If -2

Question

If -2 < a < 11 and 3 < b < 12, then which of the following is NOT always true?

A. 1 < a + b < 23 
B. -14 < a - b < 8 
C. -7 < b - a < 14 
D. 1 < b + a < 23 
E. -24 < a b < 132

chetan2u · Accepted Answer

Hi....

We will be playing around with Max and min values of both a and b depending on the operation we do..
Although a+B is same as B+a, and choices A and D are same, we need not see these...

a+b...
 For range, take max values of both for upper end and min values for lower end.
  upper end : 11+12=23 & lower end : -2+3=1.... So 1<a+b<11
A & D are correct

a-b...
 For range, take max value of a and min value of b for upper end and min value of a and max value of b for lower end.
  upper end : 11-3=8 & lower end : -2-12=-14.... So -14<a-b<8 
B is correct

b-a.
 For range, take min value of a and max value of b for upper end and max value of a and min value of b for lower end.
 upper end : 12-(-2)=14 & lower end : 3-11=-8.... So -8<b-a<14 but given is -7<b-a<14
C is Not correct

ab...
  For range, take max value of a and max value of b for upper end and min value of a and max value of b for lower end.
  upper end : 11*12=132 & lower end : -2*12=-24... So -24<ab<132
E is correct ..

C is the answer

amanvermagmat · Answer

We have range of a: -2 < a < 11. This means range of -a: -11 < -a < 2
We have range of b: 3 < b < 12. This means range of -b: -12 < -b < -3

Now, range of (a+b) or (b+a): (-2+3) < a+b < (11+12) Or 1 < a+b < 23.
So A and D are true.

Range of a-b is range of a+(-b): (-2-12) < a-b < (11-3) Or -14 < a-b < 8
So B is also true

Range of b-a is range of b+(-a): (3-11) < b-a < (12+2) Or -8 < b-a < 14
As we can see, C is not always true

Hence  C answer

GMATinsight · Answer

A. 1 < a + b < 23 Using the values given we see that (a+b) ranges from (-2+3=1) to (11+12=23) hence This option is True
B. -14 < a - b < 8 Using the values given we see that (a-b) ranges from (-2-12=-14) to (11-3=8) hence This option is True 
  C. -7 < b - a < 14 Using the values given we see that (b-a) ranges from (3-11=-8) to (12-(-2)=14) hence This option is NOT true for lowest value of (b-a)  
D. 1 < b + a < 23 Using the values given we see that (a+b) ranges from (-2+3=1) to (11+12=23) hence This option is True
E. -24 < a b < 132 Using the values given we see that (a.b) ranges from (-2*12=-24) to (11*12=132) hence This option is True

ANswer: option C

D3N0 · Answer

Ans: C
My method is a bit calculative we need to find which one is not true and for that we need to do the calculation
for A: a's min + b's min <a+b< a's max + b's max = -2+3 <a+b<11+12= 1<a+b<23 True
for B: a's min - b'max <a-b< a's max- b's min= -2-12 <a-b< 11-3 = -14<a-b<8 True
for C: b's min-a' max <b-a<b's max- a's min= 3-11 <b-a<12-(-2) = -8<b-a<14 Not True

ScottTargetTestPrep · Answer

If we add the two inequalities together, we have: 1 < a + b < 23 Thus, A is true and since a + b = b + a, D is also true. Multiplying the second inequality by -1, we have 3 > -b > -12 or -12 < -b < 3. Now, adding the latter to the first inequality, we have: –14 < a – b < 8 So B is true. Similarly, multiplying the first inequality by -1, we have 2 > -a > -11 or -11 < -a < 2. Now. adding the latter to the second inequality, we have: –8 < b – a < 14 So C is NOT true since (b - a) could be -7.5, which does not fall into -7 < b - a < 14. Answer: C

Pankaj0901 · Answer

I believe the wording of question is not correct, and can definitely be better to remove ambiguity.

If the range of  b-a  is: -8 to 14 (say, SET A) ...as explained in the above comments
Option C: -7 to 14 (say, SET B)

=> SET B is a subset of SET A. Hence, for all the values in range -7 to 14 (Option C), the value of b-a (range: -8 to 14) holds correctly. 
Please note: Question asks to select  an option which is NOT always true . But the option C will always hold true as it is the subset of A.  Hence, Option C can surely not be the answer to this question.

Request Admin to kindly check this and correct the question wording.

Bunuel · Answer

This is not true. If b = 3.1 and a = 10.9, then b - a = 3.1 - 10.9 = -7.8.

P.S. Please do not use report button. A post is enough.

chetan2u · Answer

Taking your observation further. 
Rather, Set A has to be subset of Set B for the option to be true and not vice versa. 
We know from Set A that b-a can also be something from -8 to -7, but Set B misses on it.

For example. 
Say c is a prime number. 
A) c is an integer would be true. 
B) But c is odd prime number will not although it is a subset of prime number. If c=2, the option will not stand.

Pankaj0901 · Answer

Please find my remarks below in red and blue. Taking your observation further. Rather, Set A has to be subset of Set B for the option to be true and not vice versa. We know from Set A that b-a can also be something from -8 to -7, but Set B misses on it. For example. Say c is a prime number. c={2,3,5,7,11....} Which of the following is NOT always true? A) c is an integer would be true. {-3,-2,-1,0,1,...} are also integers, which need NOT ALWAYS be Prime numbers. B) But c is odd prime number will not although it is a subset of prime number. {3,5,7,11,....} => Definitely true..as all these values are Prime numbers. If c=2, the option will not stand. (That's Ok, but does c=2 make option B "WRONG" or "NOT RIGHT". I FAIL TO UNDERSTAND THIS!) C) c is a complex number. => Not ALWAYS TRUE...similar to option A (as otherwise every solution in mathematics would be some complex number with imaginary part as 0 at most. Why should we even be zeroing down to a smaller set of range?) D) c is a Natural number. => Not ALWAYS TRUE .....and so on.... I think, there are two ways to look these questions- and none of the two perspectives is completely wrong. Thanks Bunuel and Chetan2u for the explanation (More Kudos to you guys). I understand that Option C doesn't capture the complete range, and that's not the point I am concerned with. It's clear that there could be more values of a,b (say, -10.9, 3.1, as mentioned by Bunuel). What I was trying to say here is something else. May be I need some break as despite a lot of thought I still couldn't quite comprehend. As per the question, it says "..which of the following is NOT always true?" Option C is definitely always true! There could be more eligible values which are not captured in Option C (that's completely ok), my point is Option C is NOT WRONG. I had only pointed out for a clearer wording that doesn't leave any scope of ambiguity. PS (For Bunuel)- Duly noted, report button will not be used. Thanks.

Bunuel · Answer

The question is correct and there is only one correct interpretation

The question asks: If -2 < a < 11 and 3 < b < 12, then which of the following is  NOT always true ?

Only option C is NOT always true. I don't see any ambiguity whatsoever.

Fdambro294 · Answer

Given:

-2 < a < 11

and

3 < b < 12

The question is asking the following:

Which of the Answer Choice Ranges does NOT Always have to be true for EVERY Value that the expression can take?

-C-

-7 < b - a < 14

(1st) Find the MINIMUM Lower Bound of the expression (b - a) given the Ranges in the Q Prompt

We want to first Minimize the Value that (b - a) can take.

Since a is being subtracted from b ——-> we accomplish this by making b as LOW a VALUE as we can ——- and by making a as HIGH a VALUE as we can

The Lower Value Limit for b is: +3

The Upper Value Limit for a is: +11

Thus, the expression (b - a) can take Values greater than >

+3 - +11 = (-)8

(-)8 < (b - a)

However, the Range given by Answer C is:

(-)7 < (b - a) < +14

Answer C is NOT Always a True Statement.

For example, (b - a) can equal a Value like (-)7.5 or (-)7.6 and the Range in Answer Choice C would NOT cover these Values

Therefore, the answer is C

C does NOT always have to be True

Posted from my mobile device

mira93 · Answer

Bunuel , Could you please check what is wrong with my reasoning: B) -14 So B is always correct E) -24 So E is also correct as per my logic. Could you please be so kind to point out my mistake. Much appreciated in advance!

Bunuel · Answer

The question asks: ...which of the following is  NOT  always true?

A, B, D and E are always true.

E is not always true.

MHIKER · Answer

A. a+b= 1 < a + b < 23 
B. a-b = -14 < a - b < 8  
C. b-a= -8 < b - a < 14        
D. 1 < b + a < 23  
E. -24 < a b < 132

So C is not True. Answer is C

bumpbot · Answer

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If -2 < a < 11 and 3 < b < 12, then which of the following is NOT true

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