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Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then, x cannot be less than:
- a)210
- b)The smallest value of S2
- c)The largest value of S2
- d)(G-L)
Correct answer is option 'D'. Can you explain this answer?
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Solution:
Let us assume that the smallest value of S1 is a and the largest value of S2 is b.
To make every element of S1 greater than or equal to every element of S2, we need to add the same integer x to every element of S1.
Thus, the smallest value of S1 after adding x will be a + x and the largest value of S2 after adding x will be b + x.
Therefore, x cannot be less than (b + x) - (a + x) = b - a.
Hence, the correct option is (G-L).
Explanation of options:
a) 210: This option cannot be correct as x can be less than 210 if (G-L) is less than 210.
b) The smallest value of S2: This option cannot be correct as x can be less than the smallest value of S2 if (G-L) is less than the smallest value of S2 - the largest value of S1.
c) The largest value of S2: This option cannot be correct as x can be less than the largest value of S2 if (G-L) is less than the largest value of S2 - the smallest value of S1.
d) (G-L): This is the correct option as we have proved above that x cannot be less than (G-L).
Let us assume that the smallest value of S1 is a and the largest value of S2 is b.
To make every element of S1 greater than or equal to every element of S2, we need to add the same integer x to every element of S1.
Thus, the smallest value of S1 after adding x will be a + x and the largest value of S2 after adding x will be b + x.
Therefore, x cannot be less than (b + x) - (a + x) = b - a.
Hence, the correct option is (G-L).
Explanation of options:
a) 210: This option cannot be correct as x can be less than 210 if (G-L) is less than 210.
b) The smallest value of S2: This option cannot be correct as x can be less than the smallest value of S2 if (G-L) is less than the smallest value of S2 - the largest value of S1.
c) The largest value of S2: This option cannot be correct as x can be less than the largest value of S2 if (G-L) is less than the largest value of S2 - the smallest value of S1.
d) (G-L): This is the correct option as we have proved above that x cannot be less than (G-L).
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