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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

I have OA but couldn't understand OE. Could somone explain?

E.

1) x > 2 means that x could be > 7. This goes against stem. discard.
2) x > -7. means x could be < -2 or x could be > 7. discard
3) x < 2. means x could be < -2. discard
4) -7 < x < 2. means x could be -5 which goes against stem.

You can draw a line and mark two points A(-2,0) and B(7,0),
the stem says -2 < x < 7, meaning your point, let's say C (x,0) is between A and B

so will all C
> 2 ? - not necessarily (e.g. all points -2<x<2)
> -7 ? - YES
< 2 ? - not necessarily (e.g. all points 2<x<7)
> -7 < and < 2 ? - not necessarily (same as < 2 ?)

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

I have OA but couldn't understand OE. Could somone explain?

HIMALAYA wrote:

b) x > -7

if x> -7 which means.. x can be -6 right??
but the question says.. x> -2.. and x<7.. so.. -6 does not fall in between..
OA is B..but im not convinced! _________________

Success is my only option, failure is not -- Eminem

Stem says "If it is true that x > -2 and x < 7" that means x must have values greater than -2 and less than 7.

Now take choices one by one keeping the stem in mind

a) x > 2 ------- Will all values what x can take are greater than 2 (As per stem)--- NO (Examples 1,0,-1)
b) x > -7 ------- Will all values what x can take are greater than 2 (As per stem)--- YES. All values that x can take (as per stem) will always be greater than -7
c) x < 2 ------- Will all values what x can take are greater than 2 (As per stem)--- NO (Examples 3,4,5)
d) -7 < x < 2 ------- Will all values what x can take are greater than 2 (As per stem)--- NO (3,4,5)

As said above in the number line, x can be any number from -2 to 7. Also we know that as we go from left to right on the number line the number increases. -7 is less than -2 and 7 so this is the only answer which has to be always true.