# Numbers Questions

Q:

A thief steals half the total number of loaves of bread plus 1/2 loaf from a bakery. A second thief steals half the remaining number of loaves plus 1/2 loaf and so on. After the 5th thief has stolen there are no more loaves left in the bakery. What was the total number of loaves did the bakery have at the beginning ?

 A) 21 B) 11 C) 17 D) 31

Explanation:

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.

2 5
Q:

There is a 3 digited number. 3rd digit is the square root of the 1st digit. 2nd digit is the sum of 1st and 3rd. And that number is divisible by 2,3,6,7. What is that number?

 A) 121 B) 943 C) 462 D) None

Explanation:

Assume that the number is taken as XYZ.
Condition 1 => Z = sq.root(x) => Possible digits of X is 1,4,9
Condition 2 => Y = X + Z
X Y Z
1 2 1
4 6 2
9 12 3 => (wrong because it is 4 digit.)

and 121 is not divisible by 2

1 17
Q:

Arun has certain number of books. It is not less than 15 and not more than 30. If he wants to give these books equally to 2 of his friends, then 1 book will remain. If he wants to give these books equally to 3 of his friends, then 2 books will remain. If he wants to give these books equally to 4 of his friends, then 3 books will remain. What is the number of books he had ?

 A) 19 B) 23 C) 17 D) 15

Explanation:

If he wants to give these books equally to 2 of his friends, then 1 book will remain, it means possible number of books = 15,17,19,21,23,25,27,29
If he wants to give these books equally to 3 of his friends, then 2 books will remain, it means possible number of books = 17,20,23,26,29
If he wants to give these books equally to 4 of his friends, then 3 book will remain, it means possible number of books = 15,19,23,27
common number is only 23 so it will be answer

2 13
Q:

Find the remainder when $\inline \fn_jvn \small 6^{29}$ is divided by 5 ?

 A) 0 B) 1 C) 3 D) 5

Explanation:

All powers of 6 has 6 in units place so answer will definitely be 1.

2 15
Q:

Two bus tickets from city K to L and three tickets from city K to M cost Rs. 77,  but three tickets from city K to L and two tickets from city K to M cost Rs. 73. What are the fares for cities L and M from K ?

 A) Rs. 13 and Rs. 17 B) Rs. 17 and Rs. 19 C) Rs. 23 and Rs. 17 D) Rs. 13 and Rs. 19

Explanation:

If fares for cities L and M from K are x and y respectively, then

2x + 3y = 77 or 6x + 9y = 231...(1)
3x + 2y = 73 or 6x + 4y = 146...(2)

subtracting 2 from 1, we get

5y = 85

y = Rs. 17 => x = Rs. 13