题目信息
| Month | Change in sales from previous month |
| February | +10% |
| March | −15% |
| April | +20% |
| May | −10% |
| June | +5% |
The table above shows the percent of change from the previous month in Company X's sales for February through June of last year. A positive percent indicates that Company X's sales for that month increased from the sales for the previous month, and a negative percent indicates that Company X's sales for that month decreased from the sales for the previous month. For which month were the sales closest to the sales in January?
A:February
B:March
C:April
D:May
E:June
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已选答案：
正确答案：
D:May
Arithmetic Percents
Explicit calculation incorporating a few numerical shortcuts gives the following, where J is the January sales amount.
February sales: 1.1J
March sales: 0.85(1.1J) = 0.85J + 0.85(0.1J) = 0.85J + 0.085J = 0.935J
April sales: 1.2(0.935J) = 0.935J + 0.2(0.935J) = 0.935J + 0.187J = 1.122J
May sales: 0.9(1.122J) = 1.0098J
June sales: 1.05(1.0098J) (May is clearly closer)
Alternatively, from
it follows that a percent change of x% followed by a percent change of y% is equal to a percent change of (x + y)% plus x% of y percentage points (equivalently, plus y% of x percentage points).
Percent change from January through February: The percent change is given as +10%.
Percent change from January through March: Using the rule above for x = +10 and y = −15 gives (+10 − 15)% + (+0.10)(−15%), or −5% − 1.5% = −6.5%.
Percent change from January through April: This is equivalent to a −6.5% change (percent change from January through March) followed by a +20% change, and hence using the rule above for x = −6.5 and y = +20 gives (−6.5 + 20)% + (+0.20)(−6.5%), or +13.5% − 1.3% = +12.2%.
Percent change from January through May: This is equivalent to a +12.2% change (percent change from January through April) followed by a −10% change, and hence using the rule above for x = +12.2 and y = −10 gives (+12.2 − 10)% + (−0.10)(+12.2%), or +2.2% − 1.22% = +0.98%.
Percent change from January through June: This is clearly greater than +0.98% + 5%, and hence greater in magnitude than the result for May.
From the results above, the least change in the magnitude of the percent change from January occurred for May.
The correct answer is D.
Explicit calculation incorporating a few numerical shortcuts gives the following, where J is the January sales amount.
February sales: 1.1J
March sales: 0.85(1.1J) = 0.85J + 0.85(0.1J) = 0.85J + 0.085J = 0.935J
April sales: 1.2(0.935J) = 0.935J + 0.2(0.935J) = 0.935J + 0.187J = 1.122J
May sales: 0.9(1.122J) = 1.0098J
June sales: 1.05(1.0098J) (May is clearly closer)
Alternatively, from
it follows that a percent change of x% followed by a percent change of y% is equal to a percent change of (x + y)% plus x% of y percentage points (equivalently, plus y% of x percentage points).
Percent change from January through February: The percent change is given as +10%.
Percent change from January through March: Using the rule above for x = +10 and y = −15 gives (+10 − 15)% + (+0.10)(−15%), or −5% − 1.5% = −6.5%.
Percent change from January through April: This is equivalent to a −6.5% change (percent change from January through March) followed by a +20% change, and hence using the rule above for x = −6.5 and y = +20 gives (−6.5 + 20)% + (+0.20)(−6.5%), or +13.5% − 1.3% = +12.2%.
Percent change from January through May: This is equivalent to a +12.2% change (percent change from January through April) followed by a −10% change, and hence using the rule above for x = +12.2 and y = −10 gives (+12.2 − 10)% + (−0.10)(+12.2%), or +2.2% − 1.22% = +0.98%.
Percent change from January through June: This is clearly greater than +0.98% + 5%, and hence greater in magnitude than the result for May.
From the results above, the least change in the magnitude of the percent change from January occurred for May.
The correct answer is D.
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