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og 10 inequalities prob

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by nikhilkatira » Thu Jun 17, 2010 11:26 pm
If it is true that x >-2 and x<7, which of the following must be true?

a) x > 2

b) x > -7

c) x < 2

d) -7 < x < 2

e) None of the above

please answer with explanation.
Best,
Nikhil H. Katira
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by papgust » Fri Jun 18, 2010 12:40 am
I would go with B

x lies b/w -2 and 7 (exclusive).

the question is "which of the following must be true?"

a. x>2 -- x could lie b/w -2 and 2. Need not be always > 2.

b. x > -7 -- x is always greater than -7.

c. x < 2 -- x could lie b/w 2 and 7. Need not be always < 2.

d. -7 < x < 2 -- x could lie b/w 2 and 7. Need not be always < 2.

e. None of the above -- Not applicable.
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by kvcpk » Fri Jun 18, 2010 1:06 am
Answer should be B
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by amising6 » Fri Jun 18, 2010 1:22 am
If it is true that x >-2 and x<7, which of the following must be true?

a) x > 2

b) x > -7

c) x < 2

d) -7 < x < 2

e) None of the above

let us draw the range on number line

-2 -1 0 1 2 3 4 5 6 7 x can take any value between the bold as x>-2 and x<7

so based on the given option
a) x > 2 not possible as x can also be -1 which is less than 2

b) x > -7 this is possible as x min value is -1 which is greater than -7 so x will always be greater than -7

c) x < 2 x can take value of 3 or 4 or 5 or 6 so not possible

d) -7 < x < 2 again not possible as x>-2

Ans is b
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by nikhilkatira » Fri Jun 18, 2010 1:51 am
amising6 wrote:If it is true that x >-2 and x<7, which of the following must be true?

a) x > 2

b) x > -7

c) x < 2

d) -7 < x < 2

e) None of the above

let us draw the range on number line

-2 -1 0 1 2 3 4 5 6 7 x can take any value between the bold as x>-2 and x<7

so based on the given option
a) x > 2 not possible as x can also be -1 which is less than 2

b) x > -7 this is possible as x min value is -1 which is greater than -7 so x will always be greater than -7

c) x < 2 x can take value of 3 or 4 or 5 or 6 so not possible

d) -7 < x < 2 again not possible as x>-2

Ans is b

Option B says x > -7

So according to option B, x can be -6 but that does not fit in the condition given in the question i.e. -2 < x < 7

I dont know what mistake i am making..experts pls help.

Also I have one more doubt--
When we are given a range i.e. 3 < x< 8
Can we have a solution with open ended range for example x < 15 ????
Best,
Nikhil H. Katira
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by amising6 » Fri Jun 18, 2010 2:39 am
Option B says x > -7

okie and question asks which of the following is true
and in the given range x can take value of -1 0 1 2 3 4 5 6
in all this case whatever value x take it will always be greater than -7
thats why b should be answer
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