Finding alternative operation given two examples

Question

Good day,

I am doing old maths questions, but I can't seem to figure out the answer to the following:

Ura Wong says five times seven is 38 and six times six is 39. Using Ura's method what is the answer to six times seven?

The answer key states that it is 46, but I don't know why. The possible answers are 40, 42, 44, 46, & 48. I have tried multiplying and adding 3, but that isn't an answer choice.

In my opinion the question is not clearly posed enough to give a unique answer. For example, the rule multiply then add three explains the two examples but not the answer. — subrosar, Oct 17 '21 at 19:14
@islamm Yes, I tried the method stated by subrosar. The test is multiple choice which gives the options 40, 42, 44, 46, and 48 — Saddy, Oct 17 '21 at 19:18
@Saddy you should include what have you tried in the question see : who to ask a good question — mark, Oct 17 '21 at 19:20
Oh, I apologize, I will do that in the future. Thank you for telling me :) — Saddy, Oct 17 '21 at 19:20

score 1 · Accepted Answer · answered Oct 17 '21 at 19:17

Ura is using a different base $b$ than our decimal system.

According to Ura, if $$ (38)_b = (35)_{10} \quad , \quad (39)_b = (36)_{10} \tag{1}$$

then for which digits $X,Y$

$$ (XY)_b = (42)_{10}$$

is true?

Equations in $(1)$, can be written as $$3b + 8 = 35 \quad , \quad 3b+9=36$$

which both give $b=9$. Thus in base $9$, find $X,Y$ such that $$9X+Y=42$$

Since $36 < 42 < 45$, $X=4$ and $Y=6$ satisfy.

Remark : I went for different base solution since it is tagged "contest-math" and such questions are common in junior level contests.

Wow! Genius. Thank you so much! – Saddy Oct 17 '21 at 19:21 — Saddy, Oct 17 '21 at 19:21

Finding alternative operation given two examples

1 Answers1