If 1 minus the reciprocal of (1 – x) equals the reciprocal of (1 – x), then x equals
- -2
- -1
- ½
- 2
- 3
Set 07
Beakers, Ratio of Acid to Water
Two identical beakers are filled with acid solutions, the ratio of the volume of acid to the volume of water being p:1 in one beaker and q:1 in the other beaker. If the entire contents of the two beakers are mixed together, the ratio of the volume of acid to the volume of water is:
Mrs. McGillicuddy’s Age
How old will Mrs. McGillicuddy be b years from now if she was x years old c years ago?
Brick on 2-Pan Scale
In demonstrating how a 2-pan scale works, we notice that a brick placed on one side exactly balances 3/4 of a kg plus 3/4 of a brick on the other side. If this is so, what does the brick weigh?
Brine Tank
A 700 gallon tank has 600 gallons of salt water in it; the amount of salt dissolved in the water is a half-pound per gallon. An intake valve is opened and another 100 gallons of brine is allowed to flow into the tank; this brine has 2 pounds of salt per gallon. The tank is now full. Its contents are thoroughly stirred, and then an outlet valve is opened and 100 gallons of the mixture are drained out. This process is repeated two more times. At the end, how much salt per gallon is in the 600 gallons that remain in the tank?
Gas Bill Printing
Two Columbia Gas computers each produce 48,000 gas bills in one day. One computer prints bills at the rate of 9600 per hour and the other at the rate of 7800 per hour. When the faster computer finishes its run, how many bills does the slower computer still have to print?
Tape Sale
Back in the day of analog recording tape, Amalgamated Grissom Enterprises had a sale. Professional quality tape dropped from $30 to $28 per reel, and regular quality tape dropped from $24 to $23 per reel. The Bethel Recording Studio normally spent $1440 per week on tape, 3/4 of which was used for professional quality tape. How much did they save during each week of the sale?
Minnie Spends 2/3 of Money
Minnie Minor Boots went shopping in Deans, Ben Branklin, and the Co-op. In each store she spent exactly 2/3 of her money plus 2/3 of a cent. When she was finished she had exactly a dollar left. What was her original bankroll?
Digits in Product
Let P equal the product of 3,659,893,456,789,325,678 and 342,973,489,379,256. The number of digits in P is:
- 36
- 35
- 34
- 33
- 32
Day Before Yesterday
What day of the week is it if the following statement is true?
When the day before yesterday was referred to as the day after tomorrow, the day that was then called “yesterday” was as far away from the day we now call “tomorrow” as yesterday is from the day on which we shall be able to speak of last Monday as “a week ago yesterday.”