I've been around the standardized-test block a few times. There are only so many types of questions that they ask and each one has a method to go with it. If you want practice at this sort of thing grab an SAT math practice book.
1. A physical education class has three times as many girls as boys. During a class basketball game, the girls average 18 points each, and the class as a whole averages 17 points per person. How many points does each boy score on average?
Say there are 3 girls and 1 boy in the class. The girls average 18 points, so for the three of them thats 54 points. There are 4 in the class which averages 17 points, so that's 68 points for the whole class. 68-54 gives 14 points average for the boys (like the girls would score more
).
2. Randolph has 8 ties, 6 pairs of pants, and 4 dress shirts. How many days could he possibly go without wearing the same combination of these three items?
Multiply the larger numbers first. 8*6 = 48, 48*4 = 192.
3. John is a mechanic. He makes $8.50 an hour, plus $3 extra for every oil change he performs. Last week he worked 36 hours and performed 17 oil changes. How much money did he make?
Round to nearby convenient numbers and then account for the small difference. In this case 8.50 is close to 10, so use 10 instead and then adjust for the 1.50 surplus (36*(1+0.50) = 36 + 18.
36*10 = 360, 360-36 = 324, 324-18 = 306, 17*3 = 51, 306+51 = 357.
4. A box of staples has a length of 6 cm, a width of 7 cm, and a volume of 378 cm cubed. What is the height of the box?
6*7 = 42. Guess an easy number for the height. What if the height were 10 cm? Then the volume would be 420. 378 is exactly 42 less than 420, so the height is 9 cm.
5. What is the average of all of the integers from 13 to 37?
Each high/low number pair in this sequence adds to 50 (13+37,14+36,etc.). For every two numbers you add to the sequence you add 50, so the average must be 50/2 = 25.
6. A basketball player averaged 20 points a game over the course of six games. His scores in five of those games were 23, 18, 16, 24, and 27. How many points did he score in the sixth game?
Only keep track of the difference between the individual game scores and the average.
23 = +3
18 = -2
16 = -4
24 = +4
27 = +7
Previous 5 games are +8, so the final game must be -8 or 12.
7. Arnold is about to go on a 500-mile car trip. His mechanic recommends that he buy a special highway engine oil that will save him 50 cents in gas for every 25 miles of the trip. This new oil, however, will cost $20. Is it worthwhile for Arnold to buy the oil if he has a coupon for $4 dollars off the price?
How many units of 25 miles are in the trip? 20. 20*0.50 gives 10 dollars in savings from using the oil. The oil costs Arnold 20-4=16 dollars, so Arnold should not buy the oil just for this trip but should instead have sex with Samantha. Afterwards he may enjoy a cookie for his efforts.
