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What is the level of this question?
And the likeliness of it coming in GMAT official exam?

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Please see official guide.
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1. k=20 ---> |x-3|+|x-20|<c, Clearly not sufficient
2. c=15 ---->|x-3|+|x-k|<15, Clearly not sufficient

(1)+(2)
|x-3|+|x-20|<15,
Minimum value of expression |x-3|+|x-20| is 17. This happens between 3 and 20. For any other values, expression is greater than 17.
Thus none, of the expression is true for none of the integer values of x.
Both sufficient.

Ans. C
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