2005 CEMC Gauss (Grade 7) Problems/Problem 23
Problem
Using an equal-armed balance, if balances and balances , which of the following would not balance ?
Solution 1
If balance , then would balance the equivalent of . Similarly, would balance the equivalent of . If we take each of the answers and convert them to an equivalent number of , we would have:
Therefore, and do not balance the required. The answer is .
Solution 2
Since balance , then would balance . Therefore, would balance , so since balance , then would balance , or would balance . We can now express every combination in terms of only.
, , and equals .
and equals .
and equals .
and equals .
and equals .
Therefore, since , , and equals , then it is and which will not balance with this combination. Thus, the answer is .
Solution 3
We try assigning weights to the different shapes. Since balance , assume that each weighs and each weighs . Therefore, since balance , which weigh combined, then each weighs . We then look at each of the remaining combinations.
, , and weigh .
and weigh .
and weigh .
and weigh .
and weigh .
Therefore, it is the combination of and which will not balance the other combinations. The answer is .
See Also
2005 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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CEMC Gauss (Grade 7) |