Quantitative Aptitude - Arithmetic Ability Questions

Let x be the number.

Given: x = 296n + 75 [where n is quotient] 

 --> (378n) +( 372 + 1) 

 -->37(8n + 2) + 1

Hence, when x divided by 37, 1 is the remainder.

Total number of possible ways = 

9C5 = 9 x 8 x 7 x 6 x 55 x 4 x 3 x 2 x 1 = 126

Number of favorable cases = 

$$\begin{gathered} 4C2 x 5C3 + 4C3 x 5C2 + 4C4 x 5C1 \\ 4 x 32 x 1 x 5 x 4 x 33 x 2 x 1 + 4 x 3 x 23 x 2 x 1 x 5 x 4 2 x 1 + 1 x 5 \\ = 6 x 10 + 4 x 10 + 5 \\ = 60 + 40 + 5 \\ = 105 \end{gathered}$$

Therefore, required probability = 105/126 = 5/6

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. 

Area of each tile = (41 x 41) sq.cm 

Required number of tiles = 1517 x (902/41) x 41 = 814

Given 10 men take 15 days to complete a work

=> Total mandays = 15 x 10 = 150

Let the work be 150 mandays.

=> Now 37 men can do 150 mandays in 150/37 =~ 4 days

From given data,

(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)

C.P. of 12 balls = S.P. of 17 balls = Rs.720.

Hence, C.P. of 1 ball = Rs.720/12 = Rs. 60.

Since order does not matter, use the combination formula 

C34 = 24/6 = 4

In the given series 1 4 9 16 22 36

1 = 1 x 1 

4 = 2 x 2

9 = 3 x 3

16 = 4 x 4

25 = 5 x 5 (Not 22)

36 = 6 x 6

Hence, the odd man in the series is 22.

Required number of ways= 8C5×10C6 = (8C3×10C4)= 11760.