sanju09 wrote:If -2 < a < 11 and 3 < b < 12, then which of the following is NOT 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

Given -2<a<11
and 3<b<12

So, 1<a+b<23. Hence A and D are true.

Now minimum value of a-b = -2-12=-14(for a-b to be minimum, a must be minimum and b must be maximum)
and maximum value of a-b = 11-3 = 8 (for a-b to be maximum, a must be maximum and b must be minimum)

Hence -14<a-b<8.
Choice C is also true.

Multiplying the above inequality by -1, we get
-8<b-a<14

Also minimum value of ab is -24 and maximum value of ab is 132.
Hence, -24<ab<132.
So choice E is also true.

I don't think D can be the answer because if -8<b-a<14 then obviously -7<b-a<14 is also TRUE.

Any take on this folks?

If b= 3.1 and a = 10.9

b - a = 3.1 - 10.9 = -7.8

-7 < b-a is false

==> Choice C



Cheers,
Sam

sanju09 wrote:If -2 < a < 11 and 3 < b < 12, then which of the following is NOT 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

If -14 < a-b < 8 (option B) is multiplied by -1, we get:
14 > -a+b > -8
14 > b-a > -8
-8 < b-a < 14.
Implication:
If B is true, then C is NOT true, since C indicates that -7 < b-a < 14.
In other words:
B and C cannot both be true.

Test whether B or C is true.
If we multiply 3 < b < 12 by -1, we get:
-3 > -b > -12
-12 < -b < -3

Adding together -2 < a < 11 and -12 < -b < -3, we get:
-2 + (-12) < a-b < 11 + (-3)
-14 < a-b < 8.
Since B is true, we know that C is NOT true.

The correct answer is C.