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Number System: Level 1 Test -9

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Question 1

The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1: 4, then the larger of the two number is

A

12

B

48

C

84

D

108

Question 1 Explanation:

Let the numbers by 21x and 84x. The LCM is 84 and the larger number is 84x. Thus the largest number is 84. Correct option is (c)

Question 2

The unit’s digit in the product of 7^{35} x3^{71} x 11^{55}

A

1

B

3

C

7

D

9

Question 2 Explanation:

We can easily observe that 11^{11} is divisible by 7^{35}3^{35} has the last digit as 1 Now 3^{36} is left, Thus the last digit of (3^{4})^{9} =1 So the correct option is a

Question 3

Which of the following pairs of fractions adds up to a number greater than 5?

A

$ \displaystyle \frac{13}{5},\frac{11}{6}$

B

$ \displaystyle \frac{11}{4},\frac{8}{3}$

C

$ \displaystyle \frac{7}{3},\frac{11}{5}$

D

$ \displaystyle \frac{5}{3},\frac{3}{4}$

Question 3 Explanation:

Let us evaluate the options, Option a $ \frac{133}{30}$ Option b $ \frac{65}{12}>5$ By observation, we can find that correct option is (b)

Question 4

The remainder when 7^{1987} is divided by 5 is

A

1

B

2

C

3

D

4

Question 4 Explanation:

7^{1} = 7, 7^{2} = 49; 7^{3}= 343; 7^{4}= 2401; 7^{5}= 16807 Hence, unit’s digit repeats after index 4. Remainder when 1987 is divided by 4= 3 Unit’s digit = 3 Hence, remainder non division by 5 = 3

Question 5

Unit’s digit in 13^{2003} is

A

1

B

3

C

7

D

9

Question 5 Explanation:

The question is same as finding unit’s digit of ${{3}^{2003}}={{3}^{3}}=\_7$ Thus correct option is (c)

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