Question: x = ?

Statement 1: 4 < x < 6

x could be 5 or 5.5 or 4.5 hence

NOT SUFFICIENT

Statement 2: |x| = 4x − 15

i.e. x = 4x − 15 OR -x = 4x − 15
i.e. x = 5 OR x = 3 but x = 3 doesn't satisfy |x| = 4x − 15
therefore x = 5

SUFFICIENT

Answer: Option B

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What is the value of x?

(1) 4 < x < 6
x is not integer. So, can take any value between 4 and 6

Not sufficient

(2) |x| = 4x − 15
4x - 15 = x or 4x - 15 = -x
3x = 15 or 5x = 15
x = 5 or 3

x = 3 does not satisfy the equation |x| = 4x − 15

So, x = 5

Sufficient

Option B

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SOLUTION:

Statement 1 => 4 < x < 6

=> x can take any value between 4 and 6 and we cannot obtain a specific value using Statement 1 alone.

Statement 2 => |x| = 4x − 15

=> x = 4x -15 OR x = -(4x-15) = -4x +15

=> x = 5 => x=3

At x = 3 we have |x| = 4x - 15

= 4*3 - 15

=> |x| = -3

At x=5, we have |x| = 4*5 - 15

=> +5

A modulus value cannot yield negative result and hence x=3 cannot be considered a value for x.
Thus x = 5
Hence OPTION(B)

Hope this helps
Devmitra Sen(Math)
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What is the value of x?

Stat1: 4 < x < 6, x can be 4.5, 5 or anything between 4 and 6. Not sufficient.

Stat2: |x| = 4x − 15, if x> 0, x= 5 which is okay. But if x<0, then x = 3, which doesn't satisfy, x <0. So, x = 5. Sufficient.

So, I think B.

What is the value of x?

(1) 4 < x < 6. Clearly insufficient, x can be any number from 4 to 6, not inclusive.

(2) |x| = 4x − 15. LHS is an absolute value, which is always non negative, hence RHS must also be non-negative: \(4x-15\geq{0}\) --> \(x\geq{\frac{15}{4}}\) --> \(x\) is positive, thus \(|x|=x\) --> \(x=4x-15\) --> \(x=5\). Sufficient

Answer: B.

Hope it's clear.
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