inequalities.

is it III?

range of m is 2 to 3.333

range of n is -2 to 5

I think it's a. Let's plug in numbers.
If 2<m<3.33 and -2<n<5, let's try to max and min m-n
1. m=3.32 and n=4.9 ==> 3.32-4.90= -1.58 so C is out.
2. m=3.32 and n=-1.99 ==> 3.32-(-1.99)= 5.31

I think both a and b must be true...c is definitely out.

6 < 3m < 10, so m = 3

-8 < 4n < 20, So n = -1,0,1,2,3,4

Range of m-n = 3-4, .........3-(-1) = -1, ........, 4

Both I and II work fine here.

sanjib wrote:if 6<3m<10and -8<4n<20,then which of the following must be true?
a)-3<m-n<10
b)-3<m-n<14
c)4<m-n<7

-3<m-n<5.33

hence a only must be true

If 'a' is true, then why is 'b' wrong? Please explain -

b)-3<m-n<14

real2008 wrote:

sanjib wrote:if 6<3m<10and -8<4n<20,then which of the following must be true?
a)-3<m-n<10
b)-3<m-n<14
c)4<m-n<7

-3<m-n<5.33

hence a only must be true

sanjib wrote:if 6<3m<10and -8<4n<20,then which of the following must be true?
a)-3<m-n<10
b)-3<m-n<14
c)4<m-n<7

The most important rule in inequalities is that you can only add the inequalities, but you can never subtract


6 < 3m < 10 or 2 < m < 3.33

-8 < 4n < 20 or -2 < n < 5

Our answer options have m-n, therefore, change the n's sign and shift the inequalities

-2 < n < 5, multiply by -1

2 > -n > -5

-5 < -n < 2


We now have 2 inequalities,
2 < m < 3.33
-5 < -n < 2

add the two inequalities


2-5 < m-n < 3.33+2

-3 < m-n < 5.33

Hence only option A can be true.

sanjib wrote:if 6<3m<10and -8<4n<20,then which of the following must be true?
a)-3<m-n<10
b)-3<m-n<14
c)4<m-n<7

(a) is more restrictive than (b). Therefore, if (a) must be true, (b) automatically also must be true.

Let's simplify the question to make sure we all understand that concept:

If m < 5, which of the following must be true?

a) m < 5
b) m < 6
c) m < 7

Of course (a) is a "must be true". However, if we know that m < 5, it will also be true 100% of the time that m < 6 and m < 7. So, in this example, all three are "must be true"s.

Similarly in the question posted, since:

-3 < m-n < 10

it also must be true that:

-3 < m-n < 14

As an aside, this looks like a roman numeral question; the original poster could have saved a lot of confusion by posting the ENTIRE question, including the answer choices. As a general rule, please post entire questions.