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

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gmatt1476
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The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   21 Sep 2019, 03:27
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The figures above show a hexagonal nut that has a width of \(1 \frac{5}{16}\) 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

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2019-09-21_1425.png
2019-09-21_1425.png [ 19.34 KiB | Viewed 30418 times ]
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The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   Updated on: 07 Oct 2022, 02:58
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gmatt1476 wrote:

The figures above show a hexagonal nut that has a width of \(1 \frac{5}{16}\) 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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E

Originally posted by GMATGuruNY on 21 Sep 2019, 04:00.
Last edited by GMATGuruNY on 07 Oct 2022, 02:58, edited 1 time in total.
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Archit3110
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   Updated on: 21 Sep 2019, 06:00
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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
Show Spoiler
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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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   21 Sep 2019, 05:57
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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] New post   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
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   03 Jan 2020, 16:50
MBA HOUSE KEY CONCEPT: Mixed Numbers and Rule of 3(directly proportional).

1 5/16 = (1 x 16 + 5) / 16 = 21/16

Inches 21/16 x 25.4 = 33...

So, the next integer greater than 33 and something is 34.

E :shh:
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   19 Aug 2020, 03:59
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avoid calculating sophisticated numbers. simply do this

during conversion use closest estimates..

21/16 inch x 25.4

20 / 15 x 25 = 33.33.. u know now answer is E.34
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   27 Sep 2020, 21:00
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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+5/16inches.

What 55669.png means?
If the nut has 1+5/16 inches too, why they give the information about inches of nut and of wrench separately using “and”?
And the image of the question indicates that the nut has 1+5/16 inches. But at the same time the question says “a wrench that, in order to fit the nut, must have a width of at least 1+5/16inches”??

This question is annoying geez can someone explain me why this question lends infos in this way please?


Posted from my mobile device
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   11 Nov 2020, 03:51
\(1 \frac{5}{16}\) inches = \(\frac{21}{16 }\) inches

\(21/16 * 25.4\) = \(\frac{21}{16} * 25 \frac{4}{10}\)

\(\frac{21}{16 }* \frac{254}{10}\)

\(\frac{21}{16} * \frac{127}{5} = \frac{2667}{80}\)

\(= approximately 33 \\
\)

The only answer that's greater is 34. Answer is E.
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   09 Dec 2020, 11:06
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suminha 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+5/16inches.

What 55669.png means?
If the nut has 1+5/16 inches too, why they give the information about inches of nut and of wrench separately using “and”?
And the image of the question indicates that the nut has 1+5/16 inches. But at the same time the question says “a wrench that, in order to fit the nut, must have a width of at least 1+5/16inches”??

This question is annoying geez can someone explain me why this question lends infos in this way please?
Posted from my mobile device


Even I got confused here. Adding Bunuel to make this correction
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   09 Dec 2020, 11:10
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Pritishd wrote:
suminha 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+5/16inches.

What 55669.png means?
If the nut has 1+5/16 inches too, why they give the information about inches of nut and of wrench separately using “and”?
And the image of the question indicates that the nut has 1+5/16 inches. But at the same time the question says “a wrench that, in order to fit the nut, must have a width of at least 1+5/16inches”??

This question is annoying geez can someone explain me why this question lends infos in this way please?
Posted from my mobile device


Even I got confused here. Adding Bunuel to make this correction


_________________________
Fixed. Thank you!
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   22 Dec 2020, 21:41
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Why is this question rated hard 95%? I think it's fairly simple: 1+5/16 so approximately 25.4+8=33.4, so 33 wouldn't fit at all, only option is 34.
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   06 Mar 2021, 03:19
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gmatt1476 wrote:

The figures above show a hexagonal nut that has a width of \(1 \frac{5}{16}\) 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

Show Spoiler
Attachment:
2019-09-21_1425.png



\(1 \frac{5}{16}\) \(= \frac{21}{16} ≈ \frac{21}{15}\)

1 inch ≈ 25.4 millimeters ≈ 25 millimeters

Now, \(\frac{21}{15}*25=1.4*25=35≈34\)

The answer is E
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The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   06 Mar 2021, 20:22
the key is the 5/16th. They aready give you the value of 1 inch. Other solutions involve significant calcuations with unkind numbers - highly recommend the below approach:

Approximate values:
5/16 is about 5/15 = 1/3
25.4 is roughly 25.5

Calculate the mm of 5/16ths of a inch:
25.5*1/3 = 8.5 --> 5/16th of an inch is approximately in mm

Add the given and your solution above:
1 inch + 5/16th inch = 25.4mm+8.5mm = 33.9mm which is about 34mm.
E
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   07 Mar 2021, 01:36
1 5/16= 21/16
25.4 * 21/16= 33.33 ~ 34

Posted from my mobile device
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   07 Mar 2021, 16:53
Arnobdas09 wrote:
1 5/16= 21/16
25.4 * 21/16= 33.33 ~ 34

Posted from my mobile device


Did you use a calculator? 25.4 * 21/16 seems like a ridiculously tedious calculation that can be avoided with some logic.
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   05 Apr 2021, 00:45
\(1\frac{5}{16}\) * 25.4 = 25.4 + \(\frac{5}{16}\)*25.4 = 25.4 + 5*1.6 (because 254 ~ 256 = \(16^2\)) = 25.4 + 8 = 33.4

IMO E. 34
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Re: The figures above show a hexagonal nut that has a width of 1 5/16 [#permalink] New post   30 Jul 2022, 23:08
This is how I solved it. Difference between 5/16 and 5/15 is extremely minimal. So I took

1/3 and divided 25.4. Easily got 8.46.

25 Plus 8 equals to 33. Include the .4s it has to be greater than 33.
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