1. The total of the prices of two pans is $25.94, and the price of the more expensive pan is $5.96 greater than the price of the less expensive pan. What is the price of the more expensive pan?
A. $9.99
B. $12.97
C. $14.05
D. $15.95 Correct
E. $16.98
Explanation
Let the price of the less expensive pan be x dollars. Then the more expensive pan is x + 5.96 dollars. Their sum is x + (x + 5.96) = 25.94, so 2x + 5.96 = 25.94. Subtract 5.96 from both sides: 2x = 19.98. Divide by 2: x = 9.99. The more expensive is 9.99 + 5.96 = 15.95. Choice A is 9.99, which is the less expensive pan, not the more. Choice B 12.97 does not satisfy the difference or sum. Choice C 14.05 minus 5.96 is 8.09, sum 22.14 not 25.94. Choice E 16.98 minus 5.96 is 11.02, sum 28 not 25.94. Only 15.95 works as more expensive with less at 9.99 summing to 25.94 and difference exact. This algebraic setup ensures the equations match the conditions precisely without approximation errors. Alternatives fail the basic arithmetic checks.
2. Last week at a certain grocery store, 60 employees each worked 30 hours either at a cash register or stocking shelves. Of these employees, 1/5 worked at a cash register 20 hours, ¼ worked at a cash register 12 hours, 1/3 worked at a cash register 15 hours, and the remaining employees worked at a cash register 24 hours last week. What was the average (arithmetic mean) of the numbers of hours that these employees worked stocking shelves last week?
A. 12.8 Correct
B. 14
C. 15.8
D. 16.4
E. 18
Explanation
Total hours worked by 60 employees is 60 * 30 = 1800. Employees at cash: 1/5 of 60 = 12 at 20 hours, 1/4 = 15 at 12, 1/3 = 20 at 15, remaining 60 - 12 - 15 - 20 = 13 at 24. Total cash hours: 12*20 = 240, 15*12 = 180, 20*15 = 300, 13*24 = 312, sum 240+180+300+312=1032. Stocking hours: 1800 - 1032 = 768. Average stocking: 768 / 60 = 12.8. Choice B 14.0 would require more stocking hours like 840 total, but calculation shows less. Choice C 15.8 implies 948 stocking, overestimate. Choice D 16.4 needs 984, wrong. Choice E 18.0 is 1080, half total hours, ignores cash distribution. The breakdown of cash hours by groups ensures accurate subtraction from total, avoiding averages that don't account for varying cash times. Miscalculating group sizes or hours leads to wrong totals.
3. A certain factory normally produces 500 units per hour for a 7(1/2)-hour workday. In a month with 22 workdays, no units are produced in the first 7 days because of a job action. By how many units must production increase on each of the remaining workdays of the month in order to meet normal production levels for the month?
A. 500
B. 688
C. 1,750 Correct
D. 3,750
E. 5,500
Explanation
Normal daily production: 500 * 7.5 = 3750 units. Monthly normal: 22 * 3750 = 82500. Remaining days: 22 - 7 = 15. Required per day: 82500 / 15 = 5500. Increase: 5500 - 3750 = 1750. Choice A 500 too small, ignores total deficit spread. Choice B 688 approximate miscalculation. Choice D 3750 is normal daily, not increase. Choice E 5500 is new daily, not increase. The total deficit from 7 days is 7*3750=26250, spread over 15 days: 26250/15=1750, same. Alternatives fail to compute the compensatory increase correctly over remaining period. Precise hourly to daily conversion essential.
4. Each week Ingrid earns a fixed salary and a sales commission that is a fixed percentage of her sales for that week. Ingrid has no other sources of income. Last week Ingrid's total earnings were $500 and her sales were $2,000. This week Ingrid's total earnings were $700 and her sales were $6,000. What is the percentage rate for Ingrid's sales commissions?
A. 0.05%
B. 4%
C. 5% Correct
D. 20%
E. 30%
Explanation
Let fixed salary s, rate r. s + 2000r = 500, s + 6000r = 700. Subtract: 4000r = 200, r = 0.05 or 5%. Choice A 0.05% is 0.0005, would give tiny commission. Choice B 4% or 0.04: 4000*0.04=160, not 200. Choice D 20%: 4000*0.2=800, too much. Choice E 30%: 1200, excessive. The difference in earnings over sales difference isolates r accurately. Plugging back: s + 2000*0.05= s+100=500, s=400; 400+6000*0.05=400+300=700, fits. Other rates don't balance equations.
5. In a certain list of numbers, the first number is 2, the second number is 3, and each succeeding number is the sum of all the numbers that precede it in the list. If hand k denote the 20th and 24th numbers in the list, respectively, what is the value of k/h?
A. 5
B. 8
C. 10
D. 16 Correct
E. 20
Explanation
The sequence: a1=2, a2=3, a3=5, a4=10, a5=20, a6=40,... From a3, each doubles previous. Generally, a_n = 5 * 2^{n-3} for n>=3. a20 = 5 * 2^{17}, a24=5*2^{21}, ratio 2^{4}=16. Choice A 5 misapplies early terms. Choice B 8=2^3, off by one. Choice C 10 not power of 2. Choice E 20 miscounts exponents. The recursive sum leads to geometric from a3, exponent difference 4 for positions 20 to 24. Verifying small: a4/a3=10/5=2, a5/a4=20/10=2, pattern holds.