Remainders Basics — CAT Previous-Year Questions

5 previous-year questions on Remainders Basics from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.

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5 questions

Remainders Basics · CAT PYQs

CAT 2022 Slot 1 · QA

Q1.

Let A be the largest positive integer that divides all the numbers of the form 3^k + 4^k + 5^k and B be the largest positive integer that divides all the numbesr of the form 4^k + 3(4^k) + 4^k+2, where k is any positive integer. Then (A + B) equals

CAT 2018 Slot 2 · QA

Q2.

If A = {6²ⁿ - 35n - 1: n = 1, 2, 3, ...} and B = {35(n - 1) : n = 1,2,3,...} then which of the following is true?

CAT 2005 · QA

Q3.

If x = (16³ + 17³ + 18³ + 19³), then x divided by 70 leaves a remainder of

CAT 2000 · QA

Q4.

Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

CAT 1998 · QA

Passage / Data

Answer the next 2 questions based on the following information.

A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter ΔABC.

∠BAC = 30°
I(AB) = I(AC) = 10 m

Q5.

A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.