Practice MCQ Questions and Answer on Number System

51.

The distance between the house of Rajan and Raman is 900 km and the house of former is at 100^th milestone where as the house of Raman is at 1000^th milestone. There are total 901 milestone at a regular interval of 1 km each. When you go to Raman's house from the house of Rajan which are on same highway, you will find that if the last digit (i.e. unit digit) of 3 digit number on every milestone is same as the first (i.e. hundreds digit) of the number on the next milestone is same, then these milestones must be red colour and rest will be of black. Total number of red colour milestone is:

(A) 179
(B) 90
(C) 189
(D) 100

52.

The digit at Hundred's place value of 17! is :

(A) 1
(B) 0
(C) 2
(D) 3

53.

The unit's digit in the product 274 ÃÂÃÂÃÂÃÂÃÂÃÂ 318 ÃÂÃÂÃÂÃÂÃÂÃÂ 577 ÃÂÃÂÃÂÃÂÃÂÃÂ 313 is :

(A) 2
(B) 3
(C) 4
(D) 5

54.

Let n be a natural number such that $\frac{1}{2}$ + $\frac{1}{3}$ + $\frac{1}{7}$ + $\frac{1}{n}$ ÃÂÃÂ is also a natural number. Which of the following statements is not true ?

(A) 2 divides n
(B) 3 divides n
(C) 7 divides n
(D) n > 84

Solution: $\begin{aligned} = (\frac{1}{2} + \frac{1}{3} + \frac{1}{7}) + \frac{1}{n} \\ = \frac{(21 + 14 + 6)}{42} + \frac{1}{n} \\ = (\frac{1}{42} + \frac{1}{n}) \end{aligned}$ This sum is a natural number when n = 42 So, each one of the statements that 2 divides ; 3 divides n and 7 divides n is true. Hence, n > 84 is false

55.

Which one of the following numbers is not a square of any natural number ?

(A) 17956
(B) 18225
(C) 63592
(D) 53361

56.

A string of length 221 metre is cut into two parts such that one part is $\frac{9}{4}$ th as long as the rest of the string, then the difference between the larger piece and the shorter piece is :

(A) 58 m
(B) 53 m
(C) 85 m
(D) 76 m

Solution: Let one part of string is x. Now, x + $\frac{9 x}{4}$ = 221 m x = 68 meter and, $\frac{9 x}{4}$ = 153 m Difference between two parts = 153 - 68 = 85m.

57.

A runner runs $1 \frac{1}{4}$ laps of a 5 laps race. What laps of the race remains to be run ?

(A) $\frac{15}{4}$
(B) $\frac{4}{5}$
(C) $\frac{5}{6}$
(D) $\frac{2}{3}$

Solution: Remaining distance to be run $\begin{aligned} = 5 - \frac{5}{4} \\ = \frac{20 - 5}{4} \\ = \frac{15}{4} laps \end{aligned}$

58.

Which of the following is the largest fraction ? $\frac{6}{7},$ $\frac{5}{6},$ $\frac{7}{8},$ $\frac{4}{5}$

(A) $\frac{6}{7}$
(B) $\frac{4}{5}$
(C) $\frac{5}{6}$
(D) $\frac{7}{8}$

Solution: $\begin{aligned} \frac{6}{7}, \frac{5}{6}, \frac{7}{8}, \frac{4}{5} \\ \frac{6}{7} = 0.85, \\ \frac{5}{6} = 0.83, \\ \frac{7}{8} = 0.87, \\ \frac{4}{5} = 0.80 \\ \frac{7}{8} is largest \end{aligned}$ Explanation : When the fractions are given in this order when the difference between the numerator and denominator is same so largest fraction will be largest numerator fraction and the smallest will be smallest numerator fraction. Note: - Fraction should be in the order where denominator will be larger than numerator. In this question : largest is $\frac{7}{8}$ and smallest is $\frac{4}{5}$

59.

When a number is divided by 5, the remainder is 3. What will be the remainder when sum of cube of that number and square of that number is divided by 5 ?

(A) 1
(B) 2
(C) 3
(D) 4

Solution: Let us assume any such number which when divided by 5 leaves remainder as 3. Let it be 8So, now $\begin{aligned} = \frac{{(8)}^{2} + {(8)}^{3}}{5} \\ = \frac{64 + 512}{5} \\ = \frac{576}{5} = 1 [Remainder] \end{aligned}$

60.

What is the sum of all two digit numbers that gives a remainder of 3 when they are divided by 7?

(A) 666
(B) 676
(C) 683
(D) 777

Solution: The two digit number which gives a remainder of 3 when divided by 7 are: 10, 17, 24 ..... 94. Now, these number are in AP series with 1st Term, a = 10; Number of Terms, n = 13; Last term, L = 94 andCommon Difference, d = 7. Sum, $\begin{aligned} = {n \times \frac{a + L}{2}} \\ = 13 \times 52 \\ = 676 \end{aligned}$

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Practice MCQ Questions and Answer on Number System

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