Number Range Problem

Hi,

The Possible values of N are in the range of -6 to 10.

So,n is definitely greater than -8

Ans:C

I would solve this question as follows:
n={-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A) n < 8
So pick a value of n from the above set and prove the condition true or false.
10<8 NO
9<10 NO
6<8 YES

B) n=-6
-4=-6 NO
3=-6 NO
-6=-6 YES

C) n>-8
-6>-8 YES
-5>-8 YES
1>-8 YES
6>-8 YES
For any number in the set this condition is always true.

D) -10<n<7
-10<10<7 NO
-10<8<7 NO
-10<-5<7 YES

Finally, the answer C

IMO :C

Even I came up with answer choice (C), however, I was confused about the fact that -7 is also > -8. But that is not included in the original range given in the question which is n>=-6. So how is -7 handled here?
Then I thought that since C was not completely true, the answer should be E.

A. n < 8: n could equal 8, 9 or 10
B. n = -6: n could equal -6, but it also could be greater than -6
C. n > -8: Since -6>-8 and -6 is the smallest possible value in the range given, then this must be true
D. -10 < n < 7 n could equal 8,9, or 10
E. none of the above We already pin-pointed 'C'

Answer: C

Hi,


que: If it is true that -6 <= n <= 10, which of the following must be true?

range of n ={-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10}

Ans choices:

A. n < 8: n may be out of the given range
B. n = -6: n is in the given range ==> value of n is in the given range.
C. n > -8: n may be out of the range
D. -10 < n < 7 : n may be out of the range
E. none of the above :


whats the OA?

br,

ajp

The premise is that n is between -6 and +10 inclusive of -6 and 10. Don't even assume that n has to be an integer unless stated. When you are picking a choice you are saying the premise implies this consequence. Do not confuse yourself looking at the answer and asking does the answer imply the statement. This is backwards. Its a one-way implication, If A then B. Look at the statement. See the possibilities and then toss out the answers don't completely cover all the possibilities.


if the number is between -6 and 10 inclusive:
a) does is have to be less than 8, NO, could be more
b)Does it have to be equal to -6, it could be =-6 but not necessarily
c)Does it have to be greater than -8, yes, absolutely. If it is stated that this number is greater than -6 it is certainly also greater than -8 (remember -6<=n<=10 means n>=-6 and n<10)
d) not that we have to consider it now, but given the premise, does the number have to be between -10 and 7? No. It certainly has to be greater than -10 but it could be anything beyond 7 upto and including 10, so D doesn't cover the range and is not necessarily true. Suppose n were 9.

if an option were -7<n<12 that would work because it covers the range.

So C is the only answer here that covers all the possibilities established by the premise.

Thanks everyone. The OA is C.