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

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

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

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

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.

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.

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.

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.

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.

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

Bunuel,

Could you please check what is wrong with my reasoning:

B) -14<a-b<8
if we take min of a-b, we get a little more than -14(a is more than -2, and b is less than 12)
if we take max of a-b, we get a little less than 8 (a is a little less than 11 and b is a little more than 3)
----> So B is always correct

E) -24<ab<132
If we take min of ab, we get a little more than -24 (a is a little larger than -2, b is a little smaller than 12)
If we take max of ab, we get a little less than 132 (a is a little smaller than 11, b is a little smaller than 12)
---> So E is also correct as per my logic. Could you please be so kind to point out my mistake. Much appreciated in advance!

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

A, B, D and E are always true.

E is not always true.

A. a+b= 1 < a + b < 23
B. a-b = -14 < a - b < 8 [1,-5,8,-14 we take 8 and -14]
C. b-a= -8 < b - a < 14 [Given is -7 < b - a < 14 ] [1,5,-8,14 we can take 14 and -8]
D. 1 < b + a < 23 [Same as A]
E. -24 < a b < 132 [The four values are -6,132,-24,33; we take extreme values 132 as upper limit and -24 as lower limit]

So C is not True. Answer is C

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