Question: 11 -

There are seven consecutive positive even numbers. The average of the square of the first and the last number is 712. Find the 2nd largest number.

Options:

22

25

26

30

Answer:

30

Solution:

Let, Seven consecutive even number= x, x+2, x+4, x+6, x+8, x+10, x+12  
712=(x^2+(x+12)^2)/2           
1424=x2+x2+144+24x
2x2+24x-1280=0
x2+12x-640=0
x2+(32-20)x-640=0
x2+32x-20x-640=0
x(x+32)-20(x+32)=0
(x+32)(x-20)=0
x=-32,20
2nd largest number= x+10
=20+10=30 

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Question: 12 -

The average weight of 18 workers is 50 kg. A new worker replaced an old worker whose weight is 45 kg. Hence, the average weight of the workers increased by 1 kg. What is the ratio between the old workman and new workman? 

Options:

3:4

11:12

5:7

23:35

Answer:

5:7

Solution:

Total of 18 workers= 18×50=900
New average=51 years

51×18=900-45+x
918-900+45=x
x=63
Ratio=45:63
=5:7

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Question: 13 -

The average of 7 consecutive numbers is 20. The largest of these numbers is :

Options:

23

22

24

21

Answer:

23

Solution:

Let the numbers be x, x + 1, x + 2,  x + 3, x + 4, x + 5 and x + 6,                            Then   (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.

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Question: 14 -

The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is :

Options:

 6000

9000

7000

8888

Answer:

9000

Solution:

Let their prices be 3x,  5x and 7x. Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.  Cost of cheapest item = 3x = Rs. 9000.

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Question: 15 -

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a^2+b^2+c^2/3 is :

Options:

M^2

2 (M/3)

3 M^2

M

Answer:

3 M^2

Solution:

We have : ( a + b + c) / 3 = M   or (a + b + c) = 3M.

(a+b+c)^2=(3M)^2=9M^2 
and
(a+b+c)^2<=>a^2+b^2+c^2+2(ab+bc+ca)=9M^2
 
a^2+b^2+c^2=9M^2   ,(ab+bc+ca=0)     

Required mean =(a^2+b^2+c^2/3)=9M^2/3=3M^2

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