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A teacher distributed few pens and few pencils evenly among the studen

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A teacher distributed few pens and few pencils evenly among the studen  [#permalink]

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New post 28 Jul 2017, 01:39
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Question Stats:

51% (02:34) correct 49% (01:56) wrong based on 53 sessions

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A teacher distributed few pens and few pencils evenly among the students in his class, with each student getting an equal number of pens and an equal number of pencils. How many students are there in the class?

(1) The teacher distributed 180 pens and 40 pencils.
(2) The total number of items received by each student is less than 15.

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Re: A teacher distributed few pens and few pencils evenly among the studen  [#permalink]

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New post 28 Jul 2017, 02:04
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Bunuel wrote:
A teacher distributed few pens and few pencils evenly among the students in his class, with each student getting an equal number of pens and an equal number of pencils. How many students are there in the class?

(1) The teacher distributed 180 pens and 40 pencils.
(2) The total number of items received by each student is less than 15.


(1) 180 pens and 40 pencils
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, .....
Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40

no. of students can be 2, 4, 5, 10, 20

not sufficient

(2) not sufficient

on combining
if the no. of students is 2
then each receives 110 items
if 10 then each receives 22 items

only when if there are 20 students they each receive 11 items (<15)
C
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A teacher distributed few pens and few pencils evenly among the studen  [#permalink]

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New post 23 Apr 2018, 12:31
Statement 1:
180 Pens and 40 Pencils were distributed.
So number of students must be factor of HCF(180,40) => factor of 20
still not suff

Statement 2: clearly insufficient.

Combining 1 + 2

If we take factor 10, number of pen received by students = 180/10 = 18 (which is greater than 15), which contradicts statement 2
so number of students must be greater than 10,
only factor of 20 greater than 10 is itself.

so number of students = 20 (C)
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A teacher distributed few pens and few pencils evenly among the studen &nbs [#permalink] 23 Apr 2018, 12:31
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