gmatophobia
PS Question 1 - May 10 Which of the following is/are true? I. |3x - 19| > 5 - x holds for all values of x. II. There is no value of x for which |2x - 10| < 4 - x holds. III. -|5x - 23| is negative for all values of x. A. None B. I only C. I and II only D. I and III only E. I, II and III Source: Expert’s Global | Difficulty: Hard
This is a good question that benefits from "leveraging" answer choices.
Consider the third statement: If we have x=23/5, it becomes 0 which is non negative. This allows us to eliminate E and D instantly.
2 can be easily considered by looking at extrema: the lhs has value 0 for x=5, but rhs is still bigger. For large negative values, the lhs is clearly larger than the rhs, and for large positive rhs will always be negative, and lhs is always non negative by construction. Statement 2 must be true.
Since of all choices, only C has statement 2 withiut statement 3, it must be true
gmatophobia
DS Question 1 - May 10 If m and n are non-negative integers, what is the units digit of 5^m + 6^n? (1) m + n > 2 (2) mn > 0 Source:
GMAT Club Tests | Difficulty: Medium
Take note that it states m and n are non negative integers. In other words, m and n can be 0,1,2....
Also note that any number with 5 in tbe units digit will always have 5, if it taised to a positive power. The same applies to 6 (always 6 if pos power).
Statement 1 is a trap. Consider the case of m=0, n=3. We would have units digit of 6. But if m=2, n=3, unjts digit of 1.
Statement 2 works. It will always be 1 units digit since it will be 5+6 in the units place.
B.