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17 Feb 2022, 08:45
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (02:00) correct
27%
(02:34)
wrong
based on 44
sessions
History
Date
Time
Result
Not Attempted Yet
Jack and Betty each saved $300 in 2015. In 2016, Jack saved 8 percent more than he did in 2015, and together he and Betty saved a total of $500. By what percent less did Betty save in 2016 than she did in 2015?
(A) 22.8%
(B) 33.33%
(C) 41.33%
(D) 54.33%
(E) 66.66%
(A) 22.8%
(B) 33.33%
(C) 41.33%
(D) 54.33%
(E) 66.66%
17 Feb 2022, 11:57
Kudos
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Bunuel
Breaking Down the Info:
Jack saved \(1.08 * 300 = 300 + 24 = 324\). Then Betty only saved \( 500 - 324 = 176\).
The percent change formula is \(\frac{\text{New - Old}}{\text{Old}}= \frac{176 - 300}{300} = \frac{124}{300} = -40\% - \frac{4}{300}\). That is quite close to choice C, so the answer is C.
Answer: C
17 Feb 2022, 14:22
Kudos
Bookmarks
Bunuel
Alternate approach:
The total amount saved decreases by $100 from $600 in 2015 to $500 in 2016, yielding the following average percent decrease:
\(\frac{decrease}{original} * 100 = \frac{-100}{600} * 100 ≈ -17\)%
Since Jack's percent change and Betty's percent change are both in relation to the same original amount -- $300 -- they are given EQUAL WEIGHT when calculating the average percent decrease.
Implication:
The average percent decrease (about -17) must be equal to the AVERAGE of Jack's percent increase (8) and Betty's percent decrease (x).
Thus:
\(-17 ≈ \frac{8+x}{2}\)
\(-34 ≈ x+8\)
\(- 42 ≈ x\)
Only C is sufficiently close.
