Some equations are solved on the basis of certain system. Find out the correct answer for the unsolved equation on that basis.

1. If 12 x 7 = 408 and 9 x 8 = 207 then 13 x 7 = ?

**Answer (d).** The following rule has been followed

12 x 7 = 84 is represented in reverse order by adding a 0 in between.

Similarly 9 x 8 = 72 = 207 and 13 x 7 = 91 = 109.

2. a = 11 (242) 121 ; b = 14 (392) 196 ; c = 13 (?) 169

**Answer (b).** 242 = 11² x 2;, 392 = 14² x 2; and therefore 13² x 2 = 338.

3. 323 x 41 = 14323, 137 x 72 = 27731, 48 x 87 = 7884, 34 x 75 = ?

**Answer (b).** The numbers are obtained by just placing them in reverse order from equation to solution. 323 x 41 is written in reverse order to get 14323. Similarly 137 x 72 = 27731.

4. 11 x 12 x 13 = 234, 24 x 23 x 35 = 658, 31 x 43 x 54 = ?

**Answer (d).** The first equation is solved by adding the digits of every number 11 = 2(1+1) 12 = 3(1+2) and 13 = 4(1+3) which gave 234. Similarly 2 + 4 = 6, 2 + 3 = 5 and 3 + 5 = 8. Thus 3 + 1 = 4, 4 + 3 = 7 and 5 + 4 = 9. The answer is 479.

5. 16 (210) 14, 14 (156) 12, 12 (?) 10

**Answer (a).** First equation is 16, 210 = 15² - 15 and 14. And second equation is 14, 13² - 13 and 12. Similarly the solution is 12, 11² - 11 and 10.

6. A = 3(21)247, B = 5(-)407, C = 7(49)567

**Answer (c).** The last digit of first equation that is 7 multiplied by first digit 3 gives 21 which is in brackets. Then the sum of 3 and 21 gives you 24 which is placed before 7. So is the solution for the third equation 7 x 7 = 49 + 7 = 56. Therefore the answer is 7 x 5 = 35.

7. 7 x 5 x 4 = 57354, 8 x 7 x 3 = 78563, then 6 x 8 x 5 = ?

**Answer (d).** Here first two digits in the equation are multiplied (7x5) to arrive at the middle number(35) and last digit is kept as it is. Then first two digits are reversed. Similarly, 8 x 7 = 56, 3 is taken as it was in the last place and first two digits (8 and 7) are reversed to get 78 - 56 - 3. Similarly 6 x 8 = 48 and first two digits 6 x 8 are taken as 86 - 48 - 5.

8. If 14 x 13 = 128 and 16 x 13 = 280 then 15 x 11 = ?

**Answer (b). **The product of 14 x 13 = 182 and 16 x 13 = 208. It can be seen that the last two digits have been reversed to get the answer. Since 15 x 11 = 165, the answer is 156.

9. If 264 * 2 = 6, 870 * 3 = 5, then what should be 735 * 5 be equal to

**Answer (a).** 2 + 6 + 4 = 12 and 12/2 = 6; 8 + 7 + 0 = 15 and 15/3 = 5. Therefore, 7 + 3 + 5 = 15 and 15/5 = 3.

10. A = 51 (714) 14; B = 61 (915) 15; C = 71 (1136) 16; D = 81 (?) 17

**Answer (a).** The number in the brackets is the product of the numbers outside it.

11. If 10 – 3 = 12, 12 – 4 = 13, 14 – 5 = 14, what is 16 – 6 ?

**Answer (b).** 10 - 3 = 7 + 5 = 12; 12 - 4 = 8 + 5 = 13; 14 - 5 = 9 + 5 = 14; Hence 16 - 6 = 10 + 5 = 15.

12. If 1 + 4 = 9, 2 + 8 = 18, 3 + 6 = 15, then 7 + 8 = ?

**Answer (a).** The second number is added to the sum of the numbers. Thus 1 + 4 = 5 + 4 = 9, 2 + 8 = 10 + 8 = 18. Therefore 7 + 8 = 15 + 8 = 23.

13. If 123 = 14 and 323 = 22, then 624 = ?

**Answer (c).** Add the squares of all the digits in the given number. 1^{2} + 2^{2}+ 3^{2} = 14 and 3^{2} + 2^{2}+ 3^{2} = 22. Thus 6^{2} + 2^{2}+ 4^{2} = 36 + 4 + 16 = 56

14. If 324 x 289 = 35, 441 x 484 = 43, 625 x 400 = 45, find the value of 256 x 729.

**Answer (c).** 324 is the square of 18 and 289 is the square of 17. 35 is the sum of 18 and 17. Therefore, the sum of √256 = 16 and √729 = 27 is 43.

15. If 94 + 16 = 42, 89 + 23 = 78, then 63 + 45 = ?

**Answer (c).** (9 x 4) + (1 x 6) = 42; (8 x 9) + (2 x 3) = 78. Thus, (6 x 3) + (4 x 5) = 38.

16. If 9 * 7 = 32, 13 * 7 = 120, 17 * 9 = 208, then 19 * 11 = ?

**Answer (d).** 9^{2} - 7^{2} = 32; 13^{2} - 7^{2} = 120. Thus 19^{2} - 11^{2} = 361 - 121 = 240.

17. If 8 + 8 = 72, 5 + 5 = 30 and 7 + 7 = 56, what is 6 + 6 = ?

**Answer (b).** (8 x 8) + 8 = 72; (5 x 5) + 5 = 30. Thus (6 x 6) + 6 = 42.

18. 7, 2 = 59; 5, 3 = 28; 9, 1 = 810; 2, 1 = 13; 5, 4 = ?

**Answer (a).** The first digit of the answer is the difference of two digits in the question and the second digit is the sum of two digits. Thus, 7 - 2 = 5 and 7 + 2 = 9 and the answer is 59. Therefore, 5 - 4 = 1 and 5 + 4 = 9 and the answer is 19.

19. If 8 x 2 = 61 : 8 x 5 = 04, what is 8 x 10 = ?

**Answer (b)**.

20. 27(18)3; 216(180)6; 729(?)9

**Answer (d)**. The number in brackets is the difference of the first number and the square of the second number outside the brackets. 27 - 3^{2} = 18; 216 - 36^{2} = 180. Thus 729 - 9^{2} = 648.