not true
Hence B can not be the answer.

On the other hand, for option D as others have pointed out correctly. Since x <1/2 and 1/2 <3
this implies that x <3 . This would be true for any value of x that satisfies x<1/2.

hope it helps.
_________________
Lets Kudos!!! ;-)
Black Friday Debrief
Intern
Intern
avatar
Joined: 24 Sep 2012
Posts: 26
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 26 Oct 2012, 23:22
Vips0000 wrote:
pritish2301 wrote:
Hello All,

X < 1/2 is correct, two answer choices seems to be correct
B.x<-2
D.X<3
It is not given than X is a postive or negative, integer or fraction.
In my opinion, if we consider D it can have possible answer as X = 2 or X = 1, but X has to be less than 1/2.
If we consider X < -2 for all values of X, X < 1/2 holds true.
Hence my answer was B.

Please feel free to correct me.

REgards,
Pritish


Hi Pritish,

Question says : if b< 1 and 2x-b = 0 , which of the following must be true?or in simple words ,
"if x<1/2 , which of the following must be true?"

Option B doesnt hold good for any value of x where,
\(-2 <=x <1/2\)

Consider for example, if x =0,
x<1/2 is true but x <-2 is not true
Hence B can not be the answer.

On the other hand, for option D as others have pointed out correctly. Since x <1/2 and 1/2 <3
this implies that x <3 . This would be true for any value of x that satisfies x<1/2.

hope it helps.



As you mentioned
"Consider for example, if x =0,
x<1/2 is true but x <-2 is not true
Hence B can not be the answer."

If we chose option B X can never be equal to 0, but if X<3 there is a possibility that X can be 0. Right?
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 563
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 27 Oct 2012, 21:39
pritish2301 wrote:
Vips0000 wrote:
pritish2301 wrote:
Hello All,

X < 1/2 is correct, two answer choices seems to be correct
B.x<-2
D.X<3
It is not given than X is a postive or negative, integer or fraction.
In my opinion, if we consider D it can have possible answer as X = 2 or X = 1, but X has to be less than 1/2.
If we consider X < -2 for all values of X, X < 1/2 holds true.
Hence my answer was B.

Please feel free to correct me.

REgards,
Pritish


Hi Pritish,

Question says : if b< 1 and 2x-b = 0 , which of the following must be true?or in simple words ,
"if x<1/2 , which of the following must be true?"

Option B doesnt hold good for any value of x where,
\(-2 <=x <1/2\)

Consider for example, if x =0,
x<1/2 is true but x <-2 is not true
Hence B can not be the answer.

On the other hand, for option D as others have pointed out correctly. Since x <1/2 and 1/2 <3
this implies that x <3 . This would be true for any value of x that satisfies x<1/2.

hope it helps.



As you mentioned
"Consider for example, if x =0,
x<1/2 is true but x <-2 is not true
Hence B can not be the answer."

If we chose option B X can never be equal to 0, but if X<3 there is a possibility that X can be 0. Right?

Hi Pritish,
You are getting confused here -
the reasoning follows through question stem first -
question says if x<1/2 then which of the following must be true -
This means x<1/2 is taken for granted. that is our scope. period.

now within this scope we need to find the answer. You dont choose option first and then try to fit in question, but u read option first, define the limit and then consider and choose options.
Hope it is clear. Now click kudos :P
_________________
Lets Kudos!!! ;-)
Black Friday Debrief
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58452
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 29 Oct 2012, 03:28
pritish2301 wrote:
Hello All,

X < 1/2 is correct, two answer choices seems to be correct
B.x<-2
D.X<3
It is not given than X is a postive or negative, integer or fraction.
In my opinion, if we consider D it can have possible answer as X = 2 or X = 1, but X has to be less than 1/2.
If we consider X < -2 for all values of X, X < 1/2 holds true.
Hence my answer was B.

Please feel free to correct me.

REgards,
Pritish


Notice that we are asked "which of the following MUST be true?" not COULD be true.

Now, we know that x<1/2, thus x<3 is always true.

Is x<-2 always true? No, if x=0, then x<-2, won't be true, therefore this option is not always true.

For more on Must/Could be true questions check: search.php?search_id=tag&tag_id=193 (more than 100 questions).

Hope it helps.
_________________
Intern
Intern
avatar
Joined: 24 Oct 2014
Posts: 39
Location: United States
GMAT 1: 710 Q49 V38
GMAT 2: 760 Q48 V47
GMAT ToolKit User
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 08 Apr 2015, 20:58
So I was getting confused here especially in comparison to this problem

If a^5 ≤ a, which of the following must be true?

I. –1 ≤ a ≤ 0
II. a=0
III. 0 ≤ a ≤ 1

A. None of the above
B. I only
C. II only
D. III only
E. I and III only

Here the answer is A, because of the two possible options II and III, III cannot be right because we can think of -2 and find it to satisfy the original condition and -2 doesn't fall in this range. Although II is true, there are other numbers that satisfy the condition as well.

When I looked at this problem, I am like the correct answer should be x <= 1/2. But those choices were there. The answer was totally unexpected X<3, cause I though how about x = 1, 2 or some other value between 1/2 and 3. These values don't satisfy the condition, then how is it true.
This is what I have come up with, especially dealing with inequality problems, try to find a number (outside the range given in the answer choice) and see if it satisfies the question stem. If there is none, then you have the right answer. So for eg. looking at x<3, there is no value of x>=3 that would satisfy the Question stem and hence incorrect.

This is quite tricky to wrap your head around. Very tricky! hopefully this will help me in the future.
Manager
Manager
User avatar
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
GMAT ToolKit User
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 08 Apr 2015, 22:13
nphatak wrote:
So I was getting confused here especially in comparison to this problem

If a^5 ≤ a, which of the following must be true?

I. –1 ≤ a ≤ 0
II. a=0
III. 0 ≤ a ≤ 1

A. None of the above
B. I only
C. II only
D. III only
E. I and III only

Here the answer is A, because of the two possible options II and III, III cannot be right because we can think of -2 and find it to satisfy the original condition and -2 doesn't fall in this range. Although II is true, there are other numbers that satisfy the condition as well.

When I looked at this problem, I am like the correct answer should be x <= 1/2. But those choices were there. The answer was totally unexpected X<3, cause I though how about x = 1, 2 or some other value between 1/2 and 3. These values don't satisfy the condition, then how is it true.
This is what I have come up with, especially dealing with inequality problems, try to find a number (outside the range given in the answer choice) and see if it satisfies the question stem. If there is none, then you have the right answer. So for eg. looking at x<3, there is no value of x>=3 that would satisfy the Question stem and hence incorrect.

This is quite tricky to wrap your head around. Very tricky! hopefully this will help me in the future.



Hey nphatak...Greetings!!!


I'm a little confused about the example you gave and specially the answer choices. Is this question a standard GMAT question. I don't think the GMAT tries to trick you this way or is it possible :roll: :|
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 502
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 09 Apr 2015, 02:58
Ashishmathew01081987 wrote:
nphatak wrote:
So I was getting confused here especially in comparison to this problem

If a^5 ≤ a, which of the following must be true?

I. –1 ≤ a ≤ 0
II. a=0
III. 0 ≤ a ≤ 1

A. None of the above
B. I only
C. II only
D. III only
E. I and III only

Here the answer is A, because of the two possible options II and III, III cannot be right because we can think of -2 and find it to satisfy the original condition and -2 doesn't fall in this range. Although II is true, there are other numbers that satisfy the condition as well.

When I looked at this problem, I am like the correct answer should be x <= 1/2. But those choices were there. The answer was totally unexpected X<3, cause I though how about x = 1, 2 or some other value between 1/2 and 3. These values don't satisfy the condition, then how is it true.
This is what I have come up with, especially dealing with inequality problems, try to find a number (outside the range given in the answer choice) and see if it satisfies the question stem. If there is none, then you have the right answer. So for eg. looking at x<3, there is no value of x>=3 that would satisfy the Question stem and hence incorrect.

This is quite tricky to wrap your head around. Very tricky! hopefully this will help me in the future.



Hey nphatak...Greetings!!!


I'm a little confused about the example you gave and specially the answer choices. Is this question a standard GMAT question. I don't think the GMAT tries to trick you this way or is it possible :roll: :|



it's not a tricky question , trust me .
whenever you face such inequalities , first thing to do is to draw their roots on number line .

\(a^5-a <=0\)
\(a(a^4-1) <=0\)

root are -1, 0 , 1 now as shown in attached image you can find the regions where this inequality holds .
and clearly say that answer is A .
Attachments

gmatclub.jpg
gmatclub.jpg [ 24.36 KiB | Viewed 2746 times ]

Intern
Intern
avatar
Joined: 24 Oct 2014
Posts: 39
Location: United States
GMAT 1: 710 Q49 V38
GMAT 2: 760 Q48 V47
GMAT ToolKit User
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 09 Apr 2015, 16:49
Well you see its not finding the roots that is the problem. I can find the conditions under which the inequality will hold. Its the answer choices that I said were confusing. The answer choice a=0 is true, the inequality will be 0. And when you are asked what must be true, you are like..yeah at a = 0 this is true. But the question is not if its true at one value, the question is which answer choice covers all the possible values. Not one! I am probably not able to explain what the confusion is.

If a^5 ≤ a, which of the following must be true?

I. –1 ≤ a ≤ 0
II. a=0
III. 0 ≤ a ≤ 1

A. None of the above
B. I only
C. II only
D. III only
E. I and III only
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 09 Apr 2015, 21:46
1
nphatak wrote:
Well you see its not finding the roots that is the problem. I can find the conditions under which the inequality will hold. Its the answer choices that I said were confusing. The answer choice a=0 is true, the inequality will be 0. And when you are asked what must be true, you are like..yeah at a = 0 this is true. But the question is not if its true at one value, the question is which answer choice covers all the possible values. Not one! I am probably not able to explain what the confusion is.

If a^5 ≤ a, which of the following must be true?

I. –1 ≤ a ≤ 0
II. a=0
III. 0 ≤ a ≤ 1

A. None of the above
B. I only
C. II only
D. III only
E. I and III only


So when you solve the inequality, you get a <= -1 OR 0 <= a <= 1.
a is either less than -1 or it is between 0 and 1.

Let's see what each statement says.

I. –1 ≤ a ≤ 0
This says that a must be between -1 and 0. True or False? False

II. a=0
This says that a must be 0. True or False? False. a is either less than -1 or it is between 0 and 1.

III. 0 ≤ a ≤ 1
This says that a must lie between 0 and 1. True or False? False. a is either less than -1 OR it is between 0 and 1.

Now, think if there were another statement
IV. a < 2
This says a must be less than 2. True or False? True. a is either less than -1 OR it is between 0 and 1. In any case, it will always be less than 2.

By the way, it is not a trick. It is based on logic and can easily be tested on GMAT.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
Joined: 24 Oct 2014
Posts: 39
Location: United States
GMAT 1: 710 Q49 V38
GMAT 2: 760 Q48 V47
GMAT ToolKit User
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 10 Apr 2015, 07:40
VeritasPrepKarishma wrote:
nphatak wrote:
Well you see its not finding the roots that is the problem. I can find the conditions under which the inequality will hold. Its the answer choices that I said were confusing. The answer choice a=0 is true, the inequality will be 0. And when you are asked what must be true, you are like..yeah at a = 0 this is true. But the question is not if its true at one value, the question is which answer choice covers all the possible values. Not one! I am probably not able to explain what the confusion is.

If a^5 ≤ a, which of the following must be true?

I. –1 ≤ a ≤ 0
II. a=0
III. 0 ≤ a ≤ 1

A. None of the above
B. I only
C. II only
D. III only
E. I and III only


So when you solve the inequality, you get a <= -1 OR 0 <= a <= 1.
a is either less than -1 or it is between 0 and 1.

Let's see what each statement says.

I. –1 ≤ a ≤ 0
This says that a must be between -1 and 0. True or False? False

II. a=0
This says that a must be 0. True or False? False. a is either less than -1 or it is between 0 and 1.

III. 0 ≤ a ≤ 1
This says that a must lie between 0 and 1. True or False? False. a is either less than -1 OR it is between 0 and 1.

Now, think if there were another statement
IV. a < 2
This says a must be less than 2. True or False? True. a is either less than -1 OR it is between 0 and 1. In any case, it will always be less than 2.

By the way, it is not a trick. It is based on logic and can easily be tested on GMAT.


Thanks a lot Karishma!
So the correct answer choice should cover all the possible values of a, right? The way I was interpreting this question was, which of this must be true = any subset of all the possible values has to be true and I marked that answer. Its just a failure in my understanding these kind of questions.
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: If b < 1 and 2x - b = 0, which of the following must be true?  [#permalink]

Show Tags

New post 26 Feb 2018, 11:20
tania wrote:
If b < 1 and 2x - b = 0, which of the following must be true?

A. x > -1
B. x < -2
C. x = 2
D. x < 3
E. x > 3



Manipulating the equation we have 2x = b, thus:

2x < 1

x < 1/2

Thus, x must be less than 3.

Note that the correct answer x < 3 may be confusing. Here’s the logic: we determined algebraically that x must be less than 1/2. Thus, some possible values for x are 1/4 , 0, -⅔, -5, and so on. Note that each of these values is, indeed, less than 3 (which is answer choice D). In fact, any value of x that satisfies x < 1/2 will ALSO satisfy x < 3. Hence, answer choice D is correct.

Answer: D
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: If b < 1 and 2x - b = 0, which of the following must be true?   [#permalink] 26 Feb 2018, 11:20
Display posts from previous: Sort by

If b < 1 and 2x - b = 0, which of the following must be true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne