GED Mathematical Reasoning TestQuantitative Problem Solving with Rational NumbersHard
A financial analyst is reviewing an investment portfolio. The value of the portfolio increased by 1/5 in the first quarter and then decreased by 1/10 of its new value in the second quarter. If the initial value was $12,000, what is the value of the portfolio at the end of the second quarter?
- A$15,840
- B$13,200
- C$12,960
- D$14,400
Show answer & explanationAnswer & explanation
Correct answer: C. $12,960
Initial value = $12,000. First quarter increase: 1/5 of $12,000 = $2,400. Value after first quarter: $12,000 + $2,400 = $14,400. Second quarter decrease: 1/10 of $14,400 = $1,440. Value after second quarter: $14,400 - $1,440 = $12,960.
Why the other options are wrong
- A. Incorrect. This might arise from adding 1/10 instead of subtracting, or other calculation errors.
- B. Incorrect. This would be the value if the second quarter decrease was 1/10 of the *original* value.
- D. Incorrect. This is the value after the first quarter, before the second quarter decrease.
Sequential Fractional Changes
Sequential fractional changes involve applying a fraction-based increase or decrease to a quantity, and then applying another fraction-based change to the *new* resulting quantity.
- Calculate the first change based on the initial value.
- Update the value after the first change.
- Calculate the second change based on the *updated* value.
- Apply the second change to find the final value.
Memory trick: First, increase the base; then, from that new place, decrease and embrace.