Which number is largest? - Oxford Mathematics Admissions Test 2015

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[@RobertssU]

yea in the one which has square root of 10!, you forgot to write the squared, which was already given in the denominator, so squaring it again would make it ^4

[@SadBoys.1996]

bro i dont even know what im looking at. this could be sanscript for all i know

[@mathoutloud]

We all start learning from the same level! I definitely didn’t wake up one day understanding this “language” out of nowhere ;)

[@claireloub]

For (D) can we not just say 2^5 = 32 so log2 (30) < 5 and 3^4 = 81 so log3(85) > 4 so smaller/bigger means overall it's definitely less than 5/4. For (C) you forgot the squared on the 6!, but with all the cancelling what you get is comparing 7/4 to 7/(very big)

[@mathoutloud]

This is what I eventually did, I just didn’t see that earlier in the work. I’m happy my mistake with the 6! didn’t throw off the correct answer.

[@slytherinbrian]

I always have a lot of fun with problems like this. Here was my approach: I started by comparing the first two (since 5/4 is nice and easy)... sqrt(7)/2 is sqrt(28)/4. sqrt(28) is a little bit more than 5, so (A) must be more than (B). Looking at (C), I canceled a bunch of terms and got sqrt(7)/2160, which is a VERY small number, so obviously that's not it. For (D), I observed that log2(30) is slightly less than 5, and log3(85) is slightly more than 4, which means it is less than 5/4. (E) was the trickiest, but I wanted to compare it to (A)... so I set up the question sqrt(7)/2 (1 + sqrt(6))/3. I cross multiplied to get 3 sqrt(7) 2 + 2 sqrt(6). Then I moved the coefficients inside the square roots to get sqrt(63) 2 + sqrt(24). The left side is slightly less than 8 (but greater than 7), the right side is 2 + slightly less than 5. So that means the left side is greater. So the answer is (A).

[@humanbean4014]

you missed that the 6! was squared in option C, although it didn't matter because squaring it would make the number 6! times smaller

[@RobertssU]

What program are you using?

[@mathoutloud]

The note taking software is called Drawboard.