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# If x=a+1 and b=x-2 then which of the following must be false?

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Joined: 12 Aug 2015
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Schools: Boston U '20 (M)
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If x=a+1 and b=x-2 then which of the following must be false?  [#permalink]

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Updated on: 04 Apr 2017, 00:41
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95% (hard)

Question Stats:

34% (02:36) correct 66% (02:19) wrong based on 134 sessions

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If x=a+1 and b=x+2 then which of the following must be false?

(I)a>b
(II)b>a
(III)a=b
(IV)a=b^2
(V)b=a^2

A) I and III
B) I, III, V
C) I, III, IV
D) II, III, V
E) I, III, IV, V

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Originally posted by stonecold on 01 Apr 2017, 20:03.
Last edited by stonecold on 04 Apr 2017, 00:41, edited 3 times in total.
Edited the question and moved to PS forum.
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GPA: 3.76
Re: If x=a+1 and b=x-2 then which of the following must be false?  [#permalink]

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01 Apr 2017, 21:22
If x=a+1 and b=x-2 then which of the following must be false?
(I)a>b
(II)b>a
(III)a=b
(IV)a=b^2
(V)b=a^2

A)I and III
B)I,III,V
C)I,III,IV
D)II,III,V
E)I,III,IV,V[/b]

Going with D
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Re: If x=a+1 and b=x-2 then which of the following must be false?  [#permalink]

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03 Apr 2017, 20:06
stonecold wrote:
If x=a+1 and b=x-2 then which of the following must be false?

(I)a>b
(II)b>a
(III)a=b
(IV)a=b^2
(V)b=a^2

A) I and III
B) I, III, V
C) I, III, IV
D) II, III, V
E) I, III, IV, V

why (I) is wrong !?
a=x-1,b=x-2
clearly, a>b
Intern
Joined: 18 Jan 2017
Posts: 23
Re: If x=a+1 and b=x-2 then which of the following must be false?  [#permalink]

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03 Apr 2017, 20:42
I think D would be the answer; a = x-1 and b = x-2 are provided... now one method to find the answer is to plug values; the other method is method of elimination so we will get a-b = 1...

Sent from my GT-I9060I using GMAT Club Forum mobile app
Current Student
Joined: 12 Aug 2015
Posts: 2567
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If x=a+1 and b=x-2 then which of the following must be false?  [#permalink]

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04 Apr 2017, 00:37
2
Hi everyone.
Here is what i did in this question =>

Given data => a=x-1 and b=x+2
Now we are asked which of the following must be false.

Lets see the options one by one ==>

Option 1 =>
a>b
x-1>x+2
-1>2
ALWAYS false.

Option 2=>
b>a
x+2>x-1
2>-1
ALWAYS True.
Option 3=>
a=b
x-1=x+2
-1=2
ALWAYS False.
Option 4 =>
a=b^2
x-1=(x+2)^2
x-1=x^2+4+4x
x^2+3x+5=0

CHECK THE Value of the DETERMINANT => D=> 3^2 -4*5=9-20=-11
The determinant is Negative=> NO REAL value of x

ALWAYS False.
Option 5 =>
b=a^2
x+2=(x-1)^2
x^2+1-2x=x+2
x^2-3x-1=0
CHECK the Determinant again => D= (-3)^2-4*(-1)=> 9+4=13 => POSITIVE

Hence there would be 2 values of x for sure.

Hence this may be true.

So options 1,3 and 4 are always False.

Smash that D.

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Joined: 06 Jan 2016
Posts: 26
Re: If x=a+1 and b=x-2 then which of the following must be false?  [#permalink]

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08 Apr 2017, 17:40
My approach was a hybrid:

I) & II) were straightforward FALSE/TRUE. -> Option D was ruled out
III) Didn't even made any calculation since was present in all the remaining answers
IV) Did the math
a=b^2 ; x-1 = (x+2)^2 ; x^2+3x+5=0 ; since I couldn't find any "integer" solution I flagged it FALSE
V) Did the math
b=a^2 ; x+2 = (x-1)^2 ; x^2-3x+1=0; since I couldn't find any "integer" solution I flagged it FALSE

Wrongly, I selected choice E

Making the assumption of the integer solution I didn't think of any other real number as roots of the equations on IV and V.

Thanks for this good question stonecold, even knowing that real numbers could be a possible solution, I wouldn't figure out to use the Discriminant of a Quadratic to help me out.
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If x=a+1 and b=x-2 then which of the following must be false?  [#permalink]

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15 Apr 2017, 02:47
Ans C.
Given, x= a+1 and b = x + 2, or b = a +1 +2 = a+3
So, we have b = a + 3
Now check all the cases
1. a> b -- False
2. b >a -- True
3. a = b --False
4. a = b^2
substitute in the final equation and you will get
b^2 -b +3 = 0, imaginary roots ( remember b^2-4ac) --- False
5. b = a^2
Same as above substitute and you will get a^2 -a -3 = 0, it has real roots --- True
Hence 1, 3 and 4 are false.
If x=a+1 and b=x-2 then which of the following must be false?   [#permalink] 15 Apr 2017, 02:47
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