ACT is incorrect? (June 2012 QAS Math)

musicislife73
Sat, 28 Jul 2012 01:46:28 +0000

So I just got in my question/answer service paper and reviewed the questions I missed. I don’t understand why these two are incorrect. My family and friends have tried them as well and get the same answers as me, so I’m considering e-mailing ACT. I wanted your opinions first though:

34) Jim took his large dog to Pretty Pooches for a haircut 3 times. Jim paid full price for the first 2 haircuts, and had a coupon for the 3rd haircut, giving him a 15% discount on the 3rd haircut. How much did Jim pay for the 3 haircuts? (Table on page shows that price for a large dog haircut is $55)

f. $99.75
g. $118.75
h. $137.50
j $150.00
k. $156.75

60) If abs(x) = -x, which of the following statements MUST be true?

f. x ≤ 0
g. x ≥ 0
h. x = 0
j. x ≠ 0
k. x is not a real number

34) Everyone I’ve asked comes up with k. $156.75 and it seems impossible for ACT’s answer (f. $99.75) to be correct, as the price of the first two haircuts alone would be 55+55=110, which is already greater than answer f.

60) ACT claims the answer is h. x = 0, but why not f. x ≤ 0? 0 is a definite possible value of x, because abs(0) = 0 and -0 = 0, therefore abs(0) = -0. However, why not -1? abs(-1) = 1 and -(-1) = 1, so why is answer f. incorrect?

There probably is a reasonable explanation that I’m just missing, but what are your solutions? Sorry if this seems redundant, but I’ve done the math, and if these questions are correct, my math subscore goes up 2 points and in turn raises my composite by 1, which is enough to bring me to my goal score. Especially since I want to major in math/science/engineering, I feel it is worth it to ask these questions of this board. Thoughts anyone? Thank you!