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

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If b< 1 and 2x-b = 0, which of the following must be true? [#permalink] New post 06 Dec 2009, 10:29
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Oct 2012, 23:34, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Prob from Kaplan Diagnostic test [#permalink] New post 06 Dec 2009, 11:02
Expert's post
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


2x-b=0 --> b=2x

b<1 --> 2x<1 --> x<\frac{1}{2}

As x<\frac{1}{2}, x must also be less then 3.

Answer: D.
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Re: Prob from Kaplan Diagnostic test [#permalink] New post 06 Dec 2009, 11:13
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

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Re: Prob from Kaplan Diagnostic test [#permalink] New post 26 Oct 2012, 21:12
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
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Re: Prob from Kaplan Diagnostic test [#permalink] New post 26 Oct 2012, 21:57
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.
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Re: Prob from Kaplan Diagnostic test [#permalink] New post 26 Oct 2012, 22:22
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?
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Re: Prob from Kaplan Diagnostic test [#permalink] New post 27 Oct 2012, 20:39
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
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Re: Prob from Kaplan Diagnostic test [#permalink] New post 29 Oct 2012, 02:28
Expert's post
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.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If b< 1 and 2x-b = 0, which of the following must be true? [#permalink] New post 14 Jul 2014, 13:17
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Re: If b< 1 and 2x-b = 0, which of the following must be true?   [#permalink] 14 Jul 2014, 13:17
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