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# The figures above show a hexagonal nut that has a width of 1 5/16

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Joined: 04 Sep 2017
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The figures above show a hexagonal nut that has a width of 1 5/16  [#permalink]

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21 Sep 2019, 03:27
1
5
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:28) correct 57% (02:42) wrong based on 128 sessions

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The figures above show a hexagonal nut that has a width of 55669.png inches and a wrench that, in order to fit the nut, must have a width of at least $$1 \frac{5}{16}$$ inches. Of all the wrenches that fit the nut and have widths that are whole numbers of millimeters, the wrench that fits the nut most closely has a width of how many millimeters?

(Note: 1 inch ≈ 25.4 millimeters)

A. 30
B. 31
C. 32
D. 33
E. 34

PS92751.01

Attachment:

2019-09-21_1425.png [ 19.34 KiB | Viewed 1582 times ]

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Re: The figures above show a hexagonal nut that has a width of 1 5/16  [#permalink]

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21 Sep 2019, 04:00
4
gmatt1476 wrote:

The figures above show a hexagonal nut that has a width of 55669.png inches and a wrench that, in order to fit the nut, must have a width of at least $$1 \frac{5}{16}$$ inches. Of all the wrenches that fit the nut and have widths that are whole numbers of millimeters, the wrench that fits the nut most closely has a width of how many millimeters?

(Note: 1 inch ≈ 25.4 millimeters)

A. 30
B. 31
C. 32
D. 33
E. 34

Width of the nut:
$$1 \frac{5}{16}$$ inches = $$\frac{21}{16}$$ inches

Conversion note:
$$25.4$$ millimeters per inch $$= 25\frac{2}{5}$$ millimeters per inch $$= \frac{127}{5}$$ millimeters per inch

Converting the width of the nut from inches to millimeters, we get:
$$\frac{21}{16}$$ inches * $$\frac{127}{5}$$ millimeters per inch = $$\frac{21}{16} * \frac{127}{5} = \frac{21}{5} * \frac{127}{16}$$ = (4.2)(almost 8) = more than 33 millimeters.
Of the five answer choices, only E will accommodate a width greater than 33 millimeters.

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The figures above show a hexagonal nut that has a width of 1 5/16  [#permalink]

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Updated on: 21 Sep 2019, 06:00
1
given fraction;
$$1 \frac{5}{16}$$ inches ; 21/16
and 1 inch = 25.4 mm
so at least closest measurement ; 25.4*21/16 = ~33.3 = 34

IMO E

gmatt1476 wrote:

The figures above show a hexagonal nut that has a width of 55669.png inches and a wrench that, in order to fit the nut, must have a width of at least $$1 \frac{5}{16}$$ inches. Of all the wrenches that fit the nut and have widths that are whole numbers of millimeters, the wrench that fits the nut most closely has a width of how many millimeters?

(Note: 1 inch ≈ 25.4 millimeters)

A. 30
B. 31
C. 32
D. 33
E. 34

PS92751.01

given fraction
Attachment:
2019-09-21_1425.png

Originally posted by Archit3110 on 21 Sep 2019, 05:32.
Last edited by Archit3110 on 21 Sep 2019, 06:00, edited 1 time in total.
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Joined: 04 Aug 2010
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Schools: Dartmouth College
The figures above show a hexagonal nut that has a width of 1 5/16  [#permalink]

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21 Sep 2019, 05:57
Archit3110 wrote:
given fraction;
$$1 \frac{5}{16}$$ inches ; 21/16
and 1 inch = 25.4 mm
so closest measurement ; 25.4*21/16 = 33.3 ~ 33
IMO D

Careful!

From the prompt:
a wrench that, in order to fit the nut, must have a width of at least $$1 \frac{5}{16}$$ inches
Implication:
$$w ≥ \frac{21}{16}$$ inches

In your solution, the value in red indicates that $$\frac{21}{16}$$ inches > 33 millimeters.
Thus:
$$w ≥ \frac{21}{16}$$ inches > 33 millimeters
$$w > 33$$ millimeters

Only E satisfies this condition.
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Re: The figures above show a hexagonal nut that has a width of 1 5/16  [#permalink]

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22 Nov 2019, 10:23
this is a pretty straight fwd calculation. convert inches to mm that comes around > 33 (~33.337).
Thus, ANS -> E
Re: The figures above show a hexagonal nut that has a width of 1 5/16   [#permalink] 22 Nov 2019, 10:23
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