Number Play — Hard

Q1. Consider the three statements about a sum of five whole numbers — two odd and three even: I. The sum is always even. II. The sum can equal 21. III. The sum is always greater than 10. Which statements are correct?

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

Q2. Riya picks any five even whole numbers and adds them. Her result is most certainly

• A. Even, and divisible by 2.
• B. Odd, and ending in 5.
• C. Even, and divisible by 10.
• D. Odd, and a multiple of 5.

Q3. Assertion (A): The sum 1 + 2 + 3 + ... + 100 is an even number. Reason (R): Among 1 to 100 there are 50 odd numbers, and an even count of odd numbers always sums to an even number.

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

Q4. Consider the expression 3n + 4 for whole numbers n. Three statements: I. When n = 2, the value is even. II. When n = 3, the value is odd. III. 3n + 4 is even for every whole number n. Which statements are correct?

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

Q5. For any whole number m, which is true of the expression 4m – 1?

• A. It is always even.
• B. It is even when m is even, odd when m is odd.
• C. It can be either even or odd depending on m.
• D. It is always odd.

Q6. Using the chapter rule that the nth odd number is 2n – 1, what is the 100th odd number?

• A. 100
• B. 199
• C. 201
• D. 299

Q7. Assertion (A): In a 3 × 3 magic square filled with 1 to 9, the magic sum must be 15. Reason (R): The numbers 1 to 9 add up to 45, and this total is shared equally between 3 rows.

• 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.

Q8. About a 3 × 3 magic square, consider: I. The magic sum is always three times the centre number. II. If the centre is 5, the magic sum is 15. III. If the centre is 7, the magic sum is 14. Which statements are correct?

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

Q9. Starting from the standard 1-to-9 magic square (magic sum 15, centre 5), every number is multiplied by 4. The new square has magic sum and centre equal to

• A. Magic sum 15, centre 5
• B. Magic sum 30, centre 10
• C. Magic sum 60, centre 20
• D. Magic sum 45, centre 15

Q10. The Virahanka-Fibonacci sequence is 1, 2, 3, 5, 8, 13, 21, 34, 55, ... . The next term after 55 is

• A. 60
• B. 65
• C. 100
• D. 89

Q11. After 89, the next three terms of the Virahanka-Fibonacci sequence are

• A. 144, 233, 377
• B. 100, 111, 144
• C. 98, 107, 116
• D. 178, 267, 356

Q12. Writing O for odd and E for even, the parity pattern of the Virahanka sequence 1, 2, 3, 5, 8, 13, 21, 34, ... is O, E, O, O, E, O, O, E, ... . The 12th term of the sequence is

• A. Even (E)
• B. Odd (O)
• C. Zero
• D. Cannot be decided

Q13. In the cryptarithm T + T + T = UT, each letter is a digit. The value of U + T equals

• A. 10
• B. 5
• C. 6
• D. 15

Q14. Angaan climbs an 8-step staircase taking either 1 step or 2 steps at a time. The total number of different ways he can do this equals the 8th term of the Virahanka sequence, which is

• A. 8
• B. 13
• C. 21
• D. 34

Q15. Assertion (A): A 3 × 3 magic square can have magic sum 0. Reason (R): If the centre of a 3 × 3 magic square is 0, then by 'magic sum = 3 × centre', the magic sum becomes 0; using negative whole numbers along with positives makes such a square possible.

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