Prime Time — Hard

Q1. In the idli-vada game played from 1 to 90, how many times would the children say 'idli' (including the times they say 'idli-vada')?

• A. 18
• B. 24
• C. 30
• D. 36

Q2. Consider the idli-vada game played from 1 to 90. Examine the three statements: I. 'Vada' is said 18 times in total. II. 'Idli-vada' is said 6 times in total. III. 'Idli' is said 30 times in total. Which are correct?

• A. I and II only
• B. II and III only
• C. I and III only
• D. All three

Q3. Assertion (A): 2 is the only even prime number. Reason (R): Every even number greater than 2 has 2 as a factor in addition to 1 and itself.

• A. Both A and R are true, and R is the correct explanation of A.
• B. Both A and R are true, but R is NOT the correct explanation of A.
• C. A is true, R is false.
• D. A is false, R is true.

Q4. Which of the following numbers is the product of exactly three distinct prime numbers: 45, 60, 91, 105, 330?

• A. 60
• B. 91
• C. 105
• D. 330

Q5. 13 and 31 are primes with the same digits (1 and 3) reversed. Which of the following is also such a 'reversed-digit prime pair' up to 100?

• A. 23 and 32
• B. 17 and 71
• C. 29 and 92
• D. 41 and 14

Q6. Examine the three statements: I. There is no prime number whose units digit is 4. II. A product of two primes is itself a prime. III. All even numbers are composite numbers. Which is/are correct?

• A. I and II only
• B. I only
• C. II and III only
• D. All three

Q7. Guna claims, 'Any two distinct prime numbers are co-prime.' Which of the following best evaluates this claim?

• A. False, because primes share the factor 1
• B. False, two primes always share themselves as a factor
• C. True, because two distinct primes share no factor other than 1
• D. True only when the primes are odd

Q8. Use prime factorisation to decide whether 30 and 45 are co-prime.

• A. Co-prime, since 30 and 45 share no common factor other than 1
• B. Not co-prime, since they share the prime factors 3 and 5
• C. Co-prime, since both end in different digits
• D. Cannot be determined without long division

Q9. Using prime factorisation, is 225 divisible by 27?

• A. Yes, because both are odd
• B. Yes, because 225 = 9 × 25 and 27 = 9 × 3
• C. No, because 27 has three 3s but 225 has only two 3s in its factorisation
• D. Cannot be decided without doing 225 ÷ 27

Q10. Guna says he checked the divisibility of 14560 by only two of {2, 4, 5, 8, 10} and then concluded it is divisible by all five. Which pair of numbers is sufficient to draw this conclusion?

• A. 2 and 5
• B. 4 and 10
• C. 5 and 8
• D. 2 and 4

Q11. Which of these is divisible by all of 2, 4, 5, 8 and 10: 572, 2352, 5600, 6000, 77622160?

• A. 572, 2352, 5600
• B. 5600, 6000 and 77622160
• C. Only 5600
• D. All five numbers

Q12. Anshu writes 36 as 2 × 18 and Gopika writes 36 as 6 × 6. If both continue till only primes are left, what will they get?

• A. Different prime factorisations, because they started differently
• B. The same set of primes 2, 2, 3, 3 in both cases
• C. Anshu gets 2 × 2 × 9 but Gopika stops at 6 × 6
• D. Neither will reach a prime factorisation

Q13. What is the smallest number that is a multiple of all numbers from 1 to 10, except for 7?

• A. 180
• B. 252
• C. 360
• D. 2520

Q14. Examine three statements about divisibility by 4: I. Only the last two digits decide it. II. If the last two digits form a multiple of 4, the whole number is too. III. If the whole number is divisible by 4, so is its last two-digit number. Which are correct?

• A. I and II only
• B. II and III only
• C. I and III only
• D. All three

Q15. Three prime numbers, all less than 30, have product 1955. What are they?

• A. 3, 17 and 29
• B. 5, 17 and 23
• C. 5, 19 and 23
• D. 7, 11 and 23