FILL BLANKPam, Steve, and Adrian each had a party. The number of people at Pam's party was 6 more than the number of people at Steve's party. The number of people at Steve's party was 8 fewer than the number of people at Adrian's party. No one attended more than one of the three parties. If the total number of people at the three parties was 89, what was the number of people at Adrian's party?
Answer(s): A
S = number at Steve's partyP = number at Pam's partyA = number at Adrian's partyFrom the statements:P = S + 6S = A - 8 A = S + 8P + S + A = 89Substitute (1) and (2) into (3):(S + 6) + S + (S + 8) = 893S + 14 = 893S = 75S = 25Then A = S + 8 = 25 + 8 = 33.
In a 100-milliliter solution, 9 percent of the volume is alcohol and the rest is water. How many milliliters of water must be added to this solution to make a new solution that is 6 percent alcohol?
Answer(s): C
Let x be the amount of water added. The alcohol remains 9 ml, while the new total volume is 100 + x ml. Setting 9 equal to 6 percent of the new volume:9 = 0.06 (100 + x)100 + x = 150x = 50.
FILL BLANKA group of computer users received an e-mail offering information about a computer service. Only 16 percent of the users responded to the offer for information. Eventually 46 of the users purchased the service, which represented 5 percent of those who responded to the offer for information. How many computer users received the e-mail offering information about the service?
Let N be the number of users who received the e-mail.Sixteen percent responded: 0.16N.Of those, 5 percent purchased the service: 0.05 × 0.16N = 0.008N.That equals the 46 purchasers, so0.008N = 46N = 5,750.
Which of the following inequalities indicates the order of the integers r, s, and t, from least to greatest?
Answer(s): E
s = 183 = 5,832t = 19 × 17 × 15 = 4,845Arranged from least to greatest: t < r < s.
For the list of numbers k, k - 1, k + 3, k + 1, and k + 2, where k is positive, what is the ratio of the average (arithmetic mean) of the numbers to the median of the numbers?
Sum = k + (k - 1) + (k + 3) + (k + 1) + (k + 2) = 5k + 5, so the average isArranged in increasing order, the numbers are k - 1, k, k + 1, k + 2, k + 3; the median is the middle number, k +1.Average and median are equal, so their ratio is 1.
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