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06 Feb 2020, 08:44
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
82% (00:58) correct
18%
(01:05)
wrong
based on 267
sessions
History
Date
Time
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Not Attempted Yet
A certain kind of necklace is made from 9 orange, 6 black, and 3 silver beads. What is the maximum number of these necklaces that can be made from 55 beads of each color ?
A. 18
B. 9
C. 7
D. 6
E. 3
A. 18
B. 9
C. 7
D. 6
E. 3
07 Feb 2020, 00:01
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The necklace needs to have 9 orange, 6 black and 3 silver beads. We are given 55 beads of each color. Clearly, 55 is not a multiple of any of the numbers mentioned above. Therefore, we need to look at a common multiple of 3, 6 and 9 closest to 55. This should make it clear that this is a question based on the concept of LCM.
The LCM of 3, 6 and 9 is 18. Any multiple of 18, therefore, will also be a common multiple of 3, 6 an 9. The multiple of 18 which is closest to 55 is 54.
If we have 54 orange beads, we can make 6 necklaces since each necklace has 9 orange beads. Since orange beads constitute the highest number of beads in the necklace, we need not calculate the breakup for the other colors.
But, why so? If you have 55 black beads, you can divide them into 9 groups of 6 each but, you can only use 6 groups to form necklaces. The remaining 3 groups would be useless. Similarly, 55 silver beads can be divided into 18 groups of 3 each but we can utilize only 6 of the groups.
I hope that, by now, it’s clear that we can have a maximum of 6 necklaces such that each necklace has 9 orange, 6 black and 3 silver beads.
The correct answer option is D.
When you obtain the LCM as 54, if you divide it by 3 (the number of silver beads) to obtain the maximum number as 18, you would be falling for the trap answer which is A. You need to remember that the number of orange beads is a constraint on the number of necklaces you can form.
Hope that helps!
The LCM of 3, 6 and 9 is 18. Any multiple of 18, therefore, will also be a common multiple of 3, 6 an 9. The multiple of 18 which is closest to 55 is 54.
If we have 54 orange beads, we can make 6 necklaces since each necklace has 9 orange beads. Since orange beads constitute the highest number of beads in the necklace, we need not calculate the breakup for the other colors.
But, why so? If you have 55 black beads, you can divide them into 9 groups of 6 each but, you can only use 6 groups to form necklaces. The remaining 3 groups would be useless. Similarly, 55 silver beads can be divided into 18 groups of 3 each but we can utilize only 6 of the groups.
I hope that, by now, it’s clear that we can have a maximum of 6 necklaces such that each necklace has 9 orange, 6 black and 3 silver beads.
The correct answer option is D.
When you obtain the LCM as 54, if you divide it by 3 (the number of silver beads) to obtain the maximum number as 18, you would be falling for the trap answer which is A. You need to remember that the number of orange beads is a constraint on the number of necklaces you can form.
Hope that helps!
29 Mar 2021, 11:26
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Bunuel
Solution:
Since it takes 9 orange beads to make one necklace and 55/9 = 6 R 1, 55 orange beads can make at most 6 necklaces.
Answer: D
