Numbers Questions

Let y be the total number of loaves
a be the remaining loaves after 1st thief
b be the remaining loaves after 2nd thief
and c, d..so on after 3 and 4 th
e = 0 be the remaining loaves after 5th thief

a = y - (y/2 + 1/2)
= y/2 - 1/2

b = a - (a/2 + 1/2)
= a/2 - 1/2

c = b - (b/2 + 1/2)
= b/2 - 1/2

d = c - (c/2 + 1/2)
= c/2 - 1/2

e = d - (d/2 + 1/2)
= d/2 - 1/2
we know that, e = 0,
thus by substitution, we get
d = 1
c = 3
b = 7
a = 15
y = 31
Therefore total number of bread loaves in bakery was 31.

You can find the integers which when divided by 5 have a remainder 2 by adding 2 to all multiples of 5. So we have n = 7 , 12, 17, 22 etc.

From this series we can see that n does not have to be odd.

Also n + 1 can be a prime because, for example, 12 + 1 = 13

And (n + 2) / 7 has a remainder 2 in some cases but not all.

Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases. However, adding 3 to any of the values of n will always give a multiple of 5.

To solve a pair of simultaneous equations such as those given we can add or subtract them.

Adding we get 4x + 4y = 20

Therefore 2x + 2y = 10

Divisor = 

           = 

The weight will be 250g plus (1.55 - 0.65)/0.10 units of 100g

250 + 900 = 1150

This is the maximum weight that can be sent at that price. But, weights exceeding

250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies).

Hence a package weighing 1145 will be charged $1145

The pattern is 32+42=52,  52+122=132, 72+242=252 

The next number = 82+152=172

 i.e. 17

Given the angles of a quadrilateral are in the ratio of 2:4:7:5
Let the angles of a quadrilateral are 2x, 4x, 7x, 5x
But we know that sum of the angles = 360 degrees.
=> 2x + 4x + 7x + 5x = 360
=> x = 20
Therfore, the smallest angle of the quadrilateral = 2x = 2x20 = 40 degrees.
One of the angle of the triangle = 2 x 40 = 80 degrees
The other angle is 180 - (40 + 80) = 60 degrees.

Hence the second largest angle of the triangle is 60 degrees.

We know that am×an=am+n 

∴3131-27 = 314 = 961 x 961.