A charity distributes 456 food packets to flood-affected families. Each line of families receives 4 fewer packets than the previous one. Which number of lines is not possible, if each line must receive a whole number of packets?
(a) 3
(b) 4
(c) 5
(d) 6

Question

A charity distributes 456 food packets to flood-affected families. Each line of families receives 4 fewer packets than the previous one. Which number of lines is not possible, if each line must receive a whole number of packets?
(a) 3
(b) 4
(c) 5
(d) 6

ONLiNE UPSC · Accepted Answer

We'll use:
S = total sum
n = number of terms
a = first term
d = common difference (here, &ndash;4 because each row gets 4 fewer packets)
S = n/2 * [2a + (n &minus; 1) * (&minus;4)] = 456
Now try each option:
(a) n = 3
3/2 * [2a &minus; 4(2)] = 456
&rArr; a = 156
Possible
(b) n = 4
4/2 * [2a &minus; 4(3)] = 456
&rArr; a = 120
Possible
(c) n = 5
5/2 * [2a &minus; 4(4)] = 456
&rArr; a = 99.2
Not an integer &rarr; Not Possible
(d) n = 6
6/2 * [2a &minus; 4(5)] = 456
&rArr; a = 86
Possible
Hence, option c is correct.

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M Question 1	⏱ 0
A charity distributes 456 food packets to flood-affected families. Each line of families receives 4 fewer packets than the previous one. Which number of lines is not possible, if each line must receive a whole number of packets? (a) 3 (b) 4 (c) 5 (d) 6