Ragebaiting Qs (easiest)
I take ten coins from a basket that has 100 coins. How many coins do I have now, if I had none to start with?
10 (I hope you didn't say 90).
Prime factorize 216 fully.
23 x 33
A ball bounces up to 75% of its original height when it hits the floor. How many bounces will it take for it to reach less than half the height at where it was dropped for the first time?
3 times, because it will reach 27/64 of its original height after the third bounce, which is less than half.
How many sides does a hexagon have?
6
If a 10% tax is applied to a ball that costs $9.90, how much does it cost now?
$10.89
A waiter has a glass of beer. The first customer asks for 1/2 of the glass. The second customer asks for 1/4 of the glass. The third customer asks for 1/8, and so on. How many glasses of beer are needed to serve all the customers?
Just one. Adding the numbers 1/2, 1/4, 1/8, 1/16, and so on, will approach 1 but will never reach 1.
Which positive integer has a reciprocal that is exactly the same as itself?
1
A store offers a 10% discount, but they also have a 10% tax. Would a buyer still save money, and by how much if applicable? (as a percent)
Yes, they will still save money. A 10% discount equates to 90% of the original price, while a 10% tax equates to 110%. Multiplying them together gives 1.1 x 0.9, which is 0.99 or 99% of the original price. This means that the buyer will save 1%.
A rectangular box has dimensions of length 6 cm, width 5 cm, and height 3 cm. A worker removes the cover of the box, making it open from the top. What is the resulting volume of the box?
90 cm3
A spinner has a chance of 1/3 to land on blue. If I spin the spinner three times, what is the chance of not landing on blue?
8/27
A bat and a ball cost $2.20. If the bat costs exactly $2 more than the ball, how much does the ball cost?
$0.10
Find the smallest number that must be multiplied to 7! to make it a perfect square. (7! = 7 x 6 x 5 x ... x 2 x 1).
Prime factorizing this number yields 24 x 32 x 5 x 7. To make this a perfect square, the exponents on each term must be an even number. Therefore, the smallest number it should be multiplied with is 5 x 7, or 35.
A person runs 5 km north and 12 km west. If he had ran directly from the start to the finish, how much distance would he save?
4 km. He ran a total distance of 17 km, but the shortest distance between the two points is only 13 km.
Find the dimensions of a cube where its surface area is equal to its volume.
6 x 6 x 6
A driver drives up a 30 km hill at a speed of 30 km/h. However, on the way down, he drives at a speed of 60 km/h. What was his average speed?
40 km/h
A person throws a ball 100 m straight up in the air. Assuming he catches the ball from the exact height that he threw it at, how much distance did the ball travel?
200 m, because it travels another 100 m back down.
A control room has 1000 switches, all off. 1000 workers enter the room. The first worker turns each switch and leaves. The second worker turns every second switch and leaves (so if it was on, it will now be off, and vice versa). The third worker turns every third switch, and so on. After all the workers leave, how many switches are still on?
We must first experiment with the first few switches. Switch 1 will be on and remains on because only the first worker touches it.
Switch 2 will be off because the first worker turns it on but the second one turns it back off. No other workers will touch it. So are switches 3, 5, and 7.
Switch 4 is on because the first one turns it on, second one on, and fourth one off. This can also be seen for switch 9 (first on, third off, ninth on).
So switches 1, 4, and 9 are on after inspecting. This suggests that switches with perfect square numbers will remain on. This pattern holds true for 16 (1 on, 2 off, 4 on, 8 off, 16 on), 25 (1 on, 5 off, 25 on), and 36 (1 on, 2 off, 3 on, 4 off, 6 on, 9 off, 12 on, 18 off, 36 on).
The largest perfect square less than 1000 is 961 (312). Therefore, 31 switches are still on.
There are ten bags of coins. Each coin weighs 10 grams. However, one bag is full of counterfeit coins, which weigh 11 grams each. Using a scale, and only one round of measurement, how can you determine which bag has the counterfeit coins?
Take one coin from the first bag, two from the second, three from the third, etc... all the way to ten from the tenth. Weigh the total mass; these coins should weigh a total of 550 grams if none are counterfeit. By figuring out how much excess weight (in grams) is present, we can determine which bag has the counterfeit coins. (e.g. if it weights 556 grams, then bag #6 has all the counterfeit coins.)
A cylinder with radius 4 cm and height 8 cm is chopped in half. Then, a seal is placed on the top of the cylinder, leaving a small opening for liquid to flow. What is the resulting volume of this cylinder?
16π cm3
Adam and Bob are running a 100 metre race. When Adam passes the finish line, Bob is 5 metres behind. To make it more fair, Adam must start 5 metres behind the start line. Who will win this time?
Adam wins again. They would be tied at the 95m mark, because when Adam runs 100 metres, Bob can only run 95 metres. Since Adam started 5 metres behind the line, he would've already ran 100 metres while Bob only runs 95, which would make them tied at the 95-metre mark. Adam is faster than Bob, so he will pass him in the last 5 metres and win the race.
A bacteria colony doubles in size every day. If a petri dish was completely full of bacteria on day 400, when was it a quarter full?
Day 398
Prove that 27,000,001 is not prime.
27,000,001 is equal to 27,000,000 + 1, which is 3003 + 13. Using the sum of cubes formula, this can be factored into:
(300 + 1)(3002 - (300)(1) + 12), which is equal to 301 x 89701. Since 301 and 89701 are additional factors of 27,000,001 other than 1 and itself, it is therefore not prime.
A traveller wishes to complete a 60 km road trip with an average speed of 60 km/h. If he travels the first 30 km at a speed of 30 km/h, how fast should he travel the other 30 km to achieve his goal?
It is no longer possible to achieve this goal, because the whole journey is supposed to take one hour. He already spent one hour on the first half of the trip.
A pizza has a diameter of 4 inches. Find a way to cut the pizza into eight equal slices using only three cuts with their exact dimensions (radius from the centre of the pizza). You cannot stack the slices on top of each other and cut. Each cut does not necessarily need to be straight.
Firstly, make a cut horizontally through the centre and another one vertically through the centre (both all the way through the pizza). This creates four equal slices. The last cut will be a circle that splits the overall pizza into a smaller circle and an outer ring. The outer circle and the ring must have the same area.
The area of the pizza is 4π in2. Therefore, the inner circle and the outer ring much each have an area of 2π in2 each. This means that the radius of the smaller circle must be √2 inches.
Therefore, you must cut in the following way: one cut horizontally all the way through, and one cut vertically all the way through, both passing through the centre of the pizza. The last cut is a circle that has a radius of √2 inches from the centre of the pizza. This creates eight slices: four quarter circles from the inner circle and four quarter rings from the outer ring. The outer ring has the same area as the inner circle and both of them are split into quarters, which means that each slice is equal.
A speed camera clocks a driver going at 95 km/h. 2 minutes later, after a 5-km stretch of road, another camera clocks him at 100 km/h. If the speed limit on the road is 100 km/h, do the police have the right to ticket him for speeding? Explain why or why not.
Yes, they do. The fact that he drove through a 5-km stretch of road in 2 minutes suggests that he was going at LEAST 150 km/h.