A seven-digit combination lock on a safe has zero exactly three times, does not have the digit 1 at all. What is the probability that exactly 3 of its digits are odd?
Answer(s): D
Since three digits are zero, only 4 digits are left for consideration (of which, none is zero). Since 1 does not appear in the numbers, there are 4 even numbers (without 0), and 4 odd numbers (without 1) to choose from. The probability for every digit to be odd is 1/2. There are 4 different ways to arrange 3 odd numbers and one even number in 4 places. Each of these ways has a probability of (1/2 )4. And together: 4×(1/2 )4 = 4 × 1/16=4/16
Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 8:00 am and Pipe B at 9:00 am, at what time will the pool be full?
Answer(s): C
From 8:00 am to 9:00 am, Pipe A, which fills the pool in 4 hours, was open for one hour, filling one quarter of the pool. From 9:00 am, the two Pipes worked together at the rate of: , one pool in 12 hours. Since the pool was already one quarter full at 9:00 am, it will take only 9 hours to fill the remaining three quarters of the pool. 9 hours from 9:00 am is 18:00.
In a school with 5 classes, each class has 2 students less then the previous class. How many students are there in the largest class if the total number of students at school is 95?
If X is the number of students in the largest class, then the numbers of students in the other classes are: X-2, X-4, X-6 and X-8. The total number of students is:X+(X-2)+ (X-4)+ (X-6)+ (X-8)=95 and 5X-20=95 5X=115 X=23
A 48 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
Answer(s): B
Solve a combined average problem:
The “Racing magic” takes 120 seconds to circle the racing track once. The “Charging bull” makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
The rate of the “racing magic” is 40 rounds per hour, or 1 round every 1.5 minutes. The rate of the “Charging bull” is 1 round every 120 seconds, or 1 round every 2 minutes.The best way to solve such a question is to find the least common denominator between the two rates. At that point, they will meet for the first time, and when multiplied by 2, we find the second time they meet: 1/2↔ 1/1.5= 3/6↔ 4/6. They will meet for the first time after 6 minutes and for the second time after 12 minutes.
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