Rohan purchased some pens, pencils and erasers for his young brothers and sisters for the ensuing examinations. He hadto buy atleast 11 pieces of each item in a manner that the number of pens purchased be more than the number of pencils, which is more than the number of erasers. He purchased a total of 38 pieces.If the number of pencils cannot be equally divided among his 4 brothers and sisters, how many pens did he purchase?a)11b)12c)13d)14Correct answer is option 'D'. Can you explain this answer?

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If the number of pencils cannot be equally divided among his 4 brothers and sisters, how many pens did he purchase?

a)
11
b)
12
c)
13
d)
14

Correct answer is option 'D'. Can you explain this answer?

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Rohan purchased some pens, pencils and erasers for his young brothers ...

Different possibilities for the number of pencils = 12 or 13.
Since it cannot be divided into his 4 brothers and sisters, it has to be 13.
The number of erasers should be less than the number of pencils and greater than or equal to 11. So the number of erasers can be 11 or 12.
If the number of erasers is 12, then the number of pens = 38 - 13 - 12 = 13, which is not possible as the number of pens should be more than the number of pencils.
So the number of erasers = 11 and therefore the number of pens = 14

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Rohan purchased some pens, pencils and erasers for his young brothers ...

Assume pen=11+x
pencil=11+y
eraser=11+z
11+x > 11+y >11+z
total 33+x+y+z=38
so x+y+z=5
and x>y>z
only possibility is x,y,z=3,2,1
so pen is 11+3=14

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Rohan purchased some pens, pencils and erasers for his young brothers ...

We have total pieces of item is equal to 38.
where is pen is more than pencil and pencil is more than eraser

so that we can write as 11-11-11 and adding some number it them because we have to complete the 38 pieces
pen>pencil>eraser
11+3>11+2>11
14>13>11
this result shows that pen is more than pencil them and eraser is more than which is mentioned in the question
therefore the pieces of is 14

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Rohan purchased some pens, pencils and erasers for his young brothers and sisters for the ensuing examinations. He hadto buy atleast 11 pieces of each item in a manner that the number of pens purchased be more than the number of pencils, which is more than the number of erasers. He purchased a total of 38 pieces.If the number of pencils cannot be equally divided among his 4 brothers and sisters, how many pens did he purchase?a)11b)12c)13d)14Correct answer is option 'D'. Can you explain this answer?

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