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CAT 2004 — QA Question 28

Number TheoryEasy
Passage / Data

Answer the following question based on the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

The remainder, when (1523 + 2323)  is divided by 19, is:

Answer & solution

  • A

    4

  • B

    15

  • 0

  • D

    18

Solution

(an + bn) is always divisible by (a + b) if n is odd

∴ (1523 + 2323) is divisible by (15 + 23) ie, 38.
⇒ 1523 + 2323 = 38x, which is divisible by 19.
⇒ Remainder when (1523 + 2323) is divided by 19 is 0.

Hence, option (c).

CAT 2004 QA Q28: The remainder, when (15 23 + 23 23 ) is divided by 19, is: — Solution | TheCATExam