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During a sale Arianna purchases a sweater Listed at $100. Win 20% off and 7% sale tax, how much did she pay for the discounted sweater?

Franco decides to purchase a new washing machine that sells for $1,100. After making a down payment of $125, he willpay of the remainder in monthly payments of $75. How many months will it tale for Franco to pay of the new washing machine?






Correct answer

D. $1,100 – $125 = $975. At $74 per month, it will take $975 / $75 = 13 month.

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An electronics store owner purchases DVDs from his supplier, paying $270.80 for 20 DVDs. He then sells them to his customers during a special sale, charging $53.01 for 3 DVDs. How much profit, per DVD, does the owner make during the special sale?






Correct answer

A. The store owner pays $270.80 ÷ 20 = $13.54 per DVD. He sells them for $53.01 ÷ 3 = $17.67. His profit per DVD is therefore $17.67 — $13.54 = $4.13.

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If 10 boys averaged 78% on a test for which 15 girls averaged 89%, what is the test average for all 25 students?






Correct answer

C. The class average can be found as follows: 84.6%

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In a set of 15 different integers, which of the following changes would NOT effect the value of the median of these 15 integers?






Correct answer

B. Since the median is the middle of the list of the set of integers, adding 11 to the largest integer will not affect the median. The other option—which is not one the given choices—would be to subtract some positive integer from the smallest number in the set.

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The shoes sizes of 10 men are 8, 10, 9, 12, 7, 10, 10, 11, 6, and 7. How much greater than the mode is the median?






Correct answer

B. Listing the shoe sizes from small to large, you have: 6, 7, 7, 8, 9, 10, 10, 10, 11, 12 The mode (most frequent shoe size) is 10. The median (the middle of the list) would be the average of 9 and 10, which gives 9.5. Notice that since you have an even number (10) of shoe sizes, you had to find the average of the fifth and sixth shoe sizes (9 and 10) to compute the median.

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How many two-digit positive integers are multiples of both 2 and 5?






Correct answer

B. If the positive integer is a multiple of both 3 and 5, it must also be a multiple of 15. So our two-digit multiples of 15 are: 15, 30, 45, 60, 75, and 90. So our correct answer is 6 two-digit multiples of 15.

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The first four numbers in a patterned sequence of positive integers are 1, 2, 4, 8,… . What is the tenth integer in this sequence?






Correct answer

C. The integers double as you move from one term of the sequence to the next. Therefore, the first ten integers in the sequence are: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512.

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Yuri deposits $100 into a new savings account that pays him 3% interest compounded annually. What is the accumulated value of this deposit 6 years after the day of the initial deposit?






Correct answer

B. Since the annual interest rate is 3%, the value of the account one year is 1.03 times the previous year’s value. After 6 years, the account will be worth $100 x (1.03)6 = $119.41.

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A culture of 207 bacteria triples every 12 minutes. What will the bacterial count 2 hours after the original culture of 207 was established?






Correct answer

C. A 2-hour time period represents 120 minutes. This is 10 of the 12-minute time periods in which the bacteria triples. So after 120 minutes, the initial count of 207 will grow to 207×310.

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If x and y are positive integers, and are not both even, which of the following must be even?