Question

If a match box is \[0.17{\text{ }}feet\] long, what is its length in inches the most closely comparable to the following?
(A) \[\dfrac{{51}}{{16}}{\text{ }}inch\] highlighter
(B) \[\dfrac{{31}}{8}{\text{ }}inch\] jewelry box
(C) \[\dfrac{{23}}{4}{\text{ }}inch\] lipstick
(D) \[\dfrac{{23}}{{16}}{\text{ }}inch\] staple remover
(E) \[\dfrac{{41}}{2}{\text{ }}inch\] calculator

Answer 1

Hint: While solving these types of problems first we need to know what is the relation between feet and inches. So, the relation between feet and inches is that \[1{\text{ }}foot{\text{ = 12 }}inches\]. First we will convert \[0.17{\text{ }}feet\] into \[inches\] then we will check one by one which option will be most closely comparable with the value that comes after the conversion.

Complete answer:
It is given that, a matchbox is \[0.17{\text{ }}feet\] long
And we are asked to find its length in \[inches\] which is most closely comparable to the following given options.
Now, we know that \[1{\text{ }}foot{\text{ = 12 }}inches\]
\[\therefore 0.17{\text{ }}feet = 0.17 \times 12{\text{ }}inches\]
\[ \Rightarrow 0.17{\text{ }}feet = 2.04{\text{ }}inches\]
Now, we will check all the options one by one
Option (1)
 Given, \[\dfrac{{51}}{{16}}{\text{ }}inch\] highlighter
and we have to check whether it is closely comparable with the value or not
 So, on dividing \[51\] by \[16\] ,we get
\[\dfrac{{51}}{{16}} = 3.1875\]
which is not close to the value of \[0.17{\text{ }}feet\]
Hence, option (1) is incorrect.

Option (2)
Given, \[\dfrac{{31}}{8}{\text{ }}inch\] jewelry box
and we have to check whether it is closely comparable with the value or not
So, on dividing \[31\] by \[8\] ,we get
\[\dfrac{{31}}{8} = 3.875\]
which is not close to the value of \[0.17{\text{ }}feet\]
Hence, option (2) is incorrect.

Option (3)
Given, \[\dfrac{{23}}{4}{\text{ }}inch\] lipstick
and we have to check whether it is closely comparable with the value or not
So, on dividing \[23\] by \[4\] ,we get
\[\dfrac{{23}}{4} = 5.75\]
which is not close to the value of \[0.17{\text{ }}feet\]
Hence, option (3) is incorrect.

Option (4)
Given, \[\dfrac{{23}}{{16}}{\text{ }}inch\] staple remover
and we have to check whether it is closely comparable with the value or not
On dividing \[23\] by \[16\] ,we get
\[\dfrac{{23}}{{16}} = 1.4375\]
which may be close to the value of \[0.17{\text{ }}feet\] but we need to check option (5) as well.

Option (5)
Given, \[\dfrac{{41}}{2}{\text{ }}inch\] calculator
and we have to check whether it is closely comparable with the value or not
So, on dividing \[41\] by \[2\] ,we get
\[\dfrac{{41}}{2} = 20.5\]
which is not close to the value of \[0.17{\text{ }}feet\]
Hence, option (5) is also incorrect.
So, from the above calculations we come to the conclusion that the length of matchbox which is \[0.17{\text{ }}feet\] long is most closely comparable to the \[\dfrac{{23}}{{16}}{\text{ }}inch\] staple remover
Hence, option D is correct.

Note:
Conversion of given measurements should be done properly otherwise it leads to incorrect solutions. Always try to convert all the measurements to a single measurement so that it is easier to simplify further. We can also solve this question by converting all the given options into \[feet\] and then comparing with the \[0.17{\text{ }}feet\] to get the result.
Important result:
\[1{\text{ }}inch = 0.0833{\text{ }}feet\]