Standardized Achievement Test Questions
Sample 1 SAT
A store was charged $12.60 for a particular item. If the store wants to make a profit of 10% of their selling price, what would a customer have to pay for each item?
Strategy - Trial and error & guess and check: estimate profit
Data $12.60 is the cost per item
If sell for $13.00, then profit is 10% of $13.00 or $1.30
$1.30 + $12.60 = $13.90
Therefore, $13.90 is more than $13.00 so it needs to be sold for more than $13.00.
What about $14.00, that doesn’t seem to enough, but I’ll see how much it changes and decide from there…. WOW! 10% of $14.00 is $1.40 and $12.60 + $1.40 = $14.00… COOL!
Strategy - Algebra
x = selling price
y = mark up
.1x = y
y + $12.60 = x
x - $12.60 = y
.1x + $12.60 = x
Strategy - Trial and error & guess and check: thinking repeated addition or division
$12.60/.9 = x ; Think how many .9 are in 12.6 (there are 12 ones so if there needs to be more than 12 for .9) (there are 10 nine tenths in nine, and two nine tenths are 1.8 so four would be 3.6 and 9 + 3.6 = 14.) COOL!
Sample 2 SAT
A shipper has boxes that are cubes 2x2x2. The largest box the shipper has on hand is 5x6x8. How many cubes will fit in the larger box?
Strategy Reasoning with repeated addition or division
8 cubic units and 240 cubic units,
240 cubic units / 8 cubic units = 30 boxes.
Strategy Draw a picture
Large box 5x6x8
Draw a diagram of the large box and mark the dimensions on the edges of the diagram.
2 box lengths x 3 box lengths x 4 box lengths = 24 boxes
Sample 3 FAA
A rectangular-shaped fuel tank measures 27 1/2 inches in length, 3/4 foot in width, and 8 1/4 inches depth. How many gallons will the tank contain?
(231 cubic inches = 1 gallon)
(a) 7.366 gallons (b) 8.839 gallons (c) 170,156 gallons
Note the dimensions are given in two different units. Therefore, a person who quickly multiplies the numbers together will find 27.5 * .75 * 8.25 = 7.366, which is given as suggested answer (a). The dimensions must be similiar so changing 3/4 foot to inches would probably be the way to go. This would result in (27.5 * 9 * 8.25 ) / 231 = 8.839 gallons.
Sample 4 MCAT
Two charges (+q and -q) each with mass 9.11 x 1031 kg are placed 0.5 m apart and the gravitational force (Fg) and electric force (Fe) are measured. If the ratio Fg/Fe is 1.12 x 10-77, what is the new ratio if the distance between the charges is halved?
(a) 2.24 x 10-77 (b) 1.12 x 10-77(c) 5.6 x 10-78 (d) 2.8 x 10-77
Question. Why is a nuclear physics problem on an entrance exam for medicine?