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

Question

https://gmatclub.com/forum/download/file.php?id=50454 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 2019-09-21_1425.png

GMATGuruNY · Accepted Answer

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.

E

Archit3110 · Answer

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

GMATGuruNY · Answer

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.

Santoshk31 · Answer

this is a pretty straight fwd calculation. convert inches to mm that comes around > 33 (~33.337). 
Thus, ANS -> E

Mbahousegmat · Answer

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

aaa707 · Answer

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

suminha · Answer

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

Basshead · Answer

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.

Pritishd · Answer

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

Bunuel · Answer

_________________________
Fixed. Thank you!

sipora · Answer

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.

MHIKER · Answer

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

fireagablast · Answer

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

Arnobdas09 · Answer

1 5/16= 21/16
25.4 * 21/16= 33.33 ~ 34

Posted from my mobile device

fireagablast · Answer

Did you use a calculator? 25.4 * 21/16 seems like a ridiculously tedious calculation that can be avoided with some logic.

mprodeep · Answer

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

Rainman91 · Answer

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.

Kinshook · Answer

https://gmatclub.com/forum/download/file.php?id=50454 
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?

1 \frac{5}{16} = 25 + 25*5/16 + .4 + .4*5/16 = 25 + 7.8 + .4 + .125 = 33.325 mm

Only wrench with width of 34 mm will fit most closely.

IMO E

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

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

Prep Toolkit

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