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)-3<m-n<10
b)-3<m-n<14
c)4<m-n<7
is it III?
range of m is 2 to 3.333
range of n is -2 to 5
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inequalities.
Source: Beat The GMAT — Problem Solving |
Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working.
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
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
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.
-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.
-3<m-n<5.33sanjib 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
hence a only must be true
If 'a' is true, then why is 'b' wrong? Please explain -
b)-3<m-n<14
b)-3<m-n<14
real2008 wrote:-3<m-n<5.33sanjib 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
hence a only must be true
The most important rule in inequalities is that you can only add the inequalities, but you can never subtractsanjib 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
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.
-
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(a) is more restrictive than (b). Therefore, if (a) must be true, (b) automatically also 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
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.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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