**Number System Questions for SSC MTS**

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**Question 1: **The ten’s digit of a 2-digit number is greater than the units digit by 2. If we subtract 18 from the number, the new number obtained is a number formed by interchange of the digits. Find the number.

a) 75

b) 64

c) 53

d) Cannot be determined

**Question 2: **What smallest number should be added to 2957 so that the sum is completely divisible by 17 ?

a) 9

b) 2

c) 3

d) 1

**Question 3: **Which of the following numbers can be obtained by inverting the order the digits and multiplying by an integer?

a) 3768

b) 4893

c) 6294

d) 9801

**Question 4: **Product of the three consecutive numbers whose sum is 15,

a) 120

b) 150

c) 126

d) 105

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**Question 5: **In a basket, there are 125 flowers. A man goes to worship and offers as many flowers at each temple as there are temples in the city. Thus he needs 5 baskets of flowers. Find the number of temples in the city.

a) 25

b) 24

c) 27

d) 26

**Question 6: **The least number which should be multiplied to 243 to get a perfect cube is

a) 6

b) 9

c) 2

d) 3

**Question 7: **If the operation Θ is defined for all real numbers a and b by the relation $aΘ b =a^{2}\frac{b}{{3}}$ then $2Θ {3Θ(-1)} = ?$

a) 2

b) 4

c) -4

d) -2

**Question 8: **The greatest 4 digit mimber which is a perfect square, is

a) 9999

b) 9909

c) 9801

d) 9081

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**Question 9: **The least number which is divisible by all the natural numbers upto and including 10 is

a) 7560

b) 1260

c) 5040

d) 2520

**Question 10: **The least number which when divided by 25, 40 and 60 leaves the remainder 7 in each case is

a) 609

b) 593

c) 1207

d) 607

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**Answers & Solutions:**

**1) Answer (D)**

Let the unit’s digit of the number be $y$ and ten’s digit be $x$

=> Number = $10x + y$

According to ques, =>$x – y = 2$ ————–(i)

According to question, => $10x + y – 18 = 10y + x$

=> $9x – 9y = 18$

=> $x – y = \frac{18}{9} = 2$ ————–(ii)

Equations (i) and (ii) are same and thus we have two variables and one equation

Number can be = 97 , 86 , 75 , 64 and so on and thus the solution cannot be determined.

=> Ans – (D)

**2) Answer (D)**

If 2957 is divisible 17, => 2957 = 17 $\times$ 173 + 16

Quotient is 173 and remainder is 16

Thus, smallest number that should be added to 2957 so that the sum is completely divisible by 17 = (17 – 16) = 1

=> Ans – (D)

**3) Answer (D)**

If the ratio of the number and its inverse is an integer, then given number can be obtained.

(A) : $\frac{3768}{8673}=0.4$

(B) : $\frac{4893}{3984}=1.2$

(C) : $\frac{6294}{4926}=1.2$

(D) : $\frac{9801}{1089}=9$

=> Ans – (D)

**4) Answer (A)**

Let the three consecutive numbers be $(x-1) , (x) , (x+1)$

Sum of these numbers = $x – 1 + x + x + 1 = 15$

=> $x = 5$

Numbers are = 4 , 5 & 6

Product of these numbers = 4*5*6 = 120

**5) Answer (A)**

Let the number of temples in the city be $x$

Also, he offers $x$ flowers in each temple

Total number of flowers he offered = $x^2 = 5 \times 125$

=> $x = \sqrt{625} = 25$

**6) Answer (D)**

243 = 3 * 3 * 3 * 3 * 3

= $3^3 * 3^2$

Thus, required number to be multiplied = 3

**7) Answer (C)**

It is given that $aΘ b =a^{2}\frac{b}{{3}}$

Applying the same rule for $2Θ {3Θ(-1)}$

= 2 Θ ${\frac{3^2 \times (-1)}{3}}$

= 2 Θ -3

= $\frac{2^2 \times (-3)}{3} = -4$

**8) Answer (C)**

Since the number has 4 digits, its square root will always have 2 digits.

=> Greatest 2 digit no. = 99

Greatest 4 digit no. which is perfect square = $99^2$ = 9801

**9) Answer (D)**

The least number which is divisible by all natural numbers from 1 to 10

= L.C.M.(1,2,3,4,5,6,7,8,9,10)

= 2520

**10) Answer (D)**

The least number which when divided by 25, 40 and 60 leaves the remainder 7

= L.C.M. (25,40,60) + 7

= 600 + 7 = 607

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