Number System Quiz: Quantitative Aptitude Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. Which of the following numbers is divisible by 11?

   • 85,743
   • 84,735
   • 85,734
   • 86,734

   Answer: 85,734. Alternate-digit test: 8 - 5 + 7 - 3 + 4 = 11, a multiple of 11. The others give 9, 13 and 10.

2. What is the unit digit of 7^95?

   • 3
   • 1
   • 7
   • 9

   Answer: 3. Powers of 7 end in the cycle 7, 9, 3, 1. 95 leaves remainder 3 on division by 4, so the unit digit is the 3rd term, 3.

3. How many factors (divisors) does 360 have?

   • 18
   • 20
   • 30
   • 24

   Answer: 24. 360 = 2³ × 3² × 5, so the number of factors is (3 + 1)(2 + 1)(1 + 1) = 24.

4. A number leaves a remainder of 29 when divided by 56. What remainder will it leave when divided by 8?

   • 3
   • 5
   • 1
   • 7

   Answer: 5. 8 divides 56, so the remainder is simply 29 mod 8 = 5. Check with 56 × 3 + 29 = 197, and 197 = 8 × 24 + 5.

5. What is the sum of all odd numbers from 1 to 59?

   • 841
   • 900
   • 930
   • 870

   Answer: 900. There are 30 odd numbers from 1 to 59, and the sum of the first n odd numbers is n², so 30² = 900.

6. If the six-digit number 52x936 is divisible by 9, what is the value of the digit x?

   • 1
   • 4
   • 7
   • 2

   Answer: 2. Known digits add to 5 + 2 + 9 + 3 + 6 = 25. The next multiple of 9 is 27, so x = 2 (x = 11 is not a digit).

7. How many zeros are there at the end of 100! (100 factorial)?

   • 24
   • 20
   • 25
   • 22

   Answer: 24. Count factors of 5: 100/5 = 20 and 100/25 = 4, giving 24 pairs of 2 × 5, hence 24 trailing zeros.

8. What is the remainder when 2^31 is divided by 5?

   • 1
   • 2
   • 3
   • 4

   Answer: 3. 2^4 = 16 leaves remainder 1 on division by 5. 2^31 = (2^4)^7 × 2³, so the remainder is that of 8, which is 3.

9. Which of the following is a prime number?

   • 221
   • 247
   • 253
   • 239

   Answer: 239. 221 = 13 × 17, 247 = 13 × 19 and 253 = 11 × 23. 239 has no prime factor up to 15 (its square root is about 15.5), so it is prime.

10. What is the largest four-digit number exactly divisible by 24?

    • 9,984
    • 9,996
    • 9,972
    • 9,990

    Answer: 9,984. 9,999 divided by 24 leaves remainder 15, so the answer is 9,999 - 15 = 9,984 (= 24 × 416).