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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