ASVAB (Armed Services Vocational Aptitude Battery)Mathematics Knowledge (MK)Hard
A logistics officer is planning cargo distribution. If 1/3 of a shipment is sent to Base Alpha, and 1/4 of the remaining shipment is sent to Base Bravo, what fraction of the total shipment is left?
- A7/12
- B5/12
- C1/2
- D1/4
Show answer & explanationAnswer & explanation
Correct answer: C. 1/2
Fraction sent to Alpha = 1/3. Remaining shipment = 1 - 1/3 = 2/3. Fraction sent to Bravo = 1/4 of the remaining = 1/4 * (2/3) = 2/12 = 1/6. Total sent = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2. Fraction left = 1 - 1/2 = 1/2.
Why the other options are wrong
- A. This is the total fraction sent if 1/4 was of the whole shipment, not the remainder.
- B. This is an incorrect calculation, possibly 1/3 + 1/4 = 7/12, then 1 - 7/12 = 5/12, which incorrectly assumes 1/4 is of the total, not the remainder.
- D. This is an incorrect calculation, possibly only considering the last step.
Fraction of a Remainder
Calculating a fraction of an amount that is itself a fraction of an original total.
- First, find the initial remainder after the first fraction is taken.
- Then, multiply the second fraction by that remainder.
- Often involves addition and subtraction of fractions.
Memory trick: Fractions are Fantastic for Figuring Parts.