Is |x – 3| < 7 ? (1) x > 0 (2) x < 10 GMAT Data Sufficiency

When x < 3: |x - 3| becomes -x + 3 → -x + 3 < 7 → -4 < x → -4 < x < 3
When x ≥ 3: |x - 3| becomes x - 3 → x - 3 < 7 → x < 10 → -3 ≤ x 10
So, inequality |x - 3| < 7 holds true for -4 < x < 10
S1: x > 0
Hence, insufficient
S2: x < 10
Hence, insufficient

Correct option: C

S1: x > 0
This statement is not sufficient because x > 0, x > -4.
However, the statement does not prove that x<10.
S2: x < 10
This statement is also not sufficient as it indicated that x < 10.
However, the statement does not prove that x>-4
Now, combine the two statements. The two statements say: 0 < x < 10. If x is between 0 and 10, x must also be between -4 and 10.

Correct option: C

|x – 3| < 7 means we are looking for points whose distance from 3 is less than 7. There will be many such points e.g. 4, 5, 6, -2, -1 etc that satisfy our inequality.
Points beyond 10 on the right side and points beyond -4 on the left side will have a distance of more than 7 and hence, do not satisfy our inequality.
Statement I: x > 0
There are points greater than 0 that satisfy our inequality (e.g. 1, 5, 7 etc) and there are those that do not satisfy our inequality (e.g. 11, 12, 18 etc). Hence this statement is not sufficient.
Statement II: x < 10
Again, using the same logic as above, this statement is not sufficient.
Combining the two statements, we see that all the points satisfying 0 < x < 10, satisfy our inequality. Hence we can say 'Yes, |x – 3| is less than 7'

Correct option: C