Sol. On a closer look at the series, we get to know that the successive terms represent the number of digits used in the previous number.
Look at term 1 and term 2 01, 1011
Term 2 and term 3 1011, 111021
Term 3 and term 4 111021, 31101211
We can notice that each sucessive term is obtained by first writing the number of times a digit (in succession) is used in the previous term followed by the digit itself.
So, the second term “1011” tells us that the first term has one “0“, followed by one “1“ thus making “01”.
Similarly, the third term of the series “111021” is describing the second term that has one “1”, one “0” followed by two “1″s (1011).
So the next term in the series would be describing “31101211” thus, one “3”, two “1”, one “0”, one “1”, one “2”, two “1” or 1310111221.
Q) In a peach orchard, each harvested fruit is assigned a category based on its weight. A regular peach weighs 200 gms while a premium peach weighs 250 gms. A worker accidentally put one of the baskets containing premium peaches on the regular peach shelf. All peaches look the same. How can you identify the premium peach basket in a single weighing?
Sol. Out of the 10 baskets on the shelf, take one peach from basket one, two from basket 2, three from basket 3 and so on. Depending upon the increased weight, we can know which basket has the premium peaches.
So, had all peaches been regular ones, the weight should have been 55 * 200gms = 11000 gms = 11 kg
Now, in the actual weighing, if the weight comes out to be 11.400 kg, it means the increase in weight caused by the premium peaches is 400 gms. Each premium peach is 50 gms heavier than the regular peach, thus the number of premium peaches = 400/50 = 8
Thus, basket 8 contains the premium peaches.
Q) If abcd x 4 = dcba. What is the value of a+b+c+d?
Sol. d x 4 has the unit digit a and a x 4 is d (single digit). Also ‘a’ has to be even, thus (a,d) can only be (2,8)
Now, on substituting the values and completing the product,
(2000+100b+10c+8) x 4 = 8000+100c+10b+2
Thus, 390b = 90c-30 or 13b=3c-1
Thus b = 1 and c=4 making a+b+c+d = 15