Oxford University Maths Admissions Test 2023 Question 2

University of Oxford Mathematician Dr Tom Crawford answers each Oxford Maths Admissions Test question in under 60 seconds. This is Q2 from the 2023 MAT.

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

[PeterKerenyi]

I was expecting a blitzing fast talk. He said he'll answer ALL questions in 60 sec!

[johnmaynard]

If you put the page below the image of you calculating, it will balance the image

[kozokosa]

actually, you need to look at the last 2 digits, not the last one specifically, you have squares that end with 44, 84, 24 and more, which you subconcsiously took into account but I didn't see you mention what happens when you bump the digit of tens(the 2 in 23, 24, 25, 26...)

[shrishkumarsaini]

This is the first question from a western University admission test that actually made me think for a second

[mhoeltken]

I am no english native, but should the into not be "Answering each Oxford question in one miunte" in contrast to "answering all questions in one minute"?

[alexriedel]

I think I almost got it.
But wyh not a) ?
The last digit, 9, is 3² and thus a square.
And If it is the last "two" digits how would I know?
OR would it hafe to be -09 for it to work?

[terranceparsons]

I just went straight to c), because its always c)

[deathbyentropy]

196 is 14 squared, but ends on 96 hence it doestn follow your rule. Or did I missunderstand the approach?

[simonpfehr]

I don't see how that proofs (d) can't be square. The list shows that the last digit can be a 5, but you argued by saying 35 is not on the list

It is true that all squares that end in 5 actually end in 25 and I think I found an easy way to show it

We know for a product to end in 5 one of it's factors must end in 5 so we can write the square as:

(10n + 5)²
Expanded: 100n² + 100n + 25

This proofs (d) can't be a square

[kwilson]

I don't think the explanation was helpful.
For a) I would say '1 more than 99, 999, 999' is 100, 000, 000'. '100, 000, 000 is the square of 10, 000, so 9, 999, 999 (which is only 1 less) can't be a square'.
b) ends in 3, but no square numbers end in 3 (as stated on the video)
d) ends with 35, but the only square numbers that end in '5' end in '25'.
e) ends with three zeroes, but any square number ending in '0' must end with an even number of zeroes.

[factsworld]

I just selected C bcz, of 225, which 15^2😅

[jonp]

"D ends in a 35, we don't have a 35, so it can't be that one", that is false reasoning.

There's plenty of squares, like 121, 144, 169, 196 etc which have 2 last digits which are different from the squares of the numbers 0 to 10.

Admission application rejected.

[johnnyboy]

I bet he owns a white hoodie totally covered in hand scrawled equations

[LeafBurrower]

Dire hairstyle, dude. It's 2024, not 2004.

[rydmerlin]

Do you have to mention that you had no involvement in the test itself?

[Bid_Droh_Hi]

I'm sorry for this comment, but are you emo turned mathematics tutor or methamatics turned mathematics tutor😂😂.. sorry brother... Love from India..

[jackarmstrong]

What a meaningless question that only tests exposure and memory. It does not test intelligence.

[cleverclover]

i hate this. math is just a bunch of parlor tricks when presented this way - and that's the test for admission?

[missionprodigy]

"the last digit squared will match the smaller numbers 1 through to 9". I'm not a maths professor but could you possibly have garbled that explanation any worse?

[himanshu.nehete]

bruh i could solve and i am 13 asian of course