Directions (1-5): What should come in place of question mark (?) in the following number series?

1. 1200 480 192 76.8     30.72   12.288   ?
(1) 4.9152
(2) 5.8192
(3) 6.7112
(4) 7.6132
(5) 8.5172

2. 963 927 855 747 603 423 ?
(1) 209
(2) 208
(3) 207
(4) 206
(5) 205

3. 841 961 1089 1225 1369 1521 ?
(1) 1581
(2) 1681
(3) 1781
(4) 1881
(5) 1981

4. 18 20 44 138 560 2810 ?
(1) 16818
(2) 16836
(3) 16890
(4) 16872
(5) 16890

5. 6   26 134 666 3334 16666 ?
(1) 84334
(2) 83334
(3) 83434
(4) 83443
(5) None of these

6. Two vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8:5?
(1) 7 : 9
(2) 9 : 8
(3) 9 : 7
(4) 5 : 6
(5) None of these

7. In what ratio must wheat at Rs.3.20 per kg be mixed with wheat at Rs.2.90 per kg so that the mixture be worth Rs.3.08 per kg?
(1) 3 : 4
(2) 3 : 3
(3) 3 : 2
(4) 4 : 5
(5) None of these

8. There are two sections A and B of a class, consisting of 36 and 44 students’ respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.
(1) 38 kg
(2) 38.30 kg
(3) 37.25 kg
(4) 36 kg
(5) 37 kg.

9. The average of 50 numbers is 30. If two numbers, 35 and 40 are discarded, then the average of the remaining numbers is nearly:
(1) 30
(2) 28.68
(3) 29.68
(4) 30.68
(5) 31.68

10. If each of the three non-zero numbers  a ,  b , and  c  is divisible by 3, then  abc  must be divisible by which one of the following the numbers?
(1) 8
(2) 81
(3) 27
(4) 122
(5) None of these

1. (1)
1200 ÷ 2.5 = 480
480 ÷ 2.5 = 192
192 ÷ 2.5 = 76.8
76.8 ÷ 2.5 = 30.72
30.72 ÷ 2.5 = 12.288
∴ ? = 12.288 ÷ 2.5 = 4.9152

2. (3)
963 – 1  x 36 = 963 – 36 = 927
927 - 2  x 36 = 927 – 72 = 855
855 – 3  x  36 = 855 – 108 = 747
747 – 4  x  36 = 747 – 144 = 603
603 – 5  x  36 = 603 – 180 = 423
∴ ? = 423 – 6  x  36 = 423 – 216
= 207

3. (2)
29 x  29 = 841
31 x 31 = 961
33 x 33 = 1089
35 x 35 = 1225
37 x 37 = 1369
39 x 39 = 1521
∴ ? = 41 x 41 = 1681

4. (4)
18 x 1 + 2 = 18 + 2 = 20
20 x 2 + 4 = 40 + 4 = 44
44 x 3 + 6 = 132 + 6 = 138
138 x 4 + 8 = 552 + 8 = 560
560 x 5 + 10 = 2800 + 10 = 2810
∴ ? = 2810 x 6 + 12 = 16860 + 12
= 16872

5. (2) : 6 x 5 – 4 = 26
26 x 5 + 4 = 134
134 x 5 – 4 = 666
666 x 5 + 4 = 3334
3334 x 5 – 4 = 16666
16666 x 5 + 4 = 83334

6. (1) : Spirit in 1 litre mix of A = 5/7 litre.
Spirit in 1 litre mix of B = 7/13 litre.
Spirit in 1 litre mix of C = 8/13 litre.
By rule of alligation we have required ratio X:Y

X         :       Y

5/7              7/13
\           /
(8/13)
/               \
(1/13)     :     (9/91)
Therefore required ratio = 1/13 : 9/91 = 7:9

7. (3) : C.P of a unit quantity of 1st kind  = Rs. 3.20
C.P of a unit quantity of 2nd kind  = Rs. 2.90
Mean price = Rs.3.08
C.P of unit quantity         C.P of unit quantity
of 1st kind                         of 2nd kind
(Rs. 3.20)                         (Rs. 2.90)

\                       /
Mean Price
(Rs.3.08)
/                        \

(3.08 – 2.90)          :           (3.20 – 3.08)
0.18                                      0.12

Required ratio = 0.18 : 0.12 = 3 : 2

8. (3 ) : Total weight of (36+44) Students = (36x40+44x35)kg = 2980kg
Therefore average weight of the whole class = (2980/80) kg
Therefore average weight = 37.25kg

9. (3) : Total sum of 48 numbers = (50 × 30) – (35 +40)
= 1500 – 75= 1425
Average = 1425/48
= 29.68

10. (3) : Since each one of the three numbers a, b, and c is divisible by 3, the numbers can be represented as 3p,3q, and 3r, respectively, where p, q, and r are integers.
The product of the three numbers is 3p×3q×3r=27(pqr).
Since p, q, and r are integers, pqr is an integer and therefore abc is divisible by 27.