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Quantitative Reasoning – Least number of Apples!

PSA 2014_XI_Q10. Mrs Ali gave a different number of apples to each of her five children. Any three of her children together received more apples than the remaining two children. What is the least number of apples that Mrs Ali could have given to one of her children ?
1) 1
2) 4
3) 5
4) 6

Ans: Let us attempt this by trial and error and see if we can arrive at the result. Since we are to find the least number of apples let us take that number to be 1. Also Mrs Ali gave a different number of apples to each of her five children, let us take the numbers to be successive.

1,2,3,4,5 –> This does not meet the condition of “any three of her children together received more apples than the remaining two children”.
[5+4 > 1+2+3, hence rejecting].

Let, next least number be 4.

The set will be then 4,5,6,7,8. Here also, 4+5+6 = 7+8 [not greater, thus rejecting].

Next least number be 5.

The set will be then 5,6,7,8,9. Here, 5+6+7 > 8+9 [greater, thus could be the correct answer; obviously if we take any other combination of 3 numbers it will be anyway greater than the sum of the rest two as 5,6,7 is the least sum of three numbers]. Option 3.

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