### Brain Teasers

# Preposterous Proportions

Which ONE of the following statements is FALSE?

a) Half of FIVE is FOUR.

b) A third of TWENTY is EIGHT.

c) A quarter of NINE is ONE.

d) A fifth of SIXTY-FOUR is NINE.

BONUS:

Fill in the blank below to make the following statement TRUE, consistent with the approach/pattern above (i.e. the common sense answer of "FOUR" is incorrect):

A third of TWELVE is __________.

a) Half of FIVE is FOUR.

b) A third of TWENTY is EIGHT.

c) A quarter of NINE is ONE.

d) A fifth of SIXTY-FOUR is NINE.

BONUS:

Fill in the blank below to make the following statement TRUE, consistent with the approach/pattern above (i.e. the common sense answer of "FOUR" is incorrect):

A third of TWELVE is __________.

### Hint

This doesn't work with the equivalent numbers: 5, 20, 9, and 64, nor with 12 for the bonus.### Answer

b) A third of TWENTY is EIGHT.What makes the other statements true is that, in each case, the ("is") number stated as being the given proportion of the object ("of") number is referring to the Roman numeral(s) that is/are contained within the object number.

Changing the "extra" characters to lowercase letters for the purpose of clarity, we have:

a) "fIVe" ==> Consists of 4 characters, 2 or "half" of which are "IV" = the Roman numerals for "FOUR".

c) "nIne" ==> Consists of 4 characters, 1 or "a quarter" of which is "I" = the Roman numeral for "ONE".

d) "sIXty-four" ==> Consists of 10 characters, 2 or "a fifth" of which is "IX" = the Roman numerals for "NINE".

Statement b) is false because in no way do "VIII" = the Roman numerals for "EIGHT" make up "a third" of "TWENTY" which consists of 6 characters.

And for the bonus, the answer is:

A third of TWELVE is FIFTY-FIVE.

"tweLVe" ==> Consists of 6 characters, 2 or "a third" of which are "LV" = the Roman numerals for "FIFTY-FIVE" ((L=50) + (V=5) = 55).

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