## Numerical Ability

#### Numerical Ability

1. If 137+ 276 = 435 how much is 731 + 672?
1. 534
2. 1623
3. 1403
4. 1531

1. By observation of summation, it can be seen that numbers are not in decimal. Let they have base n. Then converting all number in decimal
(137)n = [ 1 × n2 + 3n + 7n0 ]10
(276)n = [ 2n2 + 7n + 6n0 ]10
(435)n = [ 4n2 + 3n + 5n0 ]10
(731)n = [ 7n2 + 3n + 1n0 ]10
(672)n = [ 6n2 + 7n + 2n0 ]10
∴ (137)n + (276)n = (435)n
⇒ n2 + 3n + 7 + 2n2 + 7n + 6n = 4n2 + 3n + 5
⇒ n2 – 7n – 8 = 0 ⇒ n = – 1, 8
Possible base n = 8 (+ ve)
(435)n = (435)8 = [ 4 × 82 + 3 × 8 + 5 ]10 = (285)10
(731)n = (731)8 = [ 7 × 82 + 3 × 8 + 1 ]10 = (473)10
(672)n = (672)8 = [ 6 × 82 + 7 × 8 + 2 ]10 = (442)10
So , (731)8 + (672)8 = (473)10 + (442)10 = (915)10
(915)10 = (1623)8

##### Correct Option: C

By observation of summation, it can be seen that numbers are not in decimal. Let they have base n. Then converting all number in decimal
(137)n = [ 1 × n2 + 3n + 7n0 ]10
(276)n = [ 2n2 + 7n + 6n0 ]10
(435)n = [ 4n2 + 3n + 5n0 ]10
(731)n = [ 7n2 + 3n + 1n0 ]10
(672)n = [ 6n2 + 7n + 2n0 ]10
∴ (137)n + (276)n = (435)n
⇒ n2 + 3n + 7 + 2n2 + 7n + 6n = 4n2 + 3n + 5
⇒ n2 – 7n – 8 = 0 ⇒ n = – 1, 8
Possible base n = 8 (+ ve)
(435)n = (435)8 = [ 4 × 82 + 3 × 8 + 5 ]10 = (285)10
(731)n = (731)8 = [ 7 × 82 + 3 × 8 + 1 ]10 = (473)10
(672)n = (672)8 = [ 6 × 82 + 7 × 8 + 2 ]10 = (442)10
So , (731)8 + (672)8 = (473)10 + (442)10 = (915)10
(915)10 = (1623)8

1. 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is
1. 2
2. 17
3. 13
4. 3

1. ∴ 5 + 10 + 7 + x = 25 ⇒ x = 3

##### Correct Option: D ∴ 5 + 10 + 7 + x = 25 ⇒ x = 3