Word problem shortcuts · Study guide · Sol Rising

Word problem shortcuts

Arithmetic Reasoning is mostly a handful of setups in different clothes.

Distance, rate, time	$distance = rate \times time$ . Cover the one you want: $rate = distance \div time$ .
Working together	If one job takes a hours and another b hours, together it takes $\frac{a \times b}{a + b}$ . Two pipes that fill a tank in 3 and 6 hours: 18 ÷ 9 = 2 hours.
Percent change	$\frac{change}{original}$ . From 40 to 50 is up 10 ÷ 40 = 25%; from 50 back to 40 is down 10 ÷ 50 = 20%.
Two discounts in a row	Multiply what is left: 20% off then 10% off leaves 0.8 × 0.9 = 0.72, which is 28% off, not 30%.
Ratios	Add the parts. Split 40 in the ratio 3 : 5: 8 parts, 5 each, so 15 and 25.
Averages	$total = average \times count$ . To find a missing score, work out the total it needs and subtract what you have.
Simple interest	$interest = principal \times rate \times time$ . $500 at 4% for 3 years: 500 × 0.04 × 3 = $60.
Before a percent change	If $63 is the price after 10% off, it is 90% of the original: 63 ÷ 0.9 = $70.

AFOQT questions on this: Work rates · Percent change · Discounts · Ratios · Missing from an average · Simple interest · Original price

Drill it

Quick questions on just this skill, to build speed before the practice tests. Type the answers; a clock keeps your time.

Distance, rate, and time d = r × t, any way around. 80 miles in 2 hours is a speed of
Working together (a × b) ÷ (a + b). One pump fills a tank in 8 hours and another in 24 hours. Together they fill it in
Percent change Change ÷ original. A price goes from $80 to $100. It went up by
Splitting by a ratio Add the parts, find one part, multiply. Split 70 in the ratio 3 : 7. The smaller part is
Simple interest Principal × rate × time. $2,100 at 2% simple interest for 3 years earns

Questions 1 to 50 Check answers as I type Leave the answers off the PDF