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Re: Prob from Kaplan Diagnostic test [#permalink]
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.

Re: Prob from Kaplan Diagnostic test [#permalink]
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.

Re: Prob from Kaplan Diagnostic test [#permalink]
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.

Re: Prob from Kaplan Diagnostic test [#permalink]
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?

Re: Prob from Kaplan Diagnostic test [#permalink]
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
_________________

Re: Prob from Kaplan Diagnostic test [#permalink]
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.