Rick deposited $850 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar bills did he deposit?
Answer(s): D
Rick came to the bank with 70 bills and left with 10 and therefore he deposited 60 bills.Define X as the number of $5 dollar bills that he deposited and so (60 – X) is the number of $15 bills that he deposited.We can write the following equation: 5X + 15(60 – X) = 850 □ -10X = -50 □ X = 5. The number of $15 dollar bills is (60 – 5) 55.
The average (arithmetic mean) of four numbers is equal to three times the largest number. If the largest number is equal to 3, what is the sum of the other three numbers?
Answer(s): B
Let’s say the four numbers are: X, Y, Z and W.The average of all four numbers is equal to 3 times the value of the largest number: (X+Y+Z+W)/4 = 3W. W is equal to 3 and therefore (X+Y+Z+3) = 3 x 9 □ X+Y+Z = 36-3 = 33.
What is the reciprocal of (AB)/(A + B)2 ?
Answer(s): C
The reciprocal of X is 1/X and therefore the reciprocal of (AB)/(A + B)2 is (A + B)2/AB. Simplify the expression: (A + B)2/AB = (A2 + 2AB + B2)/AB = A/B + B/A + 2.
Naomi drives to the beauty parlor in 60 minutes. On the way back, her average speed is half the average speed as it was to the way to the parlor. How much time will it take Naomi to travel two round trips to the beauty parlor?
Answer(s): E
If the average speed from the beauty parlor is half of the average speed to the parlor then the time back from the parlor is twice the time it takes her to get to the parlor, thus 120 minutes.The total round trip will take Naomi (60 + 120 = 180) minutes, which is 3 hours. Two round trips will take her 6 hours.
It takes Tanya 50 minutes to drive to the country club. If the average speed of the entire round trip to the club is 87.5% of the average speed on the way to the club, how many minutes approximately will it take Tanya to drive home from the country club?
Define X as the average speed to the country club and Y as the average speed on the way back.The average speed of the entire round trip to the club is 87.5% of the average speed on the way to the club: (X+ Y)/2 = 0.875X X + Y = 1.75X □ Y = 0.75X.The average speed on the way back is 75% of the speed to the club.If the time it takes her to get to the country is T, then T/0.75 is the time it will take to get back home. 50/0.75 = approximately 66 minutes.
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