If You Pass This Difficult Mental Math Quiz, We Think You Deserve a PhD!


By: Robin Tyler

6 Min Quiz

Image: shutterstock

About This Quiz

So you pride yourself on your numbers game, do you? 

Addition, subtraction, multiplication and division. You have them all done 100%. But what about percentages? Know anything about them? A few long-winded math questions? Would that throw you off the trail?

No? Well, then you are a formidable mathlete, are you not? Like that word? I think I just made it up, but it's perfect for a math boffin like yourself. Mathlete... I like that.

Ok, mathlete. Let's really put you to the test with the most difficult mental math problems you would have come across on the world wide web. Scared? You shouldn't be. They're tough, but if you take your time, there is no reason that you won't score at least 50% on this test. 50% you say. You know you can beat that! But as we say, it's a tough test, so you're going to have to keep your wits and figures about you. 

Remember, no calculator allowed - just that biological calculator, your brain! 

Let's see how many of these tough 35 questions you can get right. Don't worry if you are really stuck - we have provided some hints to help you along.

Good luck and ace it!


If 4x4 is 16, just scale it up for 40x40. That's the easiest way, and yes, it's 1,600



It's easy when you do it in bite-sized chunks. 999 - 33 is 966. 966 - 87 is 879 and then minus the final 100 is 779.


What is 22+47?

Simple addition, it's 69. We got there by adding 2 and 4 to get 6 and then 2 and 7 to get 9, therefore 69.


To stay in a hotel costs $40 per night. You stay for three nights and check out on the fourth morning. How much will you pay?

You will only pay for the nights you slept over, so $120 in total for three nights. You had to be out of the room on the fourth morning, so you were not charged for that. (Of course, you'll also have to pay for some taxes and fees, and maybe even room service charges.)


Calculate 56+60+10-56.

The answer is 70. And its easy to get to. Look at the whole sum. If you look closely, the two 56's cancel each other out, leaving 60 plus 10!



Ok, the easiest way to approach this is by rounding 332 up to 333. If you multiply that by 3, it's easy to see it would be 999. Then take off 3 from the rounding up. Simple when you know a few shortcuts, right?



Well, we have tried to trick you here, but on closer inspection a number of the numbers cancel each other out. They are 240 and 400, leaving 120+1. And you should have had no trouble with that!



Let's break it down. 25 x 10 would give you 250, but you need to add another 25, as it was actually multiplying by 11.


What is the result of 15x0?

In math, you learn fairly early that anything multiplied by zero is zero. So that rule stands with this question. The answer is 0!


If a train leaves a station at 10 p.m., travels at 30 miles per hour and covers 120 miles, what would the time be?

It travels at 30 miles an hour. Therefore, to travel 120 miles would take four hours, so it will arrive at 2 a.m.


What is 10% of 100?

100% of 100 would be 100, so a tenth of that is 10. Easy! But you knew that, right?



Ok, lets do this a little differently. Take 5,200 and add 100, making 5,300. Now remove the 33 and it is easy to see the answer is 5,267.


What is 180/9?

Ok, this is fairly simple. What is 2x9? 18, right? Can you see a correlation? So therefore, 20x9 would equal 180. So 180 divided by 9 gives you 20.


Subtract 999 from 10. What do you have?

Oh no, a negative! But it's simple. If you had 999 and you took off 10, you would have 989. Now bring the negative back. And that is your answer: -989.



Always do what is in the brackets first, then the rest of the sum. The answer is 100. Did you get it?


If you divide 50 by 100, what do you have?

Hmmm, a little tough one here if you let it be. 100 divided by 50 would be 2, so 50 divided by 100 is 0.5.



Again, just break it into two seperate problems. First, 250 x 5 is 1,250 (250 x 4 is 1,000, plus the extra 250). Then if you take 1,250 and times it by 2, its like adding it to itself. So 1,000 plus 1,000 and 250 plus 250, added together is 2,500.


Is 7 a prime number?

Prime numbers can only be divided by 1 or themselves. Can 7 be divided by 1? Yes, it can. Can it be divided by itself? Yes it can. Can any other number divide into it to form a whole number? No. Therefore 7 is a prime number.


If I have a liter bottle of cola and I drink 250 ml's, how much is left?

One liter is 1,000 ml. If you drink 250 ml, you have drunk a quarter of the contents, leaving three-quarters. That equates to 750 ml.


1,200÷10 will equal what?

Think of it this way. 120 x 10 = 1,200. So 1,200 ÷ 10 logically is 120. Did you follow our reasoning?


What is 40x12?

Breaking it down reveals the answer quickly. 40 times 10 is 400. So times 12 means you have to add another 40 and another 40, for an overall total of 480.


What is 20% of 200?

This is fairly simple to work out, as long as you do it in increments. What do we mean? Well 10% of 200 would be 20, so logically, 20% is 40.



Lets break this down. Immediately, the 800 and 1,200 stand out to form 2,000. They are both subtracted from 3,000 to leave 1,000. Then add the 600 and 400, and you have 2,000 in total. So simple when you let the figures work for you!



Do it in sequence and it is very easy to find the answer is 801. See, 33 and 66 is 99. So the equation is 999 - 99 - 99. 999 minus the first 99 leaves you at 900, take away another 99 and you have 801.


What is 2,400÷12?

If you take 12 and you multiply it by 100, you have 1,200. Do it again and then add them together, and you have 2,400. Therefore, if you divide 2,400 by 12, you will be left with 200.


How many right angles does a cube have?

A cube has 6 equal sides, and each side has 4 equal right angles. That means 24 right angles in total. That makes sense, doesn't it?


What is 20+0.8+0.03?

To answer this easily enough, break it down into steps. The biggest number is 20, add the next biggest, 0.8 and you have 20.8. Then comes 0.03, which you can see has two decimal spaces. So the total comes to 20.83.


Add the following, please: 90+33+0.01+100+241=___?

Remember, its 0.01, not 0.1, so the answer is 464.01. Always watch your decimal places.


If a skipping rope is 2 meters long, how many 100-cm pieces could I cut it into?

100 cm is a meter, so 2 meters = 200 cm, so you could cut in into two pieces. But why would you cut you skipping rope?



Although it looks difficult to do without a calculator, it really isn't. Just break it down. Starting from the back, 100 plus 99 is 199. Also 77 and 33 is 110, add them together and you get 309.


What is the number of degrees in the right angle of a perfect right angle triangle?

A right angle triangle would have one angle equal to 90 degrees. Did you study trigonometry at school? Fascinating stuff!



Simple addition and subtraction, just take your time. So let's break it down, starting from the right. 999 +1 is 1,000. Then 1,000- 999, leaves you with 1 again. 1 plus 888 makes 889. Round that up to 900, add 333 and you have 1,233, minus 11 from the rounding up is 1,222. Add 400 and you have the answer: 1,622. Phew, that was a little tough!


How many sides does a cube have?

Always remember that a cube is a 3-D figure, so it has four sides, plus a top and a bottom. This makes six sides in all.


A man must take a pill every half an hour. He starts at 10 a.m. How many pills will he have taken by 12:01 p.m.?

He will take 5 pills, broken down as follows. First at 10 a.m., second at 10:30 a.m., third at 11:00 a.m., fourth at 11:30 a.m. and fifth at 12:00 p.m. The easiest way to approach these questions is to map it out step for step.



As we saw a moment ago, anything divided by zero is zero. Therefore 5x0 is zero, and zero added to 78 is still 78. Get it? Of course you do!


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