Cambridge Interview Question | Can You Solve This Algebra Problem With Exponents ?

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[KushagraJuneja]

At 5:00 should it not be 2^p-m(1 + 2^q-m-p+m) = 40
Though at 7:34, you did solve it correctly.

[linus]

Your substitution didn’t really make any sense, cause from that point on you don’t differ between m, p and q anymore, even though this is important cause p has to be dividable by 2 and q has to be dividable by 3. Therefore your answer is mathematically incorrect. You also can find the answer a lot faster by looking what Summands of 2 to the power of x, y and z fit into 656:
2^x + 2^y + 2^z = 656
There is only one solution for this, because 656 consists of at least 3 of these summands. The biggest one being 512, the second one 128 and the last one 16, therefore you get:
2^9 + 2^7 + 2^4 = 656
With:
2^(a) + 4^(b/2) + 8^(c/3)
= 2^9 + 2^7 + 2^4
and a, b, c as elements of N,
The only solution here is c = 9 ( 9 being the only number dividable by 3), b = 4 (4 being the only number dividable by 2) and a = 7.
If the problem has only one answer, we can find it this way, otherwise we’d have to look over the possible answers before the last step (e.x. Having 4, 8 and 9 as x, y and z, as it would be the case for 784, we’d have 9 as solution for c, but either 8 or 4 as solution for b, leaving the other one as a). Peace and have a good one!