PS and DS problems

Question 1

Is x > 0?

(1) |x+3|=4x−3

Answer 1

(1) |x+3|=4x−3 –> LHS is an absolute value, which is always non-negative (|some expression|≥0|some expression|≥0), so RHS must also be non-negative –> 4x−3≥0 –> x≥3/4, hence x>0. Sufficient. You can see here that you don’t even need to find exact value(s) of x to answer the question.

Question 2

How to put this into a formula?

The retailer has less than twice as many radios as clocks in inventory.

Answer 2

r<2*c

Question 3

Matt earned a 1000 comission on a big sale, raising his average comission by 150. If Matt’s new average comission is 400, how many sales has he made?

Answer 3

250n + 1000 = 400(n+1)
n=4

including the big comission n=5