Latest CAT Aptitude Question SOLUTION: wht is the minimum number of square marbles required to tile a floor of length 5 m 78cm and width of 3m 74cm

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wht is the minimum number of square marbles required to tile a floor of length 5 m 78cm and width of 3m 74cm

Asked In CAT KRUTHIKA (12 years ago)

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PARAG KAMRA  (12 years ago)

The marbles used to tile the floor are square marbles. Therefore, the length of the marble = width of the marble.
As we have to use whole number of marbles, the side of the square should a factor of both 5 m 78 cm and 3m 74. And it should be the highest factor of 5 m 78 cm and 3m 74.

5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm.
The HCF of 578 and 374 = 34.

Hence, the side of the square is 34.

The number of such square marbles required =(578*374)/(34*34) = 187 marbles.

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Bharat  (12 years ago)

H.C.F of 578 & 374 is 34 therefore 34 sized squares to be arrage
578=34x17 on length side 17 marbles are used
374=34x11 on width side 11 marbles are used
therefore 11x17=187 marbles are used

Is this solution Helpfull? Yes (1) | No (1)  

lakshmi reddy  (12 years ago)

5 m 78cm--->578cm and 3m 74cm---->374cm
578*374=216172
and perfect square nearer to and greater than 226576
226576-216172=10404=102*102. So minimum number of square marbles req.=102

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snehil  (12 years ago)

187 tiles of 34cm*34cm dimensions

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Vyas Akondi  (4 years ago)

Option(B) is correct

The marbles used to tile the floor are square marbles.

Therefore, the length of the marble=width of the marble.
As we have to use whole number of marbles, the side of the square should a factor of both 5 m 78 cm and 3m 74. And it should be the highest factor of 5 m 78 cm and 3m 74.

5 m 78 cm = 578 cm and 3 m 74 cm = 374 cm.
The HCF of 578 and 374 = 34.

Hence, the side of the square is 34.

The number of such square marbles required,

=578×37434×34
=17×11= 187 marbles

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