If x is an integer such that 2

Question

If x is an integer such that 2 < x < 12, 4 < x < 21, 9 > x > –1, 8 > x > 0, and x + 1 < 7, then x is (A) 3 (B) 5 (C) 6 (D) 8 (E) It cannot be determined.

Bunuel · Answer

2 < x < 12, 
4 < x < 21, 
-1 < x < 9
0 < x < 8
x<6

From above: 4 < x < 6 --> x = 5.

Answer: B.

Asifpirlo · Answer

writing these vertically clears everything.
thanks for showing up this strategy

vinny87 · Answer

you meant -1< x < 9 and not -1.8 < x < 9 right!

Bunuel · Answer

Edited the typo. Thank you.

JeffTargetTestPrep · Answer

Let’s test each choice and see which number works, that is, if it satisfies all of the given inequalities. A) 3 2 < x < 12 → 2 < 3 < 12 → Yes 4 < x < 21 → 4 < 3 < 21 → No B) 5 2 < x < 12 → 2 < 5 < 12 → Yes 4 < x < 21 → 4 < 5 < 21 → Yes 9 > x > –1 → 9 > 5 > –1 → Yes 8 > x > 0 → 8 > 5 > 0 → Yes x + 1 < 7 → 5 + 1 < 7 → Yes Answer: B

amanvermagmat · Answer

From 4<x<21, we get that x must be > 4. 
From x+1 < 7, we get that x < 6.

So x is an integer which is greater than 4 and smaller than 6. Only such integer is 5. Hence  option B

bumpbot · Answer

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If x is an integer such that 2 < x < 12, 4 < x < 21, 9 > x >

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