**1. The sum of the squares of three numbers is 83, while the sum of their products taken two at a time is 71. Their sum will be: **

1. 15

2. 142

3. 49

4. 225

**SHOW ANSWER**

**Answer 1**

Explanation: (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b + c)² = 83 + 71×2= 225

a+b+c= √225 =15

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Explanation: (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b + c)² = 83 + 71×2= 225

a+b+c= √225 =15

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**2. Three persons are walking around the ground. They take 20, 30 and 40 minutes to complete one round. If they start from a single point together, they will meet again at that point after: **

A. 1 hour

B. 15 hour

C. 21 hour

D. 2 hour

**SHOW ANSWER**

**Answer 4**

Explanation: LCM of 20, 30, 40= 120 Min = 2 hrs

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Explanation: LCM of 20, 30, 40= 120 Min = 2 hrs

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**3. A two digit number is 4 times the sum of its two digits. The number that is formed by reversing its digits is 27 more than the original number. What is the number? **

(1) 27

(2) 36

(3) 42

(4) 54

**SHOW ANSWER**

**Answer 2**

Explanation: Let the tens and unit digit of number are = x,y respectively

10x + y = 4( x +y)

Try putting from options, equation satisfy in 36

10*3 + 6= 4*3 + 4*6; reverse= 63-27=36

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Explanation: Let the tens and unit digit of number are = x,y respectively

10x + y = 4( x +y)

Try putting from options, equation satisfy in 36

10*3 + 6= 4*3 + 4*6; reverse= 63-27=36

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**4. A two digit number is 4 times the sum of its two digits. The number that is formed by reversing its digits is 27 more than the original number. What is the number? **

(1) 27

(2) 36

(3) 42

(4) 54

**SHOW ANSWER**

**Answer 2**

Explanation: Let the tens and unit digit of number are = x,y respectively

10x + y = 4( x +y)

Try putting from options, equation satisfy in 36

10*3 + 6= 4*3 + 4*6; reverse= 63-27=36

©navclasses

Explanation: Let the tens and unit digit of number are = x,y respectively

10x + y = 4( x +y)

Try putting from options, equation satisfy in 36

10*3 + 6= 4*3 + 4*6; reverse= 63-27=36

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**5. Given below are two statements. **

**Statement I: Sometimes, Ratio has units.**

Statement II: When two ratios are equal, a proportion is formed.

In the light of the above statements, choose the correct answer from the options given below:

Statement II: When two ratios are equal, a proportion is formed.

In the light of the above statements, choose the correct answer from the options given below:

1 Both Statement I and Statement II are true

2 Both Statement I and Statement II are false

3 Statement I is correct but Statement II is false

4 Statement I is incorrect but Statement II is true

**SHOW ANSWER**

**Answer 4**

Explanation: Ratios have no units.

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Explanation: Ratios have no units.

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**6. What is the remainder when 4^5 is divided by 15? **

A. 4

B. 8

C. 5

D. 11

**SHOW ANSWER**

**Answer 1**

Explanation: 4*4*4*4*4= 1024; 1024/15 remainder=4

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Explanation: 4*4*4*4*4= 1024; 1024/15 remainder=4

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**7. What is the actual profit when the profit on selling price is25%?**

(1) 33.33%

(2) 30.33%

(3) 25%

(4) 20%

**SHOW ANSWER**

**Answer 1**

Explanation: Let the selling price be 100

so profit = 25% of SP = 25

Cost price = SP – profit

= 100 – 25 = 75

Actual profit % =( profit/cost price) × 100

= (25 / 75) × 100

= 33.33 %

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Explanation: Let the selling price be 100

so profit = 25% of SP = 25

Cost price = SP – profit

= 100 – 25 = 75

Actual profit % =( profit/cost price) × 100

= (25 / 75) × 100

= 33.33 %

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**8. Statement I: Co-primes are the numbers which have only 1 as their common factor. Statement II: Factorisation is the decomposition of a number into the other numbers which when added together will give the original number. **

A. Both Statement I and Statement II are true

B. Both Statement I and Statement II are false

C. Statement I is correct but Statement II is false

D. Statement I is incorrect but Statement II is true

**SHOW ANSWER**

**Answer 3**

Explanation: A co-prime number is a set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF) will be 1. Co-prime numbers are also known as relatively prime or mutually prime numbers.

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Explanation: A co-prime number is a set of numbers or integers which have only 1 as their common factor i.e. their highest common factor (HCF) will be 1. Co-prime numbers are also known as relatively prime or mutually prime numbers.

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** 9. A pipe normally fills a tank in 12 hours, but, due to a leak, it takes 8 hours more. If the tank is full, how many hours will the leak take to empty it? **

(1) 12

(2) 22

(3) 30

(4) 33

**SHOW ANSWER**

**Answer 3**

Explanation: 1 – 1 = 1

12 x 20 X – 12 = 1

12x 20 20x – 240 = 12x,

8x = 240, x = 240/8, x= 30

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Explanation: 1 – 1 = 1

12 x 20 X – 12 = 1

12x 20 20x – 240 = 12x,

8x = 240, x = 240/8, x= 30

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**9. If 20% of (a + b) is equal to 50% of (ab) and 40% of (a-b) is equal to 70% of ab then what part of b is a? **

(1) 3/17

(2) -3/17

(3) 4/17

(4) 17/3

**SHOW ANSWER**

**Answer 1**

Explanation: 20% (a + b) = 50% (ab).. 1st eq,

40% (a – b) = 70% (ab) .. 2nd

2a + 2b = 5(ab), 4a – 4b = 7ab

To substitute and cut ab multiply 1st equation with 7 and 2nd with 5

14a + 14b = 35ab

20a – 20b = 35ab

34a – 6b = 0, by solving a/b= 6/34= 3/17

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Explanation: 20% (a + b) = 50% (ab).. 1st eq,

40% (a – b) = 70% (ab) .. 2nd

2a + 2b = 5(ab), 4a – 4b = 7ab

To substitute and cut ab multiply 1st equation with 7 and 2nd with 5

14a + 14b = 35ab

20a – 20b = 35ab

34a – 6b = 0, by solving a/b= 6/34= 3/17

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**10. Statement I: Two triangles are said to be congruent if their corresponding angles are equal and corresponding sides are proportional. Statement II: Two triangles are said to be similar if their corresponding angles and corresponding sides are equal. **

1 Both Statement I and Statement II are true

2 Both Statement I and Statement II are false

3 Statement I is correct but Statement II is false

4 Statement I is incorrect but Statement II is true

**SHOW ANSWER**

**Answer 2**

Explanation: Properties of Similar Triangles

Property 1:

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.

Property 2:

If corresponding angles of two triangles are equal, then the triangles are similar. They are called equiangular triangles.

Congruency in Triangles

Figures with the same size and shape are congruent figures. If two shapes are congruent, they remain congruent even if they are moved or rotated.

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Explanation: Properties of Similar Triangles

Property 1:

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.

Property 2:

If corresponding angles of two triangles are equal, then the triangles are similar. They are called equiangular triangles.

Congruency in Triangles

Figures with the same size and shape are congruent figures. If two shapes are congruent, they remain congruent even if they are moved or rotated.

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