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Algebra Difficulty 1.4 Junior Find the answer Canada

The operation $\nabla$ is
defined by $a \nabla b = 4a + b$ . The
value of $(5 \nabla 2) \nabla 2$
is

Pick one

Solutions — 2

Solution 1

Since $\$\frac{42\text{ cm}}{2\text{}}$
cm}}=21$, then Olivia cuts her string into 21 pieces.

Since $\$\frac{42\text{ cm}}{3\text{}}$
cm}}=14$, then Jeff cuts his string into 14 pieces.

Therefore, Olivia has $21-14=7$ more
pieces of string than Jeff.

Solution 2

From the given list, the numbers that are divisible by $2$ are $2$ , $4$ , $6$ , $8$ .

The numbers that are divisible by $3$
are $3$ , $6$ , $9$ .

The numbers that are divisible by both $2$ and $3$ are the numbers which appear in both of
the previous two lists. The only number in both lists is $6$ .

Thus, the numbers that are divisible by $2$ , or by $3$ , or by both $2$ and $3$ are $2$ , $3$ , $4$ , $6$ , $8$ , $9$ .

Since $2$ , $3$ , $4$ , $6$ , $8$ , $9$
are $6$ of the $9$ numbers listed, then the probability
that the chosen number is divisible by $2$ , or by $3$ , or by both $2$ and $3$ , is $\frac69$ .

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.