Question : Directions: Select the option that is related to the fifth term in the same way as the second term is related to the first term and the fourth term is related to the third term.
132 : 10 :: 42 : 5 :: 272 : ?
Option 1: 15
Option 2: 16
Option 3: 13
Option 4: 14
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Correct Answer: 15
Solution :
Given:
132 : 10 :: 42 : 5 :: 272 : ?
In the given pairs, add 3 to the second number, then multiply with the second number, and again add 2 to the resultant to get the first number.
Like, 132 : 10→{10 × (10 + 3)} + 2 = {10 × 13} + 2 = 130 + 2 = 132
42 : 5→{5 × (5 + 3)} + 2 = {5 × 8} + 2 = 40 + 2 = 42
Similarly, follow the same pattern for 272 : ?→Let the missing number be x.
⇒ {x × (x + 3)} + 2 = 272
⇒ {x × (x + 3)} = 272 – 2
⇒ {x
2
+ 3x} = 270
⇒ x
2
+ 3x – 270
⇒ x
2
+ 18x – 15x – 270
⇒ x(x + 18) – 15(x + 18)
⇒ (x + 18) (x – 15)
⇒ x = 15 or –18 (Since 15 is given in the options, the value of x will be 15.)
So, 15 is related to 272. Hence, the first option is correct.
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