ASVAB Arithmetic Reasoning Word Problems 4

Question 1

A sergeant is three times as old as her daughter. In 12 years, the sergeant will be twice as old as her daughter. How old is the sergeant now?

Accepted Answer

36

Answer

Let the daughter's age be D, so the sergeant is 3D. In 12 years: 3D + 12 = 2(D + 12), so 3D + 12 = 2D + 24 and D = 12. The sergeant is 3 × 12 = 36. Check: in 12 years they will be 48 and 24, and 48 is twice 24.

Question 2

A recruit deposits a $5,000 enlistment bonus in an account paying 4% interest compounded annually. How much interest has the account earned after 2 years?

Accepted Answer

$408

Answer

Year 1: $5,000 × 0.04 = $200, for a balance of $5,200. Year 2: $5,200 × 0.04 = $208, for a balance of $5,408. Total interest = $200 + $208 = $408. The $400 choice is simple interest, which ignores interest earned on interest.

Question 3

A fuel bladder at a forward operating base can be filled by Pump A in 6 hours or by Pump B in 8 hours. A leaking valve, working alone, would drain a full bladder in 12 hours. If both pumps run and the valve leaks the whole time, how long will it take to fill the empty bladder?

Accepted Answer

4 hours 48 minutes

Answer

Add the filling rates and subtract the draining rate: 1/6 + 1/8 − 1/12 = 4/24 + 3/24 − 2/24 = 5/24 of the bladder per hour. Time = 24/5 = 4.8 hours, which is 4 hours 48 minutes. The 3 hours 26 minutes choice leaves out the leak.

Question 4

A PX item originally priced at $80 is marked up 25%, then marked down 20%, and then marked up another 10%. What is the final price?

Accepted Answer

$88.00

Answer

Percent changes multiply; you can't just add them. 1.25 × 0.80 × 1.10 = 1.10, a net increase of 10%. $80 × 1.10 = $88.00. Adding the percents (+25 − 20 + 10 = +15%) gives the wrong answer of $92.

Question 5

A medic has 30 liters of a 40% antiseptic solution. How many liters of pure water must be added to dilute it to a 25% solution?

Accepted Answer

18 liters

Answer

The amount of antiseptic doesn't change: 0.40 × 30 = 12 liters. After adding x liters of water, 12 = 0.25(30 + x), so 48 = 30 + x and x = 18 liters.

ASVAB - Armed Services Vocational Aptitude Battery Practice Test

ASVAB - Armed Services Vocational Aptitude Battery Practice Test

ASVAB Arithmetic Reasoning Word Problems 4