In CAT number systems, is the first topic to be learned. The number of questions asked from this section is high and also the concepts form basics for other topics. So, here we are covering some important numbers system questions from previous asked CAT papers.

**CAT Questions on Number System with Solutions PDF:**

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**Question 1:**

A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?

a) 30

b) 24

c) 20

d) 60

**Question 2:**

In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?

a) 5

b) 8

c) 1

d) 4

**Question 3:**

Anita had to do a multiplication. In stead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

a) 1050

b) 540

c) 1440

d) 1590

**Question 4:
**

All the page numbers from a book are added, beginning at page 1. However, one page number was added twice by mistake. The sum obtained was 1000. Which page number was added twice?

a) 44

b) 45

c) 10

d) 12

**Question 5:
**

Ashish is given Rs. 158 in one-rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?

a) 11

b) 12

c) 13

d) None of these

**Question 6:
**

In some code, letters a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. We just do not know which letter represents which number. Consider the following relationships:

I. a + c = e,

II. b – d = d and

III. e + a = b

Which of the following statements is true?

a) b = 4, d = 2

b) a = 4, e = 6

c) b = 6, e = 2

d) a = 4, c = 6

**Question 7:
**

Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all the elements of S. With how many consecutive zeroes will the product end?

a) 1

b) 4

c) 5

d) 10

**Question 8:
**

The integers 34041 and 32506 when divided by a three-digit integer n leave the same remainder. What is n?

a) 289

b) 367

c) 453

d) 307

**Question 9:
**

Convert the number 1982 from base 10 to base 12. The result is:

a) 1182

b) 1912

c) 1192

d) 1292

**Question 10:
**

After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?

a) 80

b) 75

c) 41

d) 53

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**1)** Answer (a)

A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. So red light fashes after every 1/3 min and green light flashes every 2/5 min. LCM of both the fractions is 2 min .

Hence they flash together after every 2 min. So in an hour they flash together 30 times .

**2)** Answer (a)

Let the 4 digit no. be xyzw.

According to given conditions we have x+y=z+w , x+w=z,y+w=2x+2z.

With help of these quations we deduce that y=2w, z=5x.

Now the minimum value x can take is 1 so z =5 and the no. is 1854, which satisfies all the conditions. Hence option A .

**3) Answer (d)**

Let the number be X.

From the given information, 53x – 35x = 540 => 18x = 540 => x = 30

So, new product = 53*30 = 1590

4) Answer (c)

If the number of pages is 44, the sum will be 44*45/2 = 22*45 = 990

So, the number 10 was added twice

**5)** Answer (d)

The possible arrangements are 1,multiples of 2 ,remaining. So we have 1+2+4+8+16+32+64+31 = 158. Hence minimum no. of bags required is 8.

**6)** Answer (b)

We have a +c=e so possible summation 6+4=10 or 4+2 = 6.

Also b=2d so possible values 4=2*2 or 10=5*2.

So considering both we have b=10 , d=5, a=4 ,c=2, e=6.

Hence the correct option is B .

**7)** Answer (a)

For number of zeroes we must count number of 2 and 5 in prime numbers below 100.

We have just 1 such pair of 2 and 5.

Hence we have only 1 zero.

**8)** Answer (d)

The difference of the numbers = 34041 – 32506 = 1535

The number that divides both these numbers must be a factor of 1535.

307 is the only 3 digit integer that divides 1535.

**9) **Answer (c)

Quotient of 1982/12 = 165, remainder = 2

Quotient of 165/12 = 13, remainder = 9

Quotient of 13/12 = 1, remainder = 1

Remainder of 1/12 = 1

So, the required number in base 12 = 1192

**10)** Answer (d)

Since after division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively, the number is of form ((((4*4)+1)*3)+2)k = 53K

Let k = 1; the number becomes 53

If it is divided by 84, the remainder is 53.

Option d) is the correct answer.

CAT Number Systems questions given in this blog are from CAT previous year solved papers.

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