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14 Sep 2019, 09:02
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C
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On a new year day, every student of a class sends a card to every other student. The post delivers 600 cards. How many students are there in the class?
(A) 22
(B) 24
(C) 25
(D) 30
(E) 42
(A) 22
(B) 24
(C) 25
(D) 30
(E) 42
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14 Sep 2019, 09:47
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The best formula is;n/2*(n-1)=600
As each student sends card for another special student and recives card from the same student, so 2 is removed from the formula .
We've got 2*n/2*(n-1)=600
n(n-1)=600
n=25
Option C
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As each student sends card for another special student and recives card from the same student, so 2 is removed from the formula .
We've got 2*n/2*(n-1)=600
n(n-1)=600
n=25
Option C
Posted from my mobile device
15 Sep 2019, 11:16
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Let number of students = x
Number of ways in which two students can be selected out of x students is nC2. This is also the numbers of pairs of students (students send cards to each other in pairs).
For each pair of students, there will be two cards sent (A sends to B and B sends to A).
Therefore, for nC2 pairs of students, the number of cards sent = 2 x nC2 = 600 (given).
Solving:
n^2 - n - 600 = 0
(n-25)(n+24) = 0
=> n = either 25 or -24.
Discard n = -24 (since number of students will be a positive number).
Therefore, number of students =x = 25.
ANSWER: (C)
Number of ways in which two students can be selected out of x students is nC2. This is also the numbers of pairs of students (students send cards to each other in pairs).
For each pair of students, there will be two cards sent (A sends to B and B sends to A).
Therefore, for nC2 pairs of students, the number of cards sent = 2 x nC2 = 600 (given).
Solving:
n^2 - n - 600 = 0
(n-25)(n+24) = 0
=> n = either 25 or -24.
Discard n = -24 (since number of students will be a positive number).
Therefore, number of students =x = 25.
ANSWER: (C)
