The number systems chapter is one of the most important topics of the CAT quantitative aptitude section. Here are some numeracy questions that would help to analyze the current preparation level for the CAT exam. The answer link is given at the end of the page.

**Basic Numeracy Skills: ****Questions**

**1) Find the remainder when 10 ^{34} – 7 is divided by 3.**

a) 1

b) -1

c) 0

d) 2

**2) What is (127) _{8} + (12)_{6} = (?)_{5}**

a) 230

b) 124

c) 340

d) 240 e) none of these

e) none of these

**3) (11100) _{2}=(1001)_{x} . x can be?**

a) 4

b) 5

c) 3

d) 10

e) none of these

**4) A certain number gives a remainder 4 when it divides 400, a remainder of 6 when it divides 600 and a remainder of 3 when it divides 806.Which is this number?**

a) 6

b) 9

c) 13

d) 17

e) none of these

**5) If 4 ^{4x} = 1600, what is the value of (4^{x–1})^{2}?**

a) 40

b) 30

c) 20

d) 5/2

e) 7/4

**6) When a number is divided by 48, it leaves a remainder of 17. What will be the remainder when the number is divided by 12?**

a) 10

b) 7

c) 5

d)2

e) 1

**7) If a, b and c are the three positive numbers, the value of 8abc – (a + b) (b + c) (c + a) cannot exceed**

a) 3

b) 2

c) 1

d) 0

e) 4

**8) Find the remainder when (x + 1) ^{5} + (x + 2)^{4} + (x + 3)^{3} + (x + 4)^{2} + (x + 5) is divided by (x + 2), if x is a two digit number. **

a) 2

b) 7

c) 1

d) 4

e) 8

**Directions for 9 to 10:**

**J, K, L, M, N, O, P and Q represent 8 consecutive 2 digit even numbers not necessarily in that order.**

**K & O are multiples of 5. P is a multiple of 11. N/2 is an odd number. L + O = 74 Q is a multiple of 7. P + J = 76**

**9) If the numbers are arranged in the descending order, which number shall be in the third position?**

a) O

b) N

c) M

d) L

e) P

**10) What is the median of the numbers? **

a) 35

b) 39

c) 36

d) 37

e) none of these

**11) A lies between -4 and 10. B lies between 20 and 50. lies between?**

a) 2, 25

b) 0,50

c) 5,12.5

d) none of these

**Directions for questions 12-13:**

**A Fibonacci series is a number series in which the nth term is given by T _{n}= T_{n-1} +T_{n+1}. Also, T_{1}=1 and T_{2}=1 12) The 66^{th} term of the series is **

a) odd

b) even

c) cannot be determined

d) none of these

**13) If the 12 ^{th} term is 144 and the 14^{th} term is 377. What is the 15^{th} term?**

a) 502

b) 401

c) 610

d) cannot be determined

**14) Which of the following numbers satisfy the following condition in base 10?:**

**Digits are alternatively 0 with the units’ digit being non-zero 1) (100110110) _{2} 2) (110010010)_{2} 3) (11001001)**

_{2}

a) Only 1

b) Only 2

c) Only 3

d) More than 1 of 1, 2, and 3

**15) There is a machine which accepts two values A and B. The values are updated as A=A+4 and B=A(B+3).The machine stops at X>400. Input values are A=1 and B=3, how many steps are performed before the machine stops?**

a) 1

b) 3

c) machine never stops

d) 2

**16) Integers a, b, c, d are such that -5 = a = 4, -2 = b= 6, -3 = c = 8 and -4 = d = 6.If X = ab+bc+cd+da , then find the least value of X?**

a) -96

b) -72

c) 48

d) -144

e) none of these

**17) Find the remainder when 9 ^{400}+9^{401}+9^{402}………. 9^{410} is divided by 6?**

a) 0

b) 1

c) 3

d) 2

**18) The sum of n positive numbers will be which of the following, given that their product is unity?**

a) a positive integer

b) divisible by n

c) equal to n + 1/n

d) never less than n

**19) Find the smallest value of ‘X’in the four-digit numbers (981X, 982X, 983X, 984X, 985X and 986X)which give the same remainder when divided by natural number ‘x’.**

a) 3

b) 4

c) 6

d) 10

**20) Find a number which when multiplied by 13 produces a number whose digits consist entirely of 8s?**

a) 52176

b) 63376

c) 68176

d) none of these

**21) In a multiplication problem, Instead of taking 45 as one of the multipliers, Vineet took 54. As a result, the product went up by 540. What is the correct product?**

a) 2700

b) 5400

c) 1440

d) 1590

**22) The integers P,Q,R and S shown on the number line above are all equally spaced. If R and S are equal to 7 ^{12} and 7^{13}, respectively,what is the value of P?**

a) 710

b) 711

c) -713

d) 79

e) none of these

**23) Using only coins of value 2,5,10,25,50 and 100, distribute the minimum number of coins possibleto 4 people who need 57, 95, 126 and 27 in value respectively.**

a) 11

b) 8

c) 14

d) 15

**24) What is the remainder when 7 ^{7}+ 7^{77}+7^{777}+ 7^{7777}+?7^{77777777} is divided by 8?**

(a) -1

(b) 1

(c) 7

(d) 0

**25) Two different primes are said to equalize an integer if they are the same distance from the integer on either sides of the number line and the integer is said to be equalized by those integers. Which integer among the following is the most highly equalized?**

a) 20

b) 18

c) 17

d) 15

e ) 12

For the detailed answer to above questions, visit basic numeracy solutions. Keep visiting Byju’s to get more practice questions on different CAT exam topics and sections. Byju’s also provide various engaging video lessons to help the CAT aspirants prepare more effectively and ace the exam easily.