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CAT 1991 — QA Question 47

Number TheoryEasy
Passage / Data

Answer the following questions based on the information given below:

There were a hundred schools in a town. Of these, the number of schools having a play – ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as  well as a library was one fourth the number of those having a laboratory alone. The number of schools  having either a laboratory or a library or both was 35.

To decide whether a n digit number is divisible by 7, we can define a process by which its magnitude is reduced as follows: (i1, i2, i3, … , are the digits of the number, starting from the most significant digit).

i1 i2 ……. in ⇒ i1 . 3n-1 + i2 . 3n-2 + ……… + in . 30.

e.g. 259 ⇒ 2.32 + 5.31 + 9.30 = 18 + 15 + 9 = 42

Ultimately the resulting number will be seven after repeating the above process a certain number of times. After how many such stages, does the number 203 reduce to 7?

Answer & solution

  • 2

  • B

    3

  • C

    4

  • D

    1

Solution

203 = 2.32 + 0.31 + 3.30 = 18 + 0 + 1 = 21

21 = 2.31 + 1.30 = 6 + 1 = 7.

Therefore we can reduce 203 to 7 in 2 steps.

Hence, option (a).

CAT 1991 QA Q47: To decide whether a n digit number is divisible by 7, we can define a process by which its magnitude is reduce — Solution | TheCATExam