A farmer is having a total of 20 fruits (apples or oranges). He made two type packets with these fruits. All the fruits are in either apple packets of orange packets. Apple Packets contain 3 apples each and Orange packets contain 2 oranges each.
If |apple packets| < 4
Then How many packets of apples the farmer can have. When number of apple and orange packets are both positive integers above zero.
Choose the correct choice from the following answers
A) 2
B) 3
C) 4
D) 7
E) 6
Let us start by understand the meaning of 4 &gt; |Number of Apples|   1) when we write |-x| this means the same as |x|.   2) Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| &lt; b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a' - as per this scenario.....hence the value of 'a' must be between these two extremes. |x-(a)| &gt; b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b'.   Now come to the question. Let number of apple packets be ‘a’ and number of oranges packets be ‘b’. First its given |a| &lt; 4 ==&gt; |a-0| &lt; 4 ==&gt; the distance from zero is less than 4. So the point ‘a’ will be -3,-2,-1,0,1,2,3 as distance from 0 to these values is less than 4. Number of apple packets is above zero so possible values of ‘a’ left are 1,2,3.   As per the given information there are total of 20 fruits and they are in packets (3 per packet for apples and 2 per packets for oranges) so we can write it as follows:   3a + 2b = 20 ==&gt; b = 10 – (3*a)/2. If b is an integer then ‘a’ must be divisible by 2. If we take only those values of ‘a’ that are divisible by 2 then we are left with 2 only. So there are two packets of apples. If there are two packets of apples then b = 10 – (3*2)/2 ==&gt; b = 7. So we have 7 packets of oranges and 2 packets of apples. So A is the answer. 7 packets (2 orange each) and 2 packets of apples (3 apples each) make 20 fruits in total.
<result>A</result>
A farmer is having a total of 20 fruits (apples or oranges). He made two type packets with these fruits. All the fruits are in either apple packets of orange packets. Apple Packets contain 3 apples each and Orange packets contain 2 oranges each.
If |apple packets| < 4
Then How many packets of apples the farmer can have. When number of apple and orange packets are both positive integers above zero.