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# If a teacher distributed 105 candies to 50 students in her class, how

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If a teacher distributed 105 candies to 50 students in her class, how  [#permalink]

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22 Oct 2018, 00:23
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65% (hard)

Question Stats:

39% (01:21) correct 61% (01:13) wrong based on 23 sessions

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If a teacher distributed 105 candies to 50 students in her class, how many students received only one candy?

(1) None of the students received more than three candies.
(2) Fifteen students received only two candies each

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Re: If a teacher distributed 105 candies to 50 students in her class, how  [#permalink]

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22 Oct 2018, 04:24
Bunuel wrote:
If a teacher distributed 105 candies to 50 students in her class, how many students received only one candy?

(1) None of the students received more than three candies.
(2) Fifteen students received only two candies each

Question: 105 candies to distributed among 50 students, How many received 1 candy?

Statement 1: None of the students received more than three candies.
Case 1: 35 students may receive 3 candies each and no one receives one candy
Case 2: 34 students may receive 3 candies each and one receives one candy and one received two candies
NOT SUFFICIENT

Statement 2: Fifteen students received only two candies each

15*2 = 30 candies settles
Remaining candies = 105 - 30 = 75
Many cases like in statement 1 mentioned are possible for 1 candy holders so
NOT SUFFICIENT

Combining the two statements

15*2 = 30
No one received more than 3 candies
i.e. Case 1: 25 may receive 3 candies each and no one receives 1 candy
Case 2: 24 may receive 3 candies each and three receive 1 candy each
NOT SUFFICIENT

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Re: If a teacher distributed 105 candies to 50 students in her class, how  [#permalink]

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22 Oct 2018, 17:04
Bunuel wrote:
If a teacher distributed 105 candies to 50 students in her class, how many students received only one candy?

(1) None of the students received more than three candies.
(2) Fifteen students received only two candies each

(1) a + b + c = 50 (total of students) and a + 2b + 3c = 105 (total of candies)
a = number of student that received 1 candies
b = number of student that received 2 candies
c = number of student that received 3 candies

Insufficient

(2) number of student that received 2 candies is 15

Insufficient

Both together:
from (2): b = 15, then
a + b + c = 50
a + 15 + c = 50
a + c = 35
c = 35 - a

a + 2b + 3c = 105
a + 2*15 + 3*(35 - a) = 105
a + 30 + 105 - 3a = 105
2a = 30
a = 15; Since a is number of student that received 1 candies, so the answer is 15.

BOTH ARE SUFFICIENT
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If a teacher distributed 105 candies to 50 students in her class, how  [#permalink]

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22 Oct 2018, 20:13
VaCeFe wrote:
Bunuel wrote:
If a teacher distributed 105 candies to 50 students in her class, how many students received only one candy?

(1) None of the students received more than three candies.
(2) Fifteen students received only two candies each

(1) a + b + c = 50 (total of students) and a + 2b + 3c = 105 (total of candies)
a = number of student that received 1 candies
b = number of student that received 2 candies
c = number of student that received 3 candies

Insufficient

(2) number of student that received 2 candies is 15

Insufficient

Both together:
from (2): b = 15, then
a + b + c = 50
a + 15 + c = 50
a + c = 35
c = 35 - a

a + 2b + 3c = 105
a + 2*15 + 3*(35 - a) = 105
a + 30 + 105 - 3a = 105
2a = 30
a = 15; Since a is number of student that received 1 candies, so the answer is 15.

BOTH ARE SUFFICIENT

Can we assume that each student must have received at least one candy? Because in question stem it is not mentioned that each student must get at least one candy.

VaCeFe, Bunuel
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Re: If a teacher distributed 105 candies to 50 students in her class, how  [#permalink]

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22 Oct 2018, 23:05
vishalkazone wrote:
VaCeFe wrote:
Bunuel wrote:
If a teacher distributed 105 candies to 50 students in her class, how many students received only one candy?

(1) None of the students received more than three candies.
(2) Fifteen students received only two candies each

(1) a + b + c = 50 (total of students) and a + 2b + 3c = 105 (total of candies)
a = number of student that received 1 candies
b = number of student that received 2 candies
c = number of student that received 3 candies

Insufficient

(2) number of student that received 2 candies is 15

Insufficient

Both together:
from (2): b = 15, then
a + b + c = 50
a + 15 + c = 50
a + c = 35
c = 35 - a

a + 2b + 3c = 105
a + 2*15 + 3*(35 - a) = 105
a + 30 + 105 - 3a = 105
2a = 30
a = 15; Since a is number of student that received 1 candies, so the answer is 15.

BOTH ARE SUFFICIENT

Can we assume that each student must have received at least one candy? Because in question stem it is not mentioned that each student must get at least one candy.

VaCeFe, Bunuel

in general Can't assume that everyone is getting a minimum one candy and that's where my answer is differing with Bunuel answer. Bunuel please check and share if the answer should be C or E
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Re: If a teacher distributed 105 candies to 50 students in her class, how   [#permalink] 22 Oct 2018, 23:05
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