ASVAB Arithmetic Reasoning: How to Solve Word Problems

What this subtest is asking

The official description is the ability to solve arithmetic word problems. It feeds the AFQT along with Mathematics Knowledge, Word Knowledge, and Paragraph Comprehension. Mathematics Knowledge is the page for equations, exponents, and area. This page is the translation step. The formula sheet is the lookup. It is not allowed in the testing room. The FAQ says no calculator.

Use the same five moves every time.

1. Name the unknown in words.
2. Write each number with its unit.
3. Pick one relationship: part of a whole, a ratio, a rate, an average, or a conversion.
4. Calculate.
5. Ask whether the answer is larger or smaller than the starting number for a reason you can say out loud.

A wrong setup beside a right one

A coat is $80. It is discounted 20 percent. Tax is not part of the question. What is the sale price?

Wrong: 80 × 0.20 = 16, and then stop. That is the discount, not the price you pay. It is a plausible number because 16 really is 20 percent of 80.

Right: the unknown is the sale price. The discount is 0.20 × 80 = 16 dollars. The price is 80 − 16 = 64 dollars. Check: 64 is less than 80, which a discount should be. 96 would mean the discount was added.

Four more relationships

Ratio. A paint mix is 2 liters of blue for every 5 liters of white. A larger batch uses 15 liters of white and the same ratio. How much blue?

Unknown: liters of blue. White went from 5 to 15, a factor of 3. Blue scales by the same factor: 2 × 3 = 6 liters. Check: 6 to 15 is still 2 to 5. Using 15 × 2 = 30 copies the blue number onto the white amount and breaks the ratio.

Rate. A typing job pays $12 an hour plus a $30 completion fee. How long does a $90 job take, with no other fees?

Unknown: hours. 12h + 30 = 90. Then 12h = 60, so h = 5. Check: 12 × 5 = 60, and 60 + 30 = 90. Dividing 90 by 12 gives 7.5 and forgets the fee.

Average. Three shifts repaired 8, 11, and 14 vehicles. What is the average number per shift?

Unknown: the mean. Add first: 8 + 11 + 14 = 33. Divide by the three shifts: 33 / 3 = 11. The average is not the middle number just because 11 appears in the list. Here it happens to equal the middle value. On another list it will not.

Units. A hose runs for 90 minutes at 4 liters per hour. How many liters does it deliver?

Unknown: liters. 90 minutes is 1.5 hours, not 90 hours. 4 × 1.5 = 6 liters. Using 4 × 90 = 360 treats minutes as hours.

A check with new numbers

A bike was $120 and is discounted 25 percent. No tax. What is the sale price?

Twenty-five percent of 120 is 30. The sale price is 120 − 30 = 90. If you got 30, you stopped at the discount. If you got 150, you added it.

Try another original word problem in the practice set → when you want a clean item, not a repeat of these numbers. The practice score is not an AFQT.